Wednesday, April 29, 2009

A Bayesian Approach To Modeling Binary Data: The Case Of High-Intensity Crime Areas



Law, Jane & Haining, Robert
Geographical Analysis, Vol. 36. No 3 (July 2004) Ohio State University

Summary
The purpose of this paper is to apply Bayesian logistic models to binary data in order to explain how high-intensity crime areas (HIAs) are distributed in Sheffeild, England.

The article defines an HIA as an urban area experiencing high levels of violent crime. Perpetrators of crimes in HIAs often reside in the neighbors where they committ crimes, resulting in high levels of witness intimidation making it difficult to identify an HIA with full accuracy.

The article argues that Bayesian approaches are useful for spatial data analysis because of its emphasis on randomness, prior beliefs about values, and WinBUGS software that enables analysts to test hypothese with spatial elements.
Prior to using Bayesian analysis, Sheffeild was divided into Basic Command Units (BCUs). Within the BCUs were HIAs. Within both BCUs and HIAs were Enumeration Districts (EDs). EDs were then classified in terms of if they were in an HIA or not. According to the article several EDs were miscategorized because the original statistics used the standard logistic model, that did not analyze the spatial relationship between EDs. The article continues by discussing the use of Logistic Regression with WinBUGS software, to analyze random elements and spatial analysis to redesignate the EDs.




Figure 1, shows what is known as the logit function, including random effects. However it does not include spatial relationships of EDs.











In Figure 3A spatial relationships are shown with the links to W which is known as the contingency matrix. The contingency matrix is used to show the likelyhood of EDs neighboring HIAs and being at risk of spill-over crime from the HIAs making the EDs likley to become HIAs.


The paper's conclusion is that using a three stage Bayesian hierarchal model, can give estimated probabilities of EDs being HIAs, because it takes into account spatial elements between EDs. The paper also argues for "map decomposition" as another relevant way for analyzing spatial models along with Bayesian hierarchal models.

Why I Don't Like Bayesian Statistics

Gelman, Andrew, Professor of statistics and political science and director of the Applied Statistics Center at Columbia University

Summary



Professor Gelman refers to Bayesian inference as a "coherent mathematical theory," but does not trust it for scientific applications. Gelman believes that it is too easy to apply subjective beliefs about a given situation to Bayesian theory; because people want to believe their own preconceived notions and reject results statistical results they do not want to agree with. Bayesian methods according Gelman, encourage this kind of thinking.



Gelman takes special issue with political scientists like himself adopting Bayesian methods. Bayesian approaches tend to assume exchangeability of variables. However in political science it is impossible to exchange each of the 50 states, they cannot be used randomly or as samples.



Gelman continues by saying that he is not hostile to mathematics of Bayesianism, but its "philosophical foundations, that the goal of statistics is to make an optimal decision." Gelman believes that statistics are for doing "estimation and hypothesis testing," not to "minimize the average risk." He also faults the Bayesian philosophy of axiomatic reasoning because it implies that random sampling should not be done which Gelman considers to be "strike against the theory right there." He also accuses Bayesians of believing in "the irrelevance of stopping times," which means that stopping an experiment it will not change your inference. Gelman concludes by saying "the p-value does change when you alter the stopping rule, and no amount of philosophical reasoning will get you around that point."

Bayes' Formula



Author's Note: This is a great video for teaching Bayes' Theorem in its simplest form.


Summary
In order to illustrate the utility of Bayes’ Theorem, the author draws upon two simple scenarios. First, suppose someone faces the decision of needing to choose between three doors. If the person making the decision does not have any prior knowledge about the situation, the scenario creates an unconditional probability. But, once the person receives new information about the scenario, the rational person should reconsider his/her decision and subsequent probabilities.

Bayes’ Theorem is about the introduction of new information used to adjust probabilities and create conditional probabilities. In the formula, P(G/U), P is the probability that G will occur, if U happens.

To illustrate the application of Bayes’ Theorem and conditional probabilities, the author illustrates a second scenario. Pretend that there is a 70% probability that the economy will grow and a 30% probability that the economy will slow (an unconditional probability). The author owns a stock that has an 80% chance of increasing if the economy grows. That same stock, however, only has a 30% chance of increasing if the economy slows. The 80% and the second 30% are conditional probabilities; they are based on the condition that the economy will grow or slow.

The author can then determine the scenario’s four conditional probabilities:
1) What is the probability that the economy will grow and the stock will increase?
2) What is the probability that the economy will grow and the stock will decrease?
3) What is the probability that the economy will slow and the stock will increase?
4) What is the probability that the economy will slow and the stock will decrease?

To answer these questions and determine their probabilities, the author uses the equation: P(UG) = P(U/G)P(G). Notice that this equation is longer than the first because this one incorporates two conditions: the economy will grow/slow and the stock will increase/decrease.
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Bayes' Theorem for Intelligence Analysis

Jack Zlotnick
CIA Historical Review Program


Author’s Note: Released by the CIA’s Historical Program in the early 1990’s, Jack Zlotnick wrote this piece in the 1970’s. At the time, the CIA was still in the process of testing Bayes’ Theorem. Due to the ongoing testing period (at that time), Zlotnick does not offer a position on the utility and validity of the Bayesian method with regards to intelligence. In fact, Zlotnick spends a considerable amount of time in the article discussing the ways the theorem should continue to be tested.

Summary
Due to the very nature of intelligence, analysts should be naturally interested in the Bayesian Theorem. Intelligence is probabilistic in nature. Intelligence analysts usually conduct their analysis based on incomplete evidence in which they must address probabilities (thus WOEP’s).

For intelligence applications, Bayes’ Theorem is represented by the equation R=PL. “R” is the revised estimate of the odds favoring one hypothesis over another competing hypothesis (the odds of a particular hypothesis occurring after new evidence is entered into the equation). “P” is the prior estimate on the hypotheses probabilities (the odds before considering the new evidence entered into the equation). The analyst must offer judgments about “L” or the likelihood ratio. This variable is the analyst’s evaluation of the “diagnosticity” of an item of evidence. For instance, if a foreign power mobilizes its troops, what are the chances that “X” will happen over “Y”.

