game theory_博弈论.pdfVIP

2012-12-3 Shanghai University of Finance and Economics 1 LECTURE 9: GAME THEORY 2012-12-3 Shanghai University of Finance and Economics 2 Games • Game theory is the study of interacting decision makers. • Strategic Form or Normal Form Game • Extensive Form Game 2012-12-3 Shanghai University of Finance and Economics 3 Normal (Strategic) Form Game • Normal form game is defined by - a set of players - a set of strategies - a set of payoffs • Common Knowledge: each knows that another person knows that he knows and so on ……….that he knows …..(e.g. the sets of players, strategies and payoffs) • Players are fully rational, maximize expected utility given subjective beliefs and beliefs are modified when new information arrives (e.g. according to Bayes’ law) 2012-12-3 Shanghai University of Finance and Economics 4 Example 1: Matching Pennies Note: the first element in a vector of strategies denote the first player’s (Row’s) strategy, the second element denotes the second player’s (Column’s) strategy. 2012-12-3 Shanghai University of Finance and Economics 5 Example 2: The Prisoner’s Dilemma game 2012-12-3 Shanghai University of Finance and Economics 6 Solution Concepts • Pure strategies: Strategies in which a choice is made with probability of 1 • Mixed strategies: Random strategies i.e. choices are made with probability 0 and 1 • If R is the set of strategies available to Row, the set of mixed strategies is the set of all probability distributions over R where the probability of playing strategy r in R is pr (similarly for Column) 2012-12-3 Shanghai University of Finance and Economics 7 • If Row’s subjective probability distribution over Column’s set of strategies is ΠC, π is th