## Thursday, April 16, 2009

### 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.