Summary of Findings: Game Theory (3.5 out of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the articles read in advance (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst University, in September 2018 regarding Game Theory as an Analytic Method, 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 for determining optimal strategies for two or more players with numerous available strategies. Typically this “game” is displayed using a matrix of payoffs.  The underlying assumption is that players will act in a manner consistent with their own rational self-interest with the default assumption being that each player will choose a optimal strategy of maximizing his/her personal payoff. However, the application of game theory introduces a multitude of variables which will influence how a player goes about selecting their moves such as whether they are aware of the moves of other players, whether the game is sequential or simultaneous, whether the game is cooperative or non-cooperative, and many other potential factors.

Strengths:

• Develops a framework for analyzing decision-making
• Quantitative technique that players can use to arrive at an optimal strategy
• Use to develop and impose desired outcomes

Weaknesses:

• Assumes rational, intelligent decision makers
• Assumes that players have the knowledge about their own pay-offs and pay-offs of others
• Payoffs can be arbitrary/subject to interpretation
• Gets more complicated the closer it gets to reality

How-To**:

**There is an extensive range of models that fall within the parameters of game theory.  Our exercise introduced one of the most basic and classic examples of game theory: The Prisoner’s Dilemma.  

1. Define layers or decision makers
2. Determine list of strategies
3. Determine outcomes resulting from each strategy
4. Determine payoffs from the outcomes

Application of Technique:

Scenario: This is a game show wherein one player can win money, both players can win money, or neither player can win money. $100,000 is up for grabs. The players can choose to split the money or steal the money. If both players choose to “split”, they both walk away with $50,000, if one player chooses to “steal” and the other chooses to “split”, the player who chose to “steal” walks away with $100,000 and the player who chose to “split” walks away with $0. If both players choose to “steal”, both players walk away with $0.

We split 6 players into 3 teams of 2. Each player had two cups with lids -- One cup with a paper inside that said “Split”, the other cup with a paper inside that said, “steal." Players had to decide, given the situation, whether to “steal” or “split” with the other player. Assuming that players make a decision that results in the best possible outcome for each, they would presumably “steal,” resulting in neither player receiving the money.

In the case of our class, 2 teams successfully “split” and the 3rd team resulted in a “steal”/ “split”

opposition.

For Further Information:

1. EconomicsTube - Game Theory on a British Game Show!
2. How Prisoner's Dilemma may look in a situation of nuclear escalation (Scene from Sum of All Fears)
3. Wikipedia: Game Theory
4. The Evolution of Trust
5. William Spaniel's YouTube Channel dedicated to Game Theory

Game Theory as a Theory of Conflict resolution

1994

Author: Anatol Rapoport

Link: https: //books.google.com/books?hl=en&lr=&id=dOttCQAAQBAJ&oi=fnd&pg=PA1&dq=conflict+resolution+game+theory&ots=rE7GlmcoiI&sig=9BVgsbBppvn96zKbUHBWrE3BuMk#v=onepage&q=conflict%20resolution%20game%20theory&f=false   

Summary:

In the introduction of Game Theory as a Theory of Conflict Resolution, Rapoport begins by explaining how game theory is structured. Game theory, originally created by John Von Neumann, includes 1. Players, or decision makers; 2. A list of strategies; 3. Outcomes resulting from each strategy; and 4. The payoffs from the outcomes. Each player is assumed to be a rational player, with the goal to achieve their preferred payoffs. Interests may be opposed but there may be conflicts of interests, so players will utilize their skills and choose their best strategies, at least guaranteeing a minimal payoff or gaining an advantage.

Rapoport compares this constant-sum game to the game of Chess or Go, which in a way, are conflict models. The result of the game is an equilibrium, where the payoffs remain interchangeable to each player, but one player achieves his optimal strategy, and the other has to alter his optimal strategy. For the best results and equilibrium to remain, prescribing strategies to each rational player will allow both players to do as well as they possibly can in that game. Prescribing strategies work best when only two players are involved in order for the game to preserve its salience, although, there are solutions for games with N (more than two) players. Coalitions are formed if three or more players are involved. Typically the two stronger ones will link up against the weaker player or two weaker ones will link up against the stronger player. As the paper goes on, Rapoport broadens the player range to four or five players, which diverts away from an equal outcome.

Game theory is considered a descriptive, or predictive research tool in behavioral science. The theory has dissatisfied many while appealed to others. Those who were disappointed have used the game-theoretic analysis to create methods in conflict situations including, war; war planning; power politics; and business competition. Combining formal game theory to competitive expertise, caused an ineffective outcome. Rapoport raises the point that the usual explanation of this failure is that the “’effect that the real world is too complex to be stimulated by formal game-theoretic models,” misses the main point: even if real conflicts were no more complex than theoretically tractable formal games, game theory would be powerless to prescribe ‘optimal strategies’ in any but total bi-polar conflicts...”

 

Burn’s and Meeker’s paper regarding the mathematical symbolism of game theory, ultimately concludes that payoffs in any game, more specifically Prisoner’s Dilemma, does not represent the player’s utilities, which Rapoport agrees with. In any situation, real-world or theoretic, the overt payoffs do not always influence the decisions.

Critique:

I agree with Rapoport when he explains that game theory loses its distinction and strays away from equality if there are more than two players. Payoffs become more difficult to achieve and some strategies become ineffective, so they must be reformed. The course of action is bound to change and is not always as obviously perceived when prescribed the course of action in the beginning. I believe this is a great explanation on why we do not see game theory as successful as it can be in real-world situations. The misconception over the controversy has been proven wrong when used correctly. It has been applied and successful when used in some real-world situations, including military tactics. 

To Bluff or Not to Bluff

02 March 2015

Author: Drew Calvert

Featured Faculty: Ehud Kalai, Professor of Managerial Economics & Decision Sciences at Northwestern University's Kellogg School of Management & Kent Grayson, Associate Professor of Marketing at Northwestern University's Kellogg School of Management

 Link: https://insight.kellogg.northwestern.edu/article/to-bluff-or-not-to-bluff 

Summary: 

The bluff is a common strategic move that is often thought of as a clever psychological ploy when the odds are stacked against us. However, game theorists often view bluffing as primarily computationally, not psychologically. Professor Ehud Kalai argues that to win in any strategic game one should be unpredictable. If someone bluffs all the time bluffing is no longer an effective method because the opponent knows that they are likely bluffing. The same can be said when someone never bluffs. This article is set up into three sections, Mixing It Up, Knowing the Game, Knowing Yourself and High-Stakes Math.

Kalai defines strategic moves as maximizing one’s ability to be unpredictable. In court, Kalai had to show his ability to play poker and blackjack machines in both strategic and nonstrategic ways. The machines were banned from a local bar in Chicago until the he was able to prove that the machines could be played as a game of skill and not just a game of luck. Zero-sum games uses mixed strategy due to the balancing act of bluffing. This based on the assumption that the opponent is playing just as strategically.  

In non-antagonistic games it does not always pay to be unpredictable due to the requirement of full or partial cooperation. Kent Grayson, studied trust and deception.  Trust is comprised of three components: competence, honesty, and benevolence. He argues “bluffing is only effective when it is done with a measure of self-awareness.” How the company is perceived determines whether or not they can get away with bluffing without backlash.  In games bluffing can be harmless. In businesses bluffing comes at a higher risk.

Game theorists have proven mixed strategy to produce the best result. However, when the stakes are higher, some are not willing to take the risk on a bluff. In the last section, Kalai argues how randomization is tough when it comes to warfare and politics. The example he gives is during the Six-Day War between Israel and its Arab neighbors. Egyptian convoys used Israeli symbols on the roofs of their trucks to fool the Israeli bombers. The bombers were not willing to flip a coin on if the were taking out the right truck or not. The higher the pressure, the more risk-averse people become when it comes to randomizations.

Critique:

The article To Bluff or Not to Bluff was well written overall. Even though game theorist argues that bluffing is computationally, not psychologically, they still take in to account the stakes of the bluff. I think the last section on High-Stakes Math was a very strong section. Even though the math is there to support the bluff, the psychologically doubt still there. I’m not sure that will ever gone away completely because it human emotions and error. 

Turning a Weakness within Game Theory into a Strength: A Review of 'Testing' Game Theory by Daniel Hausman (2005)

Summary: 

         In Hausman’s article on testing game theory, the author identifies the primary difficulty in empirically testing the axioms of the analytic technique. In order to conduct an experiment on game theory a scientist must impose experimental conditions prior to testing. The scientist determines who the players are, what strategies are available to the players, and the payoffs for each strategy. For example, an economist may present a game theory test in which the players are two business professionals choosing a strategy based on monetary payoffs (make money or lose money). On the other hand, an evolutionary biologist may present a game theory scenario in which the players are two animals choosing a strategy based on evolutionary payoffs (survival or death). After imposing these conditions, the emergent test of game theory is what Hausman describes as a “Human Premeditated Game Theory” (HP game theory). Since every discipline produces a different game theory test, Hausman argues that the economist and evolutionary biologist are conducting their own tests of HP game theory and not tests of game theory itself. 

         Since pre-determined conditions are necessary to apply a test of game theory and since those same conditions inherently turn a test of game theory into a test of HP game theory, there is no way to test game theory itself. Thus, Hausman concludes, attempting to test the axioms of game theory is a futile effort. Instead, Hausman emphasizes the value of using game theory to test claims about people’s preferences.

         Hausman explains the varying levels of control a scientist has in determining conditions for a test of game theory. At the lowest level of difficulty is determining how many players there are and what strategies are available to those players. With slightly greater difficulty, scientists can control the beliefs players have concerning permissible strategies, the physical outcomes of strategy combinations, and the knowledge available to other players (including their beliefs about the beliefs of each other). The greatest difficulties for the scientist are determining the payoffs and the preferences of the participants. Determining the payoffs in a game theory experiment are critical because they are used "to make any substantial predictions concerning laboratory behavior". Furthermore, the payoffs are built on the assumption that the participant’s preference is to choose the strategy that offers the most favorable payoff, or the dominant strategy. 

      Yet when applied in experimental tests of game theory, there are times when individual preferences lead participants to choose the non-dominant strategy. Rather than consider this anomaly as disconfirming the effectiveness of game theory in predicting behavior, Hausman suggests that scientists should use game theoretic anomalies to study the factors influencing preferences. In an economist’s HP game theory, the economist assumes that the participant will prefer to maximize the monetary payoff by choosing the dominant strategy. However, other unknown factors (what Hausman calls preferences) may influence the participants to choose the non-dominant strategy with the lesser monetary payoff. For example, participants may care about the monetary payoffs other participants receive, what other participants trust them to do, whether the outcome is fair, etc. Hausman concludes that the true value in applying game theory is this opportunity to understand how those personal preferences are affecting decision-making.

Critique:

     The seemingly fatal flaw of applying game theory, in my opinion, is the assumption that the participant will choose to maximize personal payoff with the dominant strategy. As analysts we are taught to identify our assumptions and reconsider how those assumptions are affecting our analysis. Here, Hausman identifies the assumption that is misleading scientists and leaving them surprised when participants choose the non-dominant strategy.

   Although this assumption is a weakness, I agree with Hausman that we can turn this weakness into a strength by using game theory to understand how personal preferences affect a participant’s decision regarding the payoffs. An opportunity to expand on empirical tests of game theory is to conduct a survey of the participants alongside the experiment. These surveys should attempt to reveal the preferences, or personality characteristics, of the target population. How important are the values of fairness, generosity, or selfishness to these participants? With a large enough sample, this survey/game theory experiment can reveal two things: the target population’s beliefs regarding these factors and what factors tend carry the most influence in decision-making for very specific, HP game theory situations.

Although this combined experiment could provide a more wholistic understanding of the target population’s preferences and the decision-making process for participants, challenges remain because a scientist is limiting participants to two strategies and payoffs to only four mutual outcomes. Thus, it will be difficult to generalize results from a wide-scale study of this kind because real-world “HP game theory” situations will typically present decision-makers with more possible strategies and far more potential outcomes.

Source: Hausman, D. M., (2005). ‘Testing’ game theory. Journal of Economic Methodology. 12(2), 211-223.

   

Is an Unpredictable Leader Good for National Security? Think the goal is to keep your enemies guessing? Game theory suggests otherwise.

19 June 2018

Author: Drew Calvert

Featured Faculty: Sandeep Baliga, Professor of Managerial Economics & Decision Sciences at Northwestern University's Kellogg School of Managment

https://insight.kellogg.northwestern.edu/article/is-an-unpredictable-leader-good-for-national-security

Summary:
The urgency of having a strong nuclear deterrence strategy during the Cold War sparked a debate between economist and Nobel laureate, Thomas Schelling, and President Richard Nixon about the effectiveness of the “madman” theory of international relations.  Nixon believed that having a reputation for unpredictability was the most effective deterrent, while Schelling, by applying game theory, proved that building a reputation of consistent behavior was much more effective. 

In this article, Sandeep Baliga, a professor of management at Northwestern University’s Kellogg School of Management, echoes Schelling’s game theory insights to explore the effects of unpredictable leadership on present day national security.  Using game theory to study international relations, Professor Baliga has found that meticulous strategy, not unpredictability, is the best approach in conducting foreign policy.  As Baliga puts it: “in national security, predictability can definitely pay.” 

Author Drew Calvert brings clarity to the connection between game theory and international relations by understanding incentives and how they work.  Incentives in game theory are best described in the principal-agent problem.  In the principal-agent problem, a principal needs to incentivize an agent whose interests may not align with those of the principal.  The author gives the example of an employer who might incentivize an employee to be productive by linking salary or bonuses to outputs such as sales.  “If the employee believes the employer will renege on paying him, or that her payment is random and independent of performance, there is no incentive for the employee to work.” 

On the other hand, an agent is more likely to respond positively to incentivization if he believes the principal will stay true to his word in an agreement. 

This notion is where consistency becomes imperative for the US to build a reputation for following through on policies designed to incentivize the actions of both allies and adversaries.  The example given in the article is the United States’ efforts to influence North Korea by incentivizing the de-acceleration of North Korea’s nuclear arms program.  Calvert states “if North Korea is left without a clear sense of how the US might respond to aggression or appeasement, its leaders might choose a more reckless and destabilizing course of action.” This could hold especially true when considering other internal, and external factors the country may weigh as important. The underlying logic for designing incentives in the principal-agent problem is, in many ways, parallel to the US-foreign adversary relations.  As Schelling stated, “if your opponents believe you will keep your word, then your word can shape their actions.”

Critique:

I think many that find issue with consistency in foreign policy do so because, in an age of deliberate deception and asymmetric warfare, predictability carries with it a stigma of “outdatedness.”  International relations is complex and situational, with each situation requiring a different response.  I find game theory to be a beneficial approach to the intelligence context because of its effort to model interaction between decision makers, accounting for the unpredictability of human nature. In his book “Game Theory: Analysis of Conflict,” Roger Myerson defined game theory to be the study of mathematical models of strategic interaction between RATIONAL decision-makers.  The article attempts to apply game theory models to understand the interaction between volatile decision-makers.  The article makes the case that game theory proves volatility and unpredictability to be detrimental to incentivizing both allies and adversaries, and I don’t disagree.  My critique comes in the form of a suggestion for more research to fill the white space in the article: even if game theory proves it doesn’t pay to be “the madman,” how do we apply game theory to incentivize “the madman”?