Karl Wärneryd

We consider contestants who must choose exactly one contest, out of several, to participate in. We show that when the contest technology is of a certain type, or when the number of contestants is large, a self-allocation equilibrium, i.e., one where no contestant would wish to change his choice of contest, results in the allocation of players to contests that maximizes aggregate equilibrium effort. For a class of oligopoly models that are equivalent to contests, this implies output maximization.

During the past two centuries, western nations have successively extended the voting franchise to citizens of lower income. We explain this process of democratization as a rational way for incumbent elites to wage war effectively on other nations, as in a strategic game of international conflict handing over military spending decisions to citizens who face a lower tax cost of arming may confer a strategic delegation advantage. We find supporting empirical evidence in case studies of franchise extensions in the United Kingdom, France, and the United States.

We consider rules (strategies, commitments, contracts, or computer programs) that make behavior contingent on an opponent’s rule. The set of perfectly observable rules is not well defined. Previous contributions avoid this problem by restricting the rules deemed admissible. We instead limit the information available about rules. Each player can only observe which class, out of a collection of classes smaller than the number of rules, the opponent’s rule belongs to. For any underlying 2-player, finite, normal-form game there is a game extended with coarsely observable strategies that has equilibria with payoffs arbitrarily close to any feasible, individually rational payoff profile.

Nash proposed an interpretation of mixed strategies as the average pure-strategy play of a population of players randomly matched to play a normal-form game. If populations are finite, some equilibria of the underlying game have no such corresponding “mass-action” equilibrium. We show that for mixed strategy equilibria of 2 × 2 games, the requirement of such a correspondence is equivalent to neutral evolutionary stability.

We consider two-player, perfectly discriminatory, common-value contests (or all-pay auctions), in which one player knows the value of the contested object with certainty, and the other knows only its prior distribution. We show, among other things, that in equilibrium the players win with equal probability. This contrasts with a large class of imperfectly discriminatory contests in which the uninformed player wins with a strictly greater probability than the informed player.

We consider imperfectly discriminating, common-value, all-pay auctions (or contests) in which some players know the value of the prize, others do not. We show that if the prize is always of positive value, then all players are active in equilibrium. If the prize is of value zero with positive probability, then there is some threshold number of informed players such that if there are less, all uninformed players are active, and otherwise all uninformed players are inactive.