The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also provide an experimental analysis of a special case which captures the strategic situation of a two-st...

In order to calculate the worth of a coalition of players, the coalition needs to predict the actions of outsiders. We propose that, for a given solution concept, such predictions should be made by applying the solution concept to the “reduced society” consisting of the non-members. We illustrate by computing the r-core for the case of Bertrand competition with differentiated commodities.  200...

We provide a direct geometric bijection for the number of lattice paths that never go below the line y = kx for a positive integer k. This solution to the Generalized Ballot Problem is in the spirit of the reflection principle for the Ballot Problem (the case k = 1), but it uses rotation instead of reflection. It also gives bijective proofs of the refinements of the Generalized Ballot Problem w...

This paper analyzes a simple, repeated game of simultaneous entry and pricing. We report a surprising property of the symmetric equilibrium solution: If the number of potential competitors is increased above two, the market breaks down with higher probability, and the competitive outcome becomes less likely. More potential competition lowers welfare | another Bertrand paradox. The model can als...

We consider the issue of firstversus second-mover advantage in differentiated-product Bertrand duopoly with general demand and asymmetric linear costs. We generalize existing results for all possible combinations where prices are either strategic substitutes and/or complements, dispensing with common extraneous and restrictive assumptions. We show that a firm with a sufficiently large cost lead...

We show that in a homogeneous-good duopoly market with quality uncertainty and constant unit costs, the Bertrand paradox (i.e., marginal cost pricing) can be avoided.

* We are grateful for comments from anonymous referees and an associate editor and from seminar participants at the 1998 Winter Meetings. This paper is a substantially revised version of a chapter of Wilson's 1997 University of Arizona Ph.D. thesis. Wilson acknowledges support from a National Science Foundation dissertation grant. Reynolds did much of his work while visiting CERGE at Charles Un...

We prove existence of mixed strategy equilibria for a class of discontinuous two-player games with non-compact strategy sets. As a corollary of our main results, we obtain a continuum of mixed strategy equilibria for the firstand second-price two-bidder auctions with toeholds. We also find Klemperer’s (2000) result about the existence of mixed strategy equilibria in the classical Bertrand duopo...

This paper extends the Bertrand–Edgeworth price-setting game with finitely many firms to a game with infinitely many firms. Taking a market with one significant firm and a nonatomic fringe, we present a microfoundation of dominant-firm price leadership.  2000 Elsevier Science S.A. All rights reserved.