Tilman Börgers

“Cautious” utility maximization and iterated weak dominance

This paper examines the implications of assuming that “rational” players in a two-player noncooperative game maximize expected utility using “cautious” beliefs; i.e., beliefs that give positive probability to all “rational” strategies of the other players. The result is a solution concept that captures some of the flavor of but is not equivalent to the iterated elimination of weakly dominated strategies. The solution concept yields attractive results for some games, but suffers from nonexistence problems in other games. We interpret the nonexistence problems as showing that it is logically inconsistent to assume that rational players analyze all games on the basis of cautious expected utility maximization.

Iterated Elimination of Dominated Strategies in a Bertrand-Edgeworth Model

We consider a Bertrand-Edgeworth model of price competition. Firms have identical and constant marginal costs and finite exogeneous capacities. Firms choose prices. Our interest is in the set of those prices which are left over after the iterated elimination of dominated strategies. We show that in two circumstances this set will be close to the set containing only the marketclearing (Walrasian) price: (i) if any n − 1 out of n firms assumed to be in the market have sufficient capacity to cover demand at marginal costs; (ii) if any given total capacity is owned by a very large number of very small firms.

Perfect equilibrium histories of finite and infinite horizon games

Abstract A new approach to the approximation of the perfect equilibria of infinite horizon games through the perfect epsilon-equilibria of finite horizon truncations of such games is presented. Whereas previous limit results referred to the equilibrium strategies the limit results in this paper refer to the histories which result if players adhere to these strategies. The new approach has two advantages. First it is easier to apply. Second it shows that the existence of a perfect equilibrium of an infinite horizon game can be deduced from the existence of perfect epsilon-equilibria of finite horizon truncations of this game.

Auction Theory for Auction Design

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Undominated strategies and coordination in normalform games

This paper studies the question whether there are nondictatorial procedures for collective decision making which ensure that collective decisions are Pareto-efficient if all agents choose strategies that are not weakly dominated. It is shown that contrary to what one might expect the answer is not entirely negative.

Recent Books on Evolutionary Game Theory

Books reviewed in this article Fudenberg and David Levine, The Theory of Learning in Games Josef Hofbauer and Karl Sigmund, Evolutionary Games and Population Dynamics Larry Samuelson, Evolutionary Games and Equilibrium Selection Fernando Vega-Redondo Evolution, Games, and Economic Behavior Peyton Young, Individual Strategy and Social Structure, an Evolutionary Theory of Institutions

Complexity Constraints and Adaptive Learning: An Example

Experimental research suggests that it is very difficult for most people to make optimal decisions if their payoffs are affected by a sequence of random shocks that are independent and identically distributed (i.i.d.). Many subjects never learn to make optimal choices; others do, but take a very long time.

When does learning lead to Nash Equilibrium

This paper surveys those theoretical results on learning in games which address the question when learning leads to Nash equilibrium. The main conclusion is that the known convergence results refer to relatively small classes of games. Moreover, these results either rely on restrictive assumptions about players’ prior knowledge, or they use implicitly the assumption that players’ willingness to experiment is very large.

A counterexample to Dhillon (1998)

We provide a counterexample to Theorem 1 (A) in Dhillon (Soc Choice Welf 15:521–542, 1998).