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week3-class-print - In this lecture Strategic(or Normal...

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Strategic (or Normal) form games ECOS3012 - Strategic Behavior School of Economics, FASS University of Sydney Lecture 3, March 16, 2011 ECOS3012 - Strategic Behavior (USYD) Strategic (or Normal) form games Lecture 3, March 16, 2011 1 / 14 In this lecture 1. Knowledge vs. Common knowledge. 2. Formal description of a strategic form game. 3. Mixed strategies and corresponding payoffs. (ch 4n / ch 5o). 4. Best response, weakly and strongly dominated strategies. (ch 6 n& o). 5. Equilibrium concepts for Maximin and minimax strategies Iterated elimination of dominated strategies. (Ch7 n& o) Note. Ch 4n, or ch5o etc. refers to Chapter 4 in the new edition or Chapter 5 old edition of the Watson Text. ECOS3012 - Strategic Behavior (USYD) Strategic (or Normal) form games Lecture 3, March 16, 2011 2 / 14 Knowledge vs. Common Knowledge Definition 1 (Common Knowledge) An event E is common knowledge among a set of players if if everyone knows E, everyone knows that everyone knows E, everyone knows that everyone knows that everyone knows E, everyone knows that everyone knows that everyone knows that everyone knows E, . . . . . . What is the difference between knowledge and common-knowledge ? (To be explained in class) Throughout this course, we will be assuming that the structure of the game is common-knowledge. Except toward the end of the course, we will also assume that the payoffs are common-knowledge. ECOS3012 - Strategic Behavior (USYD) Strategic (or Normal) form games Lecture 3, March 16, 2011 3 / 14 Formal description of a Strategic Form game Recall that in a strategic form game, players choose their actions simultaneously. Therefore, we need to specify 1. The set of players, 2. What strategies are available for each player. 3. Given an array of strategies chosen by each player, what is the eventual payoff. Let N = { 1 , . . . , n } denote the set of players. S i the set of possible (pure!) strategies for Player i . s i , s i etc. will denote typical strategies. S = S 1 × · · · × S n . s = ( s 1 , . . . , s n ) is a strategy profile, i.e. a list of strategies used by the various players. s - i = ( s 1 , . . . , s i - 1 , s i + 1 , . . . , s n ) denotes the strategy profile of all players except Player i . For each i , the vNM utility u i ( s i , s - i ) be the payoff of Player i if the strategy profile ( s i , s - i ) is played. The above structure is common-knowledge among the players.

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