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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 ,
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 37

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online