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econ 208 - Economics 109 Game Theory Spring 2002 Vincent...

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1 Economics 109, Game Theory, Spring 2002, Vincent Crawford A game is a multi-person decision situation, defined by its players, its "rules" (the order of players' decisions, their feasible decisions at each point, and the information they have when making them); how players' decisions determine the outcome; and players' preferences over outcomes. I call these things the game's structure . Analyses of games must confront all the issues that arise with individual decisions, plus one that is unique to games: Because the outcome is influenced by other players' decisions as well as your own, to do well in a game you need to predict others' decisions, taking their incentives into account. This may require a mental model of other players (including a model of their models of you). Examples to illustrate issues a theory of games should address: L R Confess Don't T 2 2 1 2 Con- fess -5 -5 -10 -1 B 2 1 1 1 Don't -1 -10 -2 -2 Crusoe vs Crusoe Prisoner's Dilemma Crusoe vs. Crusoe is just two decision problems, not really a game; each player has a best decision independent of other's ( dominant ). In Prisoner's Dilemma players' decisions affect each other's payoffs but each still has a dominant decision; individual optimal decisions with payoff interactions yield a Pareto-inefficient outcome. Don't need special theory for games like this (but Prisoner's Dilemma gets more interesting when we study ways to improve its outcome).
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2 Push Wait Heads Tails Push 1 5 5 3 Heads -1 1 1 -1 Wait -1 9 0 0 Tails 1 -1 -1 1 Pigs in a Box Matching Pennies In Pigs in a Box, Row (R) is a big pig and Column (C) is a little pig. The box is a Skinner box, named for psychologist B.F. Skinner. Pushing a lever at one end yields 10 units of grain at the other. Pushing "costs" either pig 2 units of grain. If R pushes while C waits, C can eat 5 units before R lumbers down and shoves C aside. If C pushes while R waits, C cannot shove R aside and R gets all but one unit of grain. If both push, and then arrive at the grain together, C gets 3 units and R gets 7. If both wait, both get 0. In experiments with real pigs, if they settle down, it tends to be at (R Push, C Wait). C does better, although R can do anything C can do! This couldn't happen in an individual decision problem. It happens here because Wait dominates Push for C, but not for R: the way they interact in this game, only R has an incentive to Push. In games, (the right kind of) weakness can be an advantage! R might do better if he could commit himself to giving C more grain if C Pushed. Understanding this should help to understand many things in economics. E.g. corporations as legal "persons" have the right to be sued. This is a "right" because it helps enforce contracts. (If the pigs had studied game theory, they wouldn't have to "settle
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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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econ 208 - Economics 109 Game Theory Spring 2002 Vincent...

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