LEADERSHIP BY EXAMPLE IN THE WEAK‐LINK GAME

We investigate the effects of leadership in a four‐player weak‐link game. A weak‐link game is a coordination game with multiple Pareto‐ranked Nash equilibria. Because the more efficient equilibria involve a degree of strategic uncertainty groups typically find it difficult to coordinate on more efficient equilibria. We wanted to see whether leadership by example, in the form of one player acting publicly before the rest of the group, could help groups do better. Our results suggest that leadership can increase efficiency but is far from being a guarantee of success. Specifically, in a significant number of groups we observed successful leadership and increased efficiency, but in most groups efficiency was low despite the efforts of leaders. We did not find any difference between voluntary leaders and leaders that are randomly assigned. (JEL C72, H41)     

NETWORK STRUCTURE IN A LINK FORMATION GAME: AN EXPERIMENTAL STUDY

In this article, we use an experiment to evaluate the performance of alternative refinements in a Myersonian link formation game with a supermodular payoff function. Our results show that a non‐cooperative refinement, the global games (GG) approach, outperforms alternative cooperative refinements (strong Nash equilibrium, coalition‐proof Nash equilibrium, and pairwise stable Nash equilibrium) in explaining the observed experimental behavior in the static game of complete information with three players. The results are robust to some comparative statics and the GG approach shows a high predictive power under incomplete information. However, under repeated interaction or with a greater number of players, the GG approach loses predictive power, but so do the cooperative refinements. The results illustrate the importance of coordination failure in practice and the need to design mechanisms to reduce this effect in practical decision‐making problems. (JEL C70, C92, D20, D44, D82)     

Two-Player Asymmetric Contests with Ratio-Form Contest Success Functions

I examine players' equilibrium effort levels in two-player asymmetric contests with ratio-form contest success functions. I first characterize the Nash equilibrium of the simultaneous-move game. I show that the equilibrium effort ratio is equal to the valuation ratio, and that the prize dissipation ratios for the players are the same. I also show that the prize dissipation ratio for each player is less than or equal to the minimum of the players' probabilities of winning at the Nash equilibrium and thus never exceeds a half. Then I examine how the equilibrium effort ratio, the prize dissipation ratios, and the players' equilibrium effort levels respond when the players' valuations for the prize or their abilities change.     

THREE‐PLAYER TRUST GAME WITH INSIDER COMMUNICATION

We examine behavior in a three‐player trust game in which the first player may invest in the second and the second may invest in the third. Any amount sent from one player to the next is tripled. The third player decides the final allocation among three players. The baseline treatment with no communication shows that the first and second players send significant amounts and the third player reciprocates. Allowing insider communication between the second and the third players increases cooperation between these two. Interestingly, there is an external effect of insider communication: the first player who is outside communication sends 54% more and receives 289% more than in the baseline treatment. As a result, insider communication increases efficiency from 44% to 68%. (JEL C72, C91, D72)     

INFORMATION AND ENDOGENOUS DELEGATION IN A RENT‐SEEKING CONTEST

We offer a new explanation for the occurrence of delegation in rent‐seeking contests. We consider a two‐player contest for a prize of common value. The players only know that the prize is high or low, with given probabilities. Each player can hire a delegate to act on his behalf. After a delegate is hired, she privