Information, evolution and utility

Human utility embodies a number of seemingly irrational aspects. The leading example in this paper is that utilities often depend on the presence of salient unchosen alternatives. Our focus is to understand why an evolutionary process might optimally lead to such seemingly dysfunctional features in our motivations and to derive implications for the nature of our utility functions.Evolution, information, internal conflict, self control, temptation, time consistency, utility

The Simple Geometry of Perfect Information Games

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.Perfect information, Subgame perfection, Equilibrium correspondence

Existence of equilibrium in single and double private value auctions

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated and asymmetrically distributed. For double auctions, we show further that at least one equilibrium involves a positive volume of trade. The existence proof establishes new connections among existence techniques for discontinuous Bayesian games

Communication and equilibrium in discontinuous games of incomplete information

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence

Adjustment Dynamics and Rational Play in Games

When a strategic situation arises repeatedly, the possibility arises that equilibrium predictions can be justified by a dynamic adjustment process. We examine myopic adjustment dynamics, a class that includes replicator dynamics from evolutionary game theory, simple models of imitation, models of experimentation and adjustment, and some simple learning dynamics. We present a series of theorems showing conditions under which behavior that is asymptotically stable under some such dynamic is strategically stable (Kohlberg and Mertens [1986]). This behavior is thus as if the agents in the economy satisfied the extremely stringent assumptions that game theory traditionally makes about rationality and beliefs.game theory, evolution, learning, adjustment dynamics, dynamics, dynamic stability, strategic stability

Believing in Multiple Equilibria

If agents have common priors concerning the probability with which equilibrium is selected, they have an incentive to trade beforehand. If their trading process satisfies a certain notion of individual rationality, these trades will reduce and ultimately remove all uncertainty concerning equilibrium selection. In this sense, multiple equilibria engender institutions which can uniquely determine equilibrium

The Loser's Curse and Information Aggregation in Common Value Auctions

We consider an auction in which k identical objects of unknown value are auctioned off to n bidders. The k highest bidders get an object and pay the k+1st bid. Bidders receive a signal that provides information about the value of the object. We characterize the unique symmetric equilibirum of this auction. We then consider a sequence of auctions Ar with nr bidders and kr objects. We show that price converges in probability to the true value of the object if and only if both kr-->infinity and nr--kr-->infinity, i.e., the number of objects and the number of bidders who do not receive an object in equilibrium go to infinty.

Order Independence for Iterated Weak Dominance

In general, the result of the elimination of weakly dominated strategies depends on order. We define nice weak dominance. Under nice weak dominance, order does not matter. We identify an important class of games under which nice weak dominance and weak dominance are equivalent, and so order under weak dominance does not matter. For all games, the result of iterative nice weak dominance is an upper bound on he result from any order of weak dominance. The result strengthen the intuitive relationship between backward induction and weak dominance, and shed light on some computational problems relating to weak dominance.

Order Independence for Iterated Weak Dominance

In general, the result of the elimination of weakly dominated strategies depends on order. We find a condition, satisfied by the normal form of any generic extensive form, and by some important games which do not admit generic extensive forms, under which any two games resulting from the elimination of weakly dominated strategies (subject to no more eliminations being possible) are equivalent. We also extend our condition and result to the case of elimination by mixed strategies. The result strengthens the intuitive connection between backward induction and weak dominance. And, under our condition, some computational problems relating to weak dominance, which are gnerally complex, become simple.