The principle features of the Bayes Theorem distinguish it from conventional intelligence analysis in three ways. First, it forces analysts to quantify judgments that are not ordinarily expressed in numeric terms. Second, the analyst does not take the available evidence as given and draw conclusions. And third, the analyst makes his/her own judgments about the bits and pieces of evidence. He/she does not sum up the evidence as he/she would if he/she had to judge its meaning for a final conclusion. The mathematics does the summing up.

The author is skeptical that the complex tasks analysts are forced to consider can be reduced to numeric values. Bayes’ Theorem, however, may be useful for examining strategic warning by uncovering patterns of activity by foreign powers.
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Summary Of Findings: Gap Analysis (3 Out Of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the 12 articles read in advance of (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst College on 29 APR 2009 regarding Gap Analysis specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use unstructured data.

Description:
Traditionally, "gap analysis" is a method used to conduct an internal operational analysis, whereas the gap analysis identifies the "gap" between a current state and a desired endstate within a company or agency. From an intelligence analysis perspective, "gap analysis" can be used as a tool to identify the likely pathway or pathways a target may take to arrive at a given endstate from a known position. Thus, "gap analysis" does not necessarily provide an estimate, but rather provides the analyst with a list of possible actions a target may likely take. Gap analysis as an analytic technique bears a striking resemblance to several other methods, such as Indicators & Warnings and Decision Trees.

Strengths:
1) Identify the target
2) Characterize the current status of the target as well as the target's goals
3) Identify what you want to know about the target
4) List the pieces of information that you have
5) Use a systematic approach to infer what the target is likely to do in order for the target to reach its goals

Weaknesses:
* No structured method to conduct the analysis
* May not leave you with a clear estimate
* Open to bias and other cognitive downfalls (satisficing, mirror imaging, etc.)
* Overlaps with the process of other methods and modifiers (i.e. decision treees, I&W, Brainstorming, SWOT, etc.)
* Susceptible to deception
* Danger of pitfalls

How-To:
1) Identify the target
2) Characterize the current status of the target as well as the target's goals
3) Identify what you want to know about the target
4) List the pieces of information that you have
5) Use a systematic approach to infer what the target is likely to do in order for the target to reach its goals

Experience:
For the first application, the group tried to determine what thesis topic Mary, a fictional first year graduate, would write about. Professor Wheaton acted in place of Mary, and we role played in questions and answer format. The group determined the gaps needing filled would be what intelligence track she was most interested in (national security, law enforcement, or competitive), what area or topic in her previous classes interested her the most, the choice of her primary reader, and the reader's academic interests. Upon filling these gaps, the group ascertained a plausible topic for Mary's thesis.

For the second application, the group discussed Russia's long held ambitions for a warm water port, preferably on the Mediterranean. The first part of the discussion centered on hostilities between Georgia and Russia, and actions Russia could take against Georgia to maintain their sphere of influence in the Black Sea. Additionally, the group discussed what actions may be necessary in their diplomatic relations with other nations bordering the sea. After discussing how Russia could potentially gain a Black Sea port by bringing Georgia into their sphere of influence, the group discussed how Russia could proceed toward gaining access to Mediterranean ports. The group determined that Turkey would be central in future Russian objectives for ports in the Mediterranean. The group put together lists of things the Russians could do that they are not doing now that would indicate their goals of extending their influence in Georgia and Turkey.

These applications illustrated the following:
* Helped in thinking through the steps that lead to a decision
* Allowed for open discussion and debate, helping the critical thinking process
* At some points it felt like stabbing in the dark, but the estimates later became more clear as the group discussed the options
* Eliminated peripheral influences not directly related to the topic, such as administrative processes.

Sunday, April 26, 2009

Forecasting for Success: The Power of Regulatory Gap Analysis

http://www.amarexcro.com/articles/docs/RAPS_Focus_Gap_Dec2008.pdf

This paper offers a broad plan for conducting a regulatory gap analysis for biomedical products, a definition of gap analysis, when and how to use gap analysis, and the benefits of conducting a gap analysis.

"Fewer than 1% of all biomedical products conceived move beyond preclinical testing, and fewer than 10% of those products make it onto the market." Thus biomedical product developers need to harness their time wisely to improve these statistics. Conducting a gap analysis is one way to cut down on both preclinical and clinical testing times.

The paper defines gap analysis as "the process of reviewing all available information for a candidate product to assess current development status, identify potential gaps in information required for subsequent steps, and develop a strategy to fill those holes."

According to the authors, the ideal time for performing a gap analysis is in the preclinical stages. This will allow for an understanding of the products unique nature. A particular focus of the information collection step needs to be on regulatory thresholds, precedents, and milestones. Once the developers know where their gaps are located, they can formulate a strategy for developing the product according to the standards set forth by regulatory bodies. The authors suggest sharing the action plan with the regulatory board to understand their concerns over the future developmental stages.

Aside from forming the basis for a developmental plan, their are other benefits to conducting gap analysis. First, it eliminates unnecessary developmental research and development testing. With the biomedical industry in particular, time is a precious commodity. Also, the gap analysis will aid in the speed in which regulatory agencies review and approve the product, since it knows the steps the developers are following. Troubleshooting these concerns will save a lot of headache later.

Gap analysis methodology for identifying future ICT related eGovernment research topics – case of “ontology and semantic web” in the context of eGover

http://ecom.fov.uni-mb.si/proceedings.nsf/Proceedings/874F789164F6DD6DC12572EE007A6BB2/$File/Paper95.pdf

This study evaluates the the gaps between the current state of government e-services to those proposed by numerous European conventions. The authors review how they defined and identified those gaps, how they were interrelated, and the methodology used to draw conclusions.

The use of information and communication technologies (ICT) currently employed by governments is poor. The future needs demands placed on governments to meet constituent demands require the streamlined implementation of ICT. The results of this study are part of the eGovRTD2020 project for which this work was commissioned.

For the sake of the study, a gap was identified as either expressing a mismatch between issues of consideration, or an issue of research currently not under consideration. There are five main steps the authors undertook to identify gaps and actions toward future scenarios. Generally speaking, they are:
  • where are we at?
  • where can we go?
  • how do we get there from here?
  • this is how we get there.
  • this is what we need to do to get there
The researchers then grouped the gap areas together and conducted conclusions on how they were interrelated (the later via a SWOT-esque approach).

The authors highlight four key steps they considered while conducting their gap analysis. They are:
  • understand the current environment
  • understand the broader context of the environment (for a holistic view)
  • base the results on a clear assessment framework
  • support the analysis quantitatively

Saturday, April 25, 2009

Gap Analysis As A Tool For Community Economic Development

Suzette D. Barta and Mike D Woods
Oklahoma State University


Author’s Note: This article is about “sales gap analysis.” The article focuses on a project in Oklahoma in which small cities are trying to determine the health of their local economies. Particularly, the cities are trying to determine whether local buyers are spending their money within the local community or outside the community. Although this article is slightly off topic, the discussion on gap analysis does contain a couple nuggets of valuable insight.

The purpose of this article is to help community leaders understand that there are some tools available that can help local merchants better understand the weaknesses of their local retail market. Once the leaders understand the local market’s weaknesses, a competitive response plan can be drafted.

The Oklahoma projects aims to determine whether local markets have a retail surplus or a leakage of retail (Are local customers shopping within the local market? Are external customers shopping within the local market?) This determination of a retail surplus or leakage is called a sales gap analysis.

Gap analysis is a technique for identifying the strengths and weaknesses in a local retail market. In this situation, the analysis estimates how many shoppers are coming to a community to purchase retail items.

Local residents must decide for themselves whether a retail gap is acceptable, not acceptable, or even preferable. If it is deemed not acceptable, then community leaders should devise a competitive strategy to meet the needs of the community. A common misperception however, is to assume that if a gap exists, then it must be filled.

A gap analysis only indicates the possible areas of leakage. The analysis does not indicate why the leakage exists, whether or not the leakage is acceptable, or how to stop the leakage from occurring. Gap analysis is only a starting point. The information generated from a gap analysis is only valuable if it is used to stimulate further discussion and to devise an appropriate competitive strategy for action.
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Gap Analysis Strengthens Link Between Requirements And Verification

Brian Hooper and Bill St. Clair
COTS Journal


Author's Note: This article primarily discusses ways in which requirements traceability may be improved, specifically in companies working on military projects that require safety certifications. The authors highlight gap analysis as the means in which the weaknesses in requirements traceability are discovered.

Summary
Gap analysis is a technique routinely used in business to measure the development/maturity of working processes and to identify potential areas for improvement. Gap analysis provides an opportunity to examine operating processes and products typically by employing a third party to conduct the assessment. The valuable information offered by the gap analysis helps to improve a company’s processes so that when a formal assessment or certification of products is conducted, the assessment is much more likely to be passed on the first attempt.

Companies are looking outside their own market sector for best practices and approaches, techniques, and standards. Gap analysis provides a framework to isolate areas in which they need to improve. The results from a gap analysis also aid companies in efficiently refocusing their resources in order to achieve the desired improvement.

With the increased need for software control, a gap analysis of safety-critical projects (particularly military related projects) regularly flags the field of requirements traceability. Many development standards require a Requirements Traceability Matrix (RTM). Requirements traceability is a widely accepted best practice in the development industry to ensure that all requirements are implemented and that all products can be traced back to one or more requirements.

More often than not, however, traceability matrices are performed as a low-priority task. Constructing a RTM requires an enormous amount of time and money. Failure to construct an accurate RTM may result in a product failing its certification assessment.
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Teaching the New Competencies Using the Gap Analysis Approach

http://www.stfm.org/fmhub/fm2006/April/Hershey238.pdf

Summary:

Doctors Bell and Kozakowski recommend using gap analysis to aid students (in this case medical students at all levels) in evaluating their current competency levels and developing a plan for improvement.

Medical schools typically define the core competencies that their students must meet upon the completion of classes, and at the end of the program. At the residency level, physicians must demonstrate achievement in the general competency categories, as identified by the Accreditation Council for Graduate Medical Education:
  • Patient Care
  • Medical Knowledge
  • Practice-Based Learning and Improvement
  • Interpersonal/Communication Skills
  • Professionalism
  • Systems-based practice.
Additionally, the authors describe the process of faculty-conducted assessments of the learners' achieved competencies. They provide a questionnaire used by faculty at the Lake Erie College of Osteopathic Medicine as an example.

Using gap analysis.
The authors describe the process of incorporating gap analysis into this type of self-evaluation. They mention four main steps:
  1. "Articulate a desired future state"
  2. "Describe the current state"
  3. "Examine internal and external issues that must be addressed to progress from the current state to the desired future state"
  4. "Delineate strategies and tactics that will ensure that the 'gap' between current state and desired future state is narrowed"
Gap analysis has been used in this application at the Hunterdon Medical Center Family Medicine Residency Program. Meetings are held between faculty and residents in which the residents are to score where they think fall, on a scale of 0-100, when performing a specific competency. The resident is then asked to name a practicing physician who he or she views as a 100 on the same scale. The faculty member asks the resident to identify those specific behaviors and characteristics that make the physician a 100. The last step involves the faculty member asking the resident to describe his or her own behaviors in relation to those of the 100-level physician, identifying specifics steps and learning issues that can reduce that gap between their own score and the 100-level score.

In the article's summary, the authors indicate that, at the time of publication, there had been no formal evaluation of this technique's effectiveness in this application.

Applied Strategic Planning

Goodstein, Leonard D., Timothy M. Nolan, and J. W. Pfeiffer. Applied Strategic Planning: how to develop a plan that really works. New York: McGraw-Hill, 1993. Ch.11.

Much of this chapter is dedicated to addressing the results of a gap analysis. This summary will primarily focus on the information relevant to the process of conducting a gap analysis, and any associated advantages or pitfalls.

Summary:
Goodstein calls gap analysis the "moment of truth" for a strategic planning team. This analysis provides the team with the opportunity to identify specific gaps that exist between the organization's current status and the "performance required for the successful realization of its strategic business model." The organization's current status and level of performance is the product of an internal performance audit.

Probably the most important product of a gap analysis is the estimate of the size of the gap and whether or not the strategies and tools at hand are enough to reduce the size of the gap. Every effort must be taken to close each perceived gap, and the team's responsibility is to reevaluate the desired future, business model, and solutions until all gaps are closed. This may require the team to repeat the process several times, or even revisit the mission statement or business model periodically.

There are two basic approaches to reducing gaps:
  1. Transactional Solution: Requires a modification or reduction of goals
  2. Transformation Solution: Requires a reduction of the obstacles causing the gap
The authors offer some words of caution to the strategic planning team. They recommend a strong consultant in the gap analysis phase to reduce the chances of the team falling into a group think frame of mind. Additionally, it is important to ask whether or not it is realistic to assume that a particular gap even has the potential be closed. Identifying a gap in one area can result in the realization of other gaps in different areas. The team must also assess the feasibility of change when assessing the scope and nature of existing gaps.

Human Performance Improvement For Tactical Teams

Hathaway, D.J. FBI Law Enforcement Bulletin. June 2008 Volume 77 Number 6

Summary:
This article uses gap analysis, among other methods such as performance and business analysis, in order to reassess the effectiveness of the FBI's tactical teams. The article explains how in today's world, any disparity between a tactical teams standard operating procedure (SOP) and real world actions may have legal ramifications, as well as embarrass and/or damage the credibility of the agency. By using methods such as gap analysis, these shortcomings can be identified and avoided.

According to the article, a performance analysis, "explains the current state of the department's tactical team and defines the desired one...Performance analysis incorporates organizational, environmental, and gap analysis. " Thus the gap analysis is only one component of an overall performance analysis. "As the name implies, gap analysis defines the area between actual performance of the team and the desired level and, as such, constitutes the second stage of performance analysis."


"Whereas performance analysis identifies the problem or area of concern, gap analysis brings the issue to the forefront, begins to frame it in terms of human behaviors and expected outcomes, and addresses the complex issue of consequences." Tactical teams may identify a gap in shooting accuracy, which would be a performance state, and seek to correct that problem to align with the desired performance state. Consequences and outcomes addressed with this particular performance may be unnecessary loss of life and/or inability to stop a criminal.

Once the gap is identified, it needs to be prioritized. Some questions to ask are, "How often does the gap occur? How costly will it be to fix? Or, how important is the gap? What if the team did nothing? Discovering a gap does not mean that it can, should, or will be addressed." Once gaps are prioritized, they can be dealt with on a basis of whats more critical to success, and keep the analysis systematic and appropriate. As a complete method, gap analysis is only identified as a "critical step" in the "human performance improvement model" (see image above). This critical step serves to identify the performance issues and facilitate the next step, which is the investigation and correction of those issues.

Authors Comment: The article further highlights each step within the "human performance improvement model, however they were not addressed in this summary due to the focus solely on gap analysis.

Gap Analysis

Encyclopedia of Management

Summary:
According to the article, gap analysis is defined as, "studying the difference between standards and the delivery of those standards." As a method of analyzing a business model, it is important to conduct a "before-and-after" analysis prior to conducting the actual gap analysis. The before-stage is identified, such as customer expectation, and then the after-stage is identified, such as actual customer experience. The difference between the two is the "gap", and once identified the gap can be addressed.

According to the article, "Gap analysis involves internal and external analysis." In the business model, this means that a business must address the customer's needs and expectations, as well as the appropriate business response to those needs and expectations. In order to implement the external analysis, the article represents the use of focus group interviews, consisting of ten to twelve customers, who are invited to share their experiences with a business. After recording the experiences of the focus group, the article recommends the implementation of a quantitative method to rank order the identified expectations and experiences, such as a 1-10 scale. The gaps can then be easily identified according to the gaps on the scale between experiences and expectations.

Gap analysis is a useful method to identify shortcomings within a business model. The article applies to the gap analysis method exclusively to the development of better customer relations, however gap analysis can be also be applied exclusively for internal analysis as well, such as what employees may expect from employers, and vice versa.

Thursday, April 23, 2009

Intelligence Requirements and Threat Assessment

Intelligence Requirements and Threat Assessment
Ch. 10 in
Law Enforcement Intelligence: A Guide For State, Local, and Tribal Law Enforcement Agencies
by, David L. Carter, Ph.D.
School of Criminal Justice
Michigan State University

Summary:
Chapter 10 of the Law Enforcement Intelligence: A Guide For State, Local, and Tribal Law Enforcement Agencies defines an intelligence gap as an unanswered question during the analytical process where “critical information is missing that prevents a complete and accurate assessment of an issue.”

In the past, a “dragnet” approach was the traditional method for filling information gaps. This approach set out to collect mass amounts of data in the hopes that the desired data was collected. The requirements-based approach to filling gaps seeks to make collection more objective, more efficacious, and less problematic. Dr. Carter asserts that this approach is scientific in nature and that “the intelligence function can use a qualitative protocol to collect the information that is needed to fulfill requirements. This protocol is an overlay for the complete information collection processes of the intelligence cycle.” The diagram below compares the Tradition-based and the Requirements-based approaches to filling intelligence gaps:


Carter states that organization (or even intelligence need) may have to develop its own unique process to filling information gaps, however the following acts as a good guide to follow:
  1. Understand your intelligence goal
  2. Build an analytic strategy. (What types of information are needed? How can the information be collected?)
  3. Define the social network. (Who is in the network? How does their business cycle function? Who has access to the information needed? What is the social behavior?)
  4. Define logical networks. (How does the organization operate? Funding sources. Communications sources. Logistics and supply.)
  5. Define physical networks.
  6. Task the collection process. (Determine the best methods of getting the information)
  7. Get the information.
  8. Analyze the information.

Gap Analysis: As Is or To Be, What is the Question?

Gap Analysis: As Is or To Be, What is the Question?
By Dorothy Ball,
Four Thought Group

Summary:
This article describes how to use gap analysis in Business Process Improvement (BPI) strategies, relating the method to Health Care organizations. In this summary, I have attempted to relate the gap analysis process, as the author uses it, to the intelligence field - identifying and overcoming intelligence gaps.

Dorothy Ball, a senior policy and business consultant at Four Thought Group, Inc., states that gap analysis is an effective solution for businesses and organizations that have a service orientation (which includes for-profits, non-profits, and government agencies). To paraphrase, gap analysis is a method for an organization to improve performance or make gains by identifying the potential needs for that organization to move from where they are (or what intelligence you have) to where they want to be (or what intelligence is still needed). Ball describes gap analysis as a method to develop a roadmap that gets you from “where you are now (As Is) to where you want to be (To Be).”

How to:
  1. Identify what your organization looks like now (or what intelligence/information you currently have available) and what you want your organization to look like (or what intelligence/information you desire). Needs for improvement (more intelligence) is often indicated by changes such as policy, resources, environment (or events that spark inquiry). Changes may be event-driven, or ongoing.
  2. Understand the Business Process (or collection process). Ball describes the business process as “a collection of related, structured activities, or chain of business functions, activities and tasks, that produce each specific service or product… Each business process consists of inputs, method, and outputs. The inputs are required before the method can be put into practice to achieve the outcome. When the method is applied to the inputs then certain outputs will be created.”
  3. Use comparative analysis techniques to identify what is needed to get you from where you are (the Intel you have) to where you want to be (the Intel desired). Examination of the current process, and the modeling of the new process, may be necessary in order to discover the interrelationships/interconnectedness of how the current process can get you the desired results.
  4. Create a plan for implementation.

Wednesday, April 22, 2009

Gartley's Gap Theory Explained

Bobbit Steven G. Futures December 2008

Retrieved From: FindArticles.com. 27 Apr, 2009. http://findarticles.com/p/articles/mi_qa5282/is_20081201/ai_n31108517/


Bobbit's goal in the article to explain to traders how to deal price gaps in the stock market. Gaps in prices of a stock happen when "the current bar opens above the high or below the low of the previous bar." The term "gap" is often used as a verb throughout the article. Human emotion manipulates markets and cause frequent "gapping."


Bobbit explains the "natural sequence of gaps" in a Gap Succession Chart. The sequence begins with the "breakaway gap" which indicate a change in pricing trends of a given stock. Next is the "measuring gap," according to Bobbit who cites H.M. Gartley measuring gaps are the most difficult for an analyst to spot but also the most important because spotting them can lead to better predictions of where the price is going to go. Next is the "exhaustion gap" which according to the article is the easiest to spot because they happen during significant "up or down" moves of a stock's price. Bobbit concludes the article with several mathematical equations to help determine where gaps may occur while charting prices.

Benchmark Your CI Capabilities: Using A Self Diagnosis Framework

By Singh, Arjan & Beurschgens, Andrew, Fuld & Company
Competitive Intelligence Magazine Volume 9, Number 1, January-February 2006

This article discusses the Self-Diagnostic Framework (SDF). SDF is a tool for analysts and proprietary Competitive Intelligence (CI) professionals to benchmark the current level of their CI capabilities compared to "world class CI capability." SDF incorporates gap analysis to provide recommendations for companies to improve their CI functions.

The authors explain how there are four development stages a CI department can go through. The first stage is known as "stick fetching." This is when CI is used by decision makers (DM) after they are well into their decision making process. DMs will request information from a CI department who have been at a distance from the decision making process and therefore have little understanding as to why certain information is needed. The next stage is the "pilot stage." This happens when an organization expresses a committment to further develop a CI function and give it a "mandate" to help in the decision making process. After the pilot stage is the "proficient stage" where an organization's CI team is proficient in most of the elements in the SDF. Once they have all the elements in SDF covered they are considered to have achieved the "world-class" stage.


The SDF is broken down into eleven attributes. An analyst or team of analysts, look at each attribute and determine which stage they are in for that attribute.

The article describes how two european companies used the SDF to finds gaps and inedaquacies in their CI functions. Both companies were successful in further developing value added CI functions in their organizations.


Summary Of Findings: Game Theory (4 out of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the 12 articles read in advance of (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst College on 22 APR 2009 regarding Game Theory specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use unstructured data.

Description:

Game theory is a method based on applied mathematics and economic theory. It can be useful when attempting to analyze (and ultimately predict) the strategic interactions between two or more actors and the way in which their actions influence future decisions. Game theory assumes that all actors are rational, and can be influenced by various individuals and factors. Games typically involve five common elements: players, strategies, rules, outcomes, and payoffs.

Strengths:

-assumes rational actors
-assumes actors will adjust their actions based on the actions of other actors
-not clearly differentiated from role-playing, simulations, and/or decision trees
-very mathematically based (can be intimidating)
-difficult to quantify options, strategies, and motivations
-may not be a valid method to produce an accurate estimation (see Game Theory, Simulated Interaction, and Unaided Judgment For Forecasting Decisions in Conflict: Further Evidence)
--In real world applications, identifying all of the key players and outcomes can be difficult

Weaknesses:

-Visual step-by-step trail to a conclusion/estimate
-Ability to quantify variables in play
-Emphasis on mathematics and scientifc method
-Applicable to multiple fields (economics, conflict, etc)
-90% rate of success according to BDM

How-To:

Game Theory varies in complexity and in application, however, each application has the following in common:

*Establish the players and the complexity of the game being played, so as to understand the rules which govern the players and the game.
*Identify the possible outcomes for the choices the players can make (although this is particularly difficult as not all decisions can be predicted)
*Establish measurable values for predicted outcomes.
*Eliminate dominated strategies and employ dominate strategies. Repeat this step until a clear, singular strategy emerges or equilibrium is reached between the players.
*Employ selected strategy.

Experience:

As a class, we visited www.gametheory.net and played the repeatable version of Prisoner's Delemma under the "Interactive Materials" tab. Each student played the game at their personal computers. Our objective as we played against the five "personalities" was to identify the particular strategies employed by the computer (in addition to scoring the most utility points). Some of the strategies employed by the computers personalities included "tit-for-tat" and "tit-for-two tats."

Monday, April 20, 2009

Game Theory, Political Economy, and the Evolving Study of War and Peace

By Bruce Bueno de Mesquita

http://www.apsanet.org/imgtest/APSRNov06BuenoDeMesquita.pdf

Summary:

Studies of war and peace increasingly center around domestic interests and institutions for clues on how to shape international affairs. This change in thinking coincides with advances made in non-cooperative game theory and political economy modeling.

De Mesquita refutes realism and state-centric theories as logical explanations for the causes of war. He simultaneously enhances the validity of the liberal peace theory by examining the influences which democrats need to consider when threatening or declaring war.

Realism's claim about a balance of power needed to maintain international stability is refuted by the political economy approach. Simply put, the political economy approach states that the causes of and solutions to international conflict can best be understood by looking within states. It treats leaders as the object of study, not the states as realism does.

A game-theoretic focus concludes that war conducted by rationally acting states is always ex post inefficient. Leaders conduct wars at times to maintain a hold on power, since their domestic constituencies would likely vote them out of office (for democratic states). Autocracies have the advantage of not needing to concern itself with the well-being of their citizenry since they do not face election.

Game theory also validates the liberal peace theory. It claims that leaders (as the object of the political-economy approach to international relations) will only wage war when the outcome is victory, as a 93% success rate for wars initiated by democracies indicate. Since both sides need to consider their reelection prospects, a negotiated settlement to the conflict is the preferred method for resolving conflicts between democratic nations.
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Game Theory

http://msl1.mit.edu/ESD10/block4/4.4_-_Game_Theory.pdf

Summary:

Game theory is the branch of decision theory concerned with interdependent decisions. Participants, or players, in a situation, or game, compete to achieve objectives with similar resources. The goal of game theory is not necessarily to "win," but rather to identify an optimal strategy. The sequence of moves a player uses is called a "strategy," and does not need to be wholly unique.

There are two categories of games: sequential and simultaneous. In sequential games, participants take turns acting. The basic strategic rule when applying game theory in this situation is to "look ahead and reason back." This starts with the last decision to be made, then working back through the problem to choose the course of action the other player would make until an initial decision needs made.


Simultaneous games require a more robust analysis due to their overall complexity. There is no "final move" per say in these games. In simultaneous games all possible combinations must be laid out. Players in this type of game should identify their dominate strategy and dominated strategy, the later should never be employed. Thus, the overall range of choices can be limited. Players then can go back to assess if there is another dominate strategy they can employ from the remain outcomes, as well as determine if there is another dominated strategy. This sequence can be replicated until a final strategy is reached, or if a dominate strategy is no longer evident.


In simultaneous games, comptitors without a clear dominate strategy should seek out equalibrium in relation to the other. Equilibrium is reached when both competitors do not have an incentive to change strategy.

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Introduction to Game Theory

Introduction to Game Theory
by Open Options Corporation - 2007

Summary:
Open Options Corporation defines Game Theory as "a branch of applied mathematics and economics that studies strategic situations where there are several stakeholders, each with different goals, whose actions can affect one another." According to the author, the benefit of conducting a Game Theory analysis is that it reveals the interactions of likely outcomes in situations where the end result is dependent on the actions of others, giving the analyst a better understanding of the situation and courses of action.

After a brief Game Theory history and credential check, Open Options discusses how Game Theory is applicable in business. Since the world of business focuses on competing against others with the goal of maximizing your own rewards, Game Theory is a natural fit to analyze possible business strategies.
"However, real business decisions have significant complications that are often ignored by abstract, academic game theory":
  1. Real business decisions almost always have many players, a challenge for classical game theory.
  2. Complex relationships among the players sometimes exist (i.e. some common and some competing issues exist between players).
  3. Business outcomes are often not easy to reduce to a common measure for value such as dollars or expected utility. Rather, strategic interests, long term relationships and the personal goals of the CEO or founder can be critically influential.
Other advanced Game Theory options exist to help model and solve complexities within business strategies, these include: n-player, non-cooperative, nonzero-sum, non-simultaneous, asymmetric, & ordinal game theories.

Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict

Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict
Brightman, Hank J. 2007. "Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict." Air & Space Power Journal 21, no. 3: 35-41. Military & Government Collection, EBSCOhost (accessed April 20, 2009).

* Actual article was accessed through Mercyhurst College's EBSCOhost subscription - link to article was found as a Google cached site.

Summary:
The 2007 article written by Dr. Hank Brightman, an associate Criminal Justice professor at Saint Peter's College and a USN Information Warfare Officer at the US Naval War College's War Gaming Department, posits that game theory suggests that US and Coalition forces stationed in Iraq will suffer an increasing rate of casualties the longer they remain in Iraq. The reasoning behind this statement is that both Domestic Insurgents (DI) and Indigenous Security Forces (ISF) will "turn away from attacking each other towards a point of mathematical corruption." It is at this theoretical point that US and Coalition forces will be the target of ISF intelligence-fed DI attacks. ISF refers to Iraqi military as well as state and local police; DI refers to various domestic insurgent groups within Iraq.

Brightman reviews the "prisoner's dilemma" and zero-sum game theory, and states that the prisoner's dilemma is an example of a simple form game (SFG). SFGs have two players that strive for the highest payoff at the end of a move or event (known as the Pareto Optimal position). As SFG applies to the Iraqi conflict, ISFs and DIs are the two players.
Extensive Form Games (EFG) are more complex than SFGs as they feature two or more players that are engaged in move-for-move exchanges, leaving the players less concerned with intermediate payoffs and focused on the ultimate payoff. EFGs are typically not zero-sum games and are distinguished by multiple moves, leaving players not only focused on broad strategy, but also smaller sub-strategies that counter the other players' moves. However, as time progresses in EFGs, the model becomes susceptible to "strange attractors" that "affect the players' willingness to adhere to previously stated rules and therefore decrease the overall stability of the game." US and Coalition forces would be considered strange actors in both the SFG and EFG models.

As time elapses the players (ISF & DI) become more frustrated and ultimately begin to reduce their expectation for the ultimate payoff. As this happens, each player considers negotiating with the opponent as a means of reducing losses - this is known as bargaining toward equilibrium, or a Pareto Improvement). "When both players have reached a point at which they can achieve the highest aggregate payoff, the game ends in preferred equilibrium."

"However, the influence of strange attractors in a model that will become increasingly unstable (bifurcated) over time often induces the players to hasten their desire for a Pareto Improvement position instead of a superior (Pareto Optimal) position - even though doing so may lessen their ultimate payoff." The strange attractors cause frustration which preempts the players from achieving the preferred equilibrium (the point in the prisoner's dilemma where both prisoners remain silent and gain the most) and instead yield the inchoate or Nash equilibrium (the point in the prisoner's dilemma where both prisoners confess to the crime).

*Author's note: the article delves further into the SFG and EFG situations as they relate to the Iraq Conflict, however, due to length they have been cut from this summary.

Sunday, April 19, 2009

Exploring The Structure Of Terrorist WMD Decisions: A Game Theory Approach

Raymond E Franck & Francois Melese
Defense and Security Analysis Vol. 20, No. 4, pp355-372, December 2004

Franck and Melese begin the article by breaking terrorist groups into two categories, political and fanatic. Regardless of the category the goals of a terrorist operation are to "damagea target government and influence a target audience." Terrorist organizations that fall into the fanatics category are more likely to view inflicting damage as a main objective, as oppose to influencing a target audience. Therefore they are more likely to be attracted to using WMDs.

When applying game theory, the authors' model is a set of four stages or "moves." The first move is from the terrorists and involves making a decision between acquiring WMD or staying with conventional weapons. The arguments for acquiring a WMD depend on the certainty of inflicting mass casualties, damaging the target government, and influencing the target audience. The arguments against acquiring a WMD are the costs, and increase in vulnerability to government counter-terrorism efforts. The second move is the decision of a target government to counter a potential WMD attack with "defensive" or "disruptive" measures. In the third move the ball in back in the terrorist's court over whether to carry out an attack with a WMD.




















The final move is not from governments or terrorists but "chance." The authors lay out four possible outcomes.

  • ineffective operation (i.e., failure to achieve intended damage and casualties);
  • effective operation which impresses the audience;
  • effective operation which alienates the audience; and an
  • effective operation that has a neutral effect on the audience.


In the second diagram the authors demonstrate how the probabilities of the different outcomes can depend on availability and use of WMD or conventional weapons and the government's use of defensive or disruptive countermeasures.

What follows are two tables that show the function of a player's decision. Table 1a shows probabilities that an attack will be effective and Table 1B shows probabilities of whether the attack will have its intended effect on its target audience. The variables presented in the tables are used in equations for the game to give governments an idea of whether they should invest in defensive or disruptive counter-measures.










The authors conclude that political terrorist groups even if they possess a WMD are less likely to use it than fanatic groups for fear of alienating their target audience. The kind of counter-measures a government utilizes is also a major factor in whether terrorists would pursue the WMD option or not. If terrorist feel that disruptive operations against them are too effective then they may be encouraged to carry out more conventional attacks.

Game Theory

The New School: History Of Economic Thought (HET) Website

According to HET Game Theory developed as a method for examining economic decision making. The theory was first organized by John von Neumann and Oskar Morgenstern's joint 1944 publication, Theory of Games and Economic Behavior. Game Theory is where decisions about strategy are based on actions of other agents or adversaries.

The theory was updated by John Nash in 1950, with the "Nash Equilibrium." The Nash Equilibrium happens when all players produce the best responses to the actions of other players. According to HET, the concept of the Nash Equilibrium can be traced back to French Economist Augustin Cournot in 1838 The first textbook on game theory was published in 1957 by R. Duncan Luce and Howard Raiffa. In the textbook Luce and Raiffa perfected the "Iterated Elimination of Dominated Stratgies (IEDS) for Strategic Normal Games" and the concept of "Repeated Game." Other game theorists in the 1950s and 1960s were H.W. Kuhn with games with "imperfect information" (i.e. players do not know the previous moves of other players); William Vickery with Auctions; Reinhard Selten with "Subgame Perfect Equilibrium" that uses backward induction; and Lloyd Shapely with the "Shapley Value."

The HET goes on to explain how "Evolutionary game theory" developed later and was designed to explain the results from what appeared to be cooperation between human institutions. Strategist Thomas C. Schelling argued that what appeared to be cooperation of social institutions in settling conflicst are actually maintained with threats of retaliation and punishment. HET then lists Nobel Laureates for Game Theory such as Nash, Selten, and Vickery.

Thursday, April 16, 2009

Game theory, simulated interaction, and unaided judgement for forecasting decisions in conflicts: Further evidence

Kesten C. Green

Summary
Green's article, published in the International Journal of Forcasting (2005), is a validity study that compares the accuracy of game theory, simulated interactions (role playing), and unaided judgment as methods in forecasting decisions in conflicts. It provides further evidence to support his earlier research, which indicated that expert game theorists' forecasts had less accuracy than those of novice (student) role players.

It is important to note here that these methods were tested in experiments involving specific conflict situations only. Not all game theorists recommend game theory for generating forecasts in specific situations.


Green's 2002 study reflected the accuracy of the three methods for forecasting conflict decisions. Participants in the study were asked to select the most likely decision (in 5 conflict situations) from a list. The results of the study did not bode well for the game theory experts (participants, % accuracy):
  • University Students (using unaided judgment), 27%
  • Game Theory Experts, 28%
  • University Students (using role playing/simulated interactions), 61%
Green's 2002 study drew some attention from his peers and game theorists, who commented that perhaps some conflict situations are more appropriate for use with game theory than others. The 2005 study utilized the same basic process, and was administered to participants representing the aforementioned three methods. It was directed at three (actual) conflicts, unrelated to the five used in the 2002 study:
  1. Personal Grievance. An employee of a New Zealand student association felt there was a disparity between her work and the level of pay she was receiving. Upon the administration's evaluation of her situation, it was discovered that she was being compensated above the top-level of pay in her salary bracket. While her manager did not consider cutting her salary, she did arrange for a mediator to set up a meeting between the parties, as it was obvious she would not be elligible for a pay increase in the near future. Participants were to choose from several decisions.
  2. Telco Takeover. This situation presented the participants with the conflict stemming from a corporate takeover battle between Alltel and CenturyTel. In 2001, executives from the much smaller CenturyTel company presented an offer that involved the sale of their mobile phone division to Alltel, which Alltel declined. Soon after, Alltel returned to CenturyTel with an offer to buy all of the company at 40% more than the share price. The board of CenturyTel fought to prevent an Alltel takeover. Participants were to forecast the execution of the deal and predict the basis of terms.
  3. Water Dispute. This conflict raged over Syria's and Iraq's claims to access of the Euphrates River in 1975. The flow of water into Iraq had been slowed following Syria's construction of a dam across the Euphrates to create a reservoir in Syria. Both sides mobilized for war, and Saudi Arabia called both parties together for mediation. Participants in the study were to forecast whether Syria would increase water flow from the dam or whether Iraq would declare war and bomb Syria's dam.
Since the findings of this research were to be compared with those of the 2002 study, Green took steps to evenly match the conflict situations with game theorists' and other decision makers' interests, i.e. types of organizations involved, nature of the disputes, and familiarity of situations.

Results
The findings of this follow-up study are entirely consistent with the 2002 study. Game theory experts and unaided novices had a much lower forecast accuracy than novices who implemented role playing (simulated interactions) in predicting the eight conflict decisions.

Three predictions on the future of Iran, and the math to back it up

Bruce Bueno de Mesquita
Lecture, TED Video

Summary

The basis of Bruce Bueno de Mesquita's TED Talk is to apply the game theory approach to the question: What is Iran likely to do in the next couple years? In order to attempt to predict complex questions such as this, he insists that we (analysts) science instead of continuing to rely on "seat-of-the-pants wisdom". This type of analysis and its resulting prediction can be used in most types of complex negotiations and conflicts, or any situation involving coercion. It has applications in business mergers, environmental policy, education, litigation, politics, etc.

Game theory is a branch of mathematics. It makes three key assumptions about people:
  1. People seek what is best for them ("rationally self-interested)
  2. People have a set system of beliefs and values
  3. People face limitations.
Since all people are rational and always tend to act in their own best interests (with the exception of 2 year-olds and schizophrenics), this tool can be applied to most any individual (even terrorists).

The first step is to consider who the people are who influence a rational person into believing that something (a change in policy, a position, belief, etc.) is in their own best interests. Presidents, for example, surround themselves with advisers, who in turn surround themselves with their own advisers, creating a pyramid of influence. Since many people go into the process of shaping a decision, we must pay attention to all of the actors.

At first glance, this may seem like a relatively simple task, considering the small number of cabinet-level advisers privy to the president. However, using simple math factorials, we see there are 120 interaction linkages between just one person and four of her advisers.
Once we double the number of decision makers to 10, we are left with the staggering number 10!, or 3.6 million linkage interactions. Obviously computers are an invaluable part of this type of analysis.At this point, there are several main things that one needs to know in order to conduct this analysis:
  • Who are the players that have a stake in the outcome?
  • What do they say they want?
  • How focused are they on the problem at hand?
  • How much influence do they have on the decision maker; how much clout?
In shaping policy, all people care about two main things: the outcome and receiving credit for their work. De Mesquita points out that most people fall between the outcome and the credit, and if we know to what extent they lean, we can influence their behavior. This leads us to determine what are their choices, values, chances they are willing to take, and their beliefs about other people. This information can be gathered from the Internet, news sources, and experts.

History is not relevant to this type of analysis. The computer does not factor for history and past actions (history is of little importance to de Mesquita, who refers to the Westerfield publication from Yale University Press that cites a declassified CIA study indicating that 90% of the time models were right even when the experts were not).

In applying the method to the question of Iran, de Mesquita focused the analysis on making 3 predictions:
  1. What is Iran likely to do about nuclear weapons?
  2. What is in store for the theocratic regime?
  3. What does the future look like for Ahmadinejad?
The image below reflects the dynamics of interaction within Iran. The lines indicate the most likely level of aggresiveness in Iran's nuclear weapons development. The white line indicates the likely course if Iran were to be left to its own devices, removing the international influences and pressure.

  • The equilibrium is when the government of Iran will acheive its nationalist pride by making weapons grade fuel, but will stop short of obtaining enough to build a bomb.
  • The final image shows the computer-generated results for the projected winners and losers in Iranian politics. The obvious winners are the moneyed interests (whose influence is likely to get stronger with the state of the financial crisis). The "quietists" are likely to gain political clout as they perceive Iran moving politically in the wrong direction. It also appears that Ahmadinejad is the ultimate loser, as his already low influence continues to wane.
  • Comment: While Bruce Bueno de Mesquita offers here an interesting presentation and some interesting charts to advocate game theory, he provides little to no information about the actual process of his methodology.
  • What Is Game Theory And What Are Some Of Its Applications?

    Saul I. Gass
    Professor emeritus at the University of Maryland


    Summary
    After learning how to play the game tick-tack-toe, players typically discover a strategy of play that enables them to achieve at least a draw and potentially a win if the opponent makes a mistake. Sticking to that strategy ensures that the player will not lose. This illustrates the essential aspects of game theory.

    Games with perfect information, such as tick-tack-toe, allow for the development of a pure strategy, an overall plan specifying moves to be taken in all eventualities that can arise. Games without perfect information (e.g. poker), however, offer a challenge because there is no pure strategy that ensures a win.

    Players of games with imperfect information must then reconcile the questions: What is the optimal mix of strategies to play? How much do I expect to win?

    Players must seek an equilibrium solution or a mixed set of strategies for each player, so that each player has no reason to deviate from that strategy, assuming all other players stick to their equilibrium strategy. This then creates the important generalization of a solution for game theory. All many-person non-cooperative finite strategy games have at least one equilibrium solution.

    It is important to note, however, that for many competitive situations, game theory does not really solve the problem. Rather, game theory helps to illuminate the problem and offers players a different way of interpreting the competitive interactions and possible results. Game theory is a standard tool of analysis for professionals working the fields of operations research, economics, regulation, military, retail marketing, politics, conflict analysis, and many more.

    Specific real-world situations include missile defense, sale price wars, NASCAR racing, military conflicts, conflict resolution, the stock market, telecommunications, elections and voting, and arbitration to name a few.
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    What Is Game Theory

    David K. Levine
    Department of Economics, UCLA


    Summary
    Game theory provides a simple representation of a variety of important situations. There are two main branches of game theory: cooperative and noncooperative game theory. David Levine of UCLA defines noncooperative game theory as “dealing largely with how intelligence individuals interact with one another in an effort to achieve their own goals.” Noncooperative game theory is the subject of Levine’s article. (Note: Levine does not define cooperative game theory).

    One way to approach a noncooperative game is to list the players and their respective alternative choices (called actions or strategies) available. Consider for example the game Prisoner’s Dilemma. In the case of this two-player game, the actions of one player form the rows of a matrix while the opposing player’s actions from the columns. The entries into the matrix represent the utility or payoff to the two players. (Note: Levine does not discuss how he derived the values).

    Higher numbers represent higher values in utility. If neither suspect confesses, both prisoners (or players) go free and split the proceeds of their crime (represented by a value of 5). If one player confesses and the other does not, however, the prisoner who confesses testifies against the other in exchange for going free and gets the entire value of 10 utility points; while the other player who did not confess goes to prison, resulting in the low utility score of -4. If both prisoners confess, then both are given a reduced term, but are convicted, which is represented by a utility value of 1.

    An intelligent player of the game should quickly understand that no what he/she believes that his/her opponent will do, it is always better to confess. If the partner in the other cell is not confessing, it is possible to get a 10 instead of a 5. If the partner in the other cell is confessing, it is possible to get a 1 instead of a -4.

    Author's Note: Levine offers a second example in which he examines the question, ""If we were all better people the world would be a better place." Although the discussion was interesting (Levine disproves the statement), the discussion was not helpful in understanding the dynamics of game theory.
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