Game Theory/Game Theory Kristine Joy E. Carpio Department of Mathematics De La Salle University Term

Game Theory Kristine Joy E. Carpio Department of Mathematics De La Salle University Term Outline Game Theory Presentation of Game Theory Strategies and Solutions for Simultaneous Games Backward Induction References Definition of the Model Game theory studies the consequences of strategic interaction between rational agents (players) pursuing their own unique objectives, in a clearly defined framework. Such interactions can be negotiation, competition, mutual assistance, provision of a good or service, etc., which are all possible actions that will lead to a result. The outcome results in a payoff, positive or negative, for each individual who took part in the game. Assumptions The hypotheses that support game theory are 1. The rationality of agents (players), which drives them to achieve the best possible solution for them, is measured by what is known as ’utility’; 2. Each player knows, besides his own, the set strategies and earnings functions of every other player (complete information); 3. Each participant makes the best decisions for himself in order to maximize his utility (if dealing with an individual) or his profit (when dealing with a business), knowing that the others do the same; 4. The choices made in the past are known by all the participants. Utility is not a measure of material or monetary payoff, but a subjective measure of player satisfaction. Game Formalities A strategic game is characterized by a set of game rules concerning 1. the players, 2. the strategies (actions or decisions), 3. the sequence of decisions (game progress), 4. the payoffs or utility of the players (in terms of their strategies), and 5. the information available to the players. This information can be complete (perfect) or incomplete (imperfect). What would be the player’s best strategy to different moves of the other players to achieve the ”best” or maximum payoff? Prisoner’s Dilemma The prisoners’ dilemma is a game which involves two suspects, say P and Q, arrested by police and who must decide whether to confess or not. If one confesses but the other doesn’t, the prisoner which confesses gets a lighter prison term (1 year) but the prisoner which doesn’t confess get a very harsh term (8 years). If neither confesses, they both get lighter terms (2 years each); but if both confess, both of them get a strict term (4 years each). Methods of Representing a Game 1. Normal Form A table of numbers with the strategies listed along the margins of the table and the payoffs for the participants in the cells of the table. 2. Extensive Form A game can be shown as a tree diagram in which the strategic decision is shown as a branch point. Extensive form games are suitable for sequential decision-making while games in normal form are used to analyze one-shot games. In one-shot games, each player chooses one action and all of them chooses simultaneously.