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200CLectureNotes - Lecture Notes for Economics 200C: Games...

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1 Lecture Notes for Economics 200C: Games and Information Vincent Crawford, revised March 2000; do not reproduce except for personal use 1. Introduction MWG 217-233; Kreps 355-384; Varian 259-265; McMillan 3-41 Robert Gibbons, "An Introduction to Applicable Game Theory," Journal of Economic Perspectives (Winter 1997), 127-149 (or you can substitute his book) Noncooperative game theory tries to explain outcomes (including cooperation) from the basic data of the situation, in contrast to cooperative game theory, which assumes unlimited communication and cooperation and tries to characterize the limits of the set of possible cooperative agreements. In "parlor" games players often have opposed preferences; such games are called zero-sum . But noncooperative game theory spans the entire range of interactive decision problems from pure conflict to pure cooperation (coordination games); most applications have elements of both. A game is defined by specifying its structure : the players, the "rules" (the order of players' decisions, their feasible decisions at each point, and the information they have when making them); how their decisions jointly determine the outcome of the game; and their preferences over possible outcomes. Any uncertainty about the outcome is handled by assigning payoffs (von Neumann-Morgenstern utilities) to the possible outcomes and assuming that players' preferences over uncertain outcomes can be represented by expected-payoff maximization. Assume game is a complete model of the situation; if not, make it one, e.g. by including decision to participate. Assume numbers of players, decisions, and periods are finite, but can relax as needed. Something is mutual knowledge if all players know it, and common knowledge if all know it, all know that all know it, and so on. Assume common knowledge of structure (allows uncertainty with commonly known distributions modeled as "moves by nature"): games of complete information . Can represent a game by its extensive form or game tree. E.g. contracting by ultimatum (MWG uses Matching Pennies, Kreps has abstract examples): Two players, R(ow) and C(olumn); two feasible contracts, X and Y. R proposes X or Y to C, who must either accept (a) or reject (r). If C accepts, the proposed contract is enforced; if C rejects, the outcome is a third alternative, Z. R prefers Y to X to Z, and C prefers X to Y to Z. R's preferences are represented by vN-M utility or payoff function u(y)=2, u(x)=1, u(z)=0; and C's preferences by v 2 (x)=2, v 2 (y)=1, v 2 (z)=0. Draw game trees when C can observe R's proposal before deciding whether to accept, and when C cannot. Order of decision nodes has some flexibility, but must respect timing of information flows. Players assumed to have perfect recall of their own past moves and other information; tree must reflect this. Each decision node belongs to an information set ,
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2 the nodes the player whose decision it is cannot distinguish (and at which he must therefore make the same decision). All nodes in an information set must belong to the same player and have the set of same feasible decisions. Identify each information set by
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This note was uploaded on 09/19/2011 for the course ECON 208 taught by Professor Sobel,j during the Spring '08 term at UCSD.

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200CLectureNotes - Lecture Notes for Economics 200C: Games...

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