Thursday, April 11, 2013

Summary of Findings (Green Team): Game Theory (2.875 out of 5 Stars)

Game Theory
Green Team
Rating (2.875 out of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the 8 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 April 2013 regarding Game Theory specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use unstructured data.

Description:
Bruce Bueno de Mesquita defines game theory as “ a body of reasoning, grounded in mathematics but readily understood intuitively as a reflection of how people may behave, particularly in situations that involve high stakes for them. It is part of a family of theories that assume people are rational, meaning that they do what they believe (perhaps mistakenly) is in their best interest.” The method attempts to identify potential actions and reactions from players using a variety of factors, the most important of which is the belief that players will act in their best interest. Additionally, this theory maintains the understanding that individuals will make rational decisions and that rationality will not necessarily end with the most optimal solution for both (or more) parties.

Strengths:

• Can use and evaluate a range of unstructured data
• Can be used in many fields including economics, international relations, and intelligence
• Some models of game theory are simple, though models increase in sophistication and difficulty

Weaknesses:

• Relies heavily on individuals acting in their best interests - does not account for altruistic behavior
• Single play games are not very useful and in reality, games/scenarios cannot or will not always be repeated
• Complex applications of game theory require substantial knowledge of math and statistics
• Context heavy, relying on isolated, hypothetical scenarios
• Operates under a number of assumptions, including actors’ motivations and psyches

How-To:

1. Find a problem that can be modeled through game theory (nothing overly complex with too many factors).  Make sure the simplified essence of the problem is used.
2. List all actors and options.  A table is the most common representation technique -- since it visually portrays a payout matrix
3. Assign values to each of the potential outcomes.
4. Weigh potential outcomes according to these values.
5. Describe situations in which these outcomes are likely to occur and then choose the most likely, regardless if it is the ‘best’ outcome or not.

Personal Application of Technique:
The class was tasked with finding the optimal outcome for themselves in a pirate puzzle application of game theory. In this application of the pirate puzzle, five pirates have an understanding of rank that is respected on the ship. The pirates must decide how to divvy up a bounty of twenty gold (chocolate) coins. Players operated under the assumption that they wanted the twenty gold coins.  The highest ranking pirate makes the initial proposal to divide the coins, knowing he must gain majority’s approval in order for the proposal to pass. In our example, the pirate who fails to gain the majority vote is out of the running for the gold coins and the next highest ranking pirate makes his own proposal until one proposal is agreed upon. In the event of a tie, the highest ranking pirate involved in the proposal casts the deciding vote. The game was run twice in order to increase the presentation of different options.

In both instances, the highest ranking pirate in the class failed to gain the majority vote and was eliminated from the running. Instead, in the first instance, the game was played out to the third ranking pirate. The next iteration ended with the second highest ranked pirate, who was able to appeal to the lowest ranked pirate to earn a fifty-percent vote. Despite what game theory suggests, the lowest ranked pirate in our scenario was not satisfied with an offer of a single coin, or a few coins, even knowing she could be left with none if she let game continue. During the second round of the game, the individuals acted more to their interests rather than attempting to appease everyone.

Rating:  2.875 out of 5 stars

For Further Information:
Stewart, I. (1999). Mathematical recreations: A puzzle for pirates. Scientific American, 98-99. Retrieved from http://www.cse.iitb.ac.in/~saifhhasan/files/pirate_puzzle.pdf

Source: Mesquita, B (2011) Applications of Game Theory in Support of Intelligence Analysis. Intelligence Analysis: Behavioral and Social Scientific Foundations, 57-82. Retrieved from http://www.nap.edu/openbook.php?record_id=13062&page=57