Games and Information

Abstract

This chapter is an introduction to game theory, and to its application to situations of asymmetric information. It covers simultaneous and sequential games, dominant strategies, Nash equilibrium, backward induction, subgame perfection, repeated games, Bayesian games, sequential rationality, behavioural strategies, perfect Bayesian equilibrium, sequential equilibrium. The Centipede game is taken as an incentive to be critical of the usual definition of rationality; some doubts are also raised about the universal certainty that dominant strategies will always be played: some examples of Prisoners’ Dilemma suggest as plausible that players may choose ‘Cooperate’. The treatment of auctions is limited but rigorous, it is proved that a first-price sealed-bid (independent-private-values) auction and a second-price sealed-bid auction generate the same expected revenue for the seller, and on this basis the revenue equivalence theorem is sketched; for common-value auctions the winner’s curse is examined in detail. Then the chapter passes to asymmetric information, and discusses principal-agent, moral hazard, adverse selection, screening, signalling, and the intuitive criterion of Cho and Kreps. The dependence of all these analyses on the assumption that agents choose on the basis of VNM expected utility, which does not seem to correspond to how people actually choose, is noticed.