On the Power of Dominated Players in Team Competitions

2007

We analyse incentive problems in team and partnership structures where the only available information to condition a contract on is some noisy ranking of the partners' efforts. This enables us to ensure both first best efficient effort levels for all partners and the redistribution of output only among partners. Our efficiency result is obtained for a wide range of cost and production functions. (JEL C7, D7, D8, L2.

International Journal of Game Theory, 2008

This paper continues research initiated in Wooders, Cartwright and Selten (2001). We are indebted to Bhaskar Dutta and Ehud Kalai for stimulating and helpful comments.

Przegląd Statystyczny, 2019

The paper examines an infinitely repeated 3-player extension of the Prisoner’s Dilemma game. We consider a 3-player game in the normal form with incomplete information, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage, players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players’ payoffs do not exceed the nondeviating player payoff more than by a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired b...

Economic Theory, 2015

The Folk Theorem for infinitely repeated games with imperfect public monitoring implies that for a general class of games, nearly efficient payoffs can be supported in perfect public equilibrium (PPE) provided the monitoring structure is sufficiently rich and players are arbitrarily patient. This paper shows that for stage games in which actions of players interfere strongly with each other, exactly efficient payoffs can be supported in PPE even when the monitoring structure is not rich and players are not arbitrarily patient. The class of stage games we study abstracts many environments including resource sharing. Keywords repeated games • imperfect public monitoring • perfect public equilibrium • efficient outcomes • repeated resource allocation • repeated partnership • repeated contest Mathematics Subject Classification (2000) JEL C72 • C73 • D02 This research was supported by National Science Foundation (NSF) Grants No. 0830556, (van der Schaar, Xiao) and 0617027 (Zame) and by the Einaudi Institute for Economics and Finance (Zame). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of any funding agency.

Operations Research and Decisions , 2015

We study the process, called the IEDI process, of iterated elimination of (strictly) dominated strategies and inessential players for finite strategic games. Such elimination may reduce the size of a game considerably, for example, from a game with a large number of players to one with a few players. We extend two existing results to our context; the preservation of Nash equilibria and order-independence. These give a way of computing the set of Nash equilibria for an initial situation from the endgame. Then, we reverse our perspective to ask the question of what initial situations end up at a given final game. We assess what situations underlie an endgame. We give conditions for the pattern of player sets required for a resulting sequence of the IEDI process to an endgame. We illustrate our development with a few extensions of the Battle of the Sexes.

CEPR Discussion Paper Series, 2017

This paper provides new general results for winner-take-all rank-order tournaments with additive and multiplicative noise. We show that the comparative statics of the individual equilibrium effort with respect to the number of players follow the shape of the density the noise distribution. For aggregate effort, a similar relation holds for the failure (hazard) rate of the noise distribution. The equilibrium effort decreases as noise becomes more dispersed, in the sense of the dispersive order or appropriately defined entropy. These results are then extended to the case of a stochastic number of players, and new results on the effects of population uncertainty are obtained. All relevant results for the Tullock contest follow as a special case.

1998

SSRN Electronic Journal

Agents form coalitions with other agents. The coalition that forms with the largest power wins the tournament. A partition of the agents is a no threat equilibrium (NTE) if whenever a group of agents gains by forming their own coalition, there exist another group of agents that gains by forming their own coalition and harms at least one agent who initially deviated from the partition. We characterize the class of preferences over group of agents that guarantees the existence of a NTE partition. This class of preferences includes more limited versions where the CORE, the traditional equilibria, does not exists.

2004

We study the concepts of minimal dominating and maximal irredundant sets of vertices in tournaments.

Social Choice and Welfare, 2010

This article uncovers dynamic properties of the von Neumann–Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of tournament games. The exploration of a specific class of Markov perfect equilibria in these “dynamic tournament games” yields a new solution concept for weak tournaments—the A-stable set. The alternatives in an A-stable set constitute persistent, long-run policy outcomes in the corresponding dynamic tournament games. We find that, in any weak tournament, the class of A-stable sets coincides with that of von Neumann–Morgenstern stable sets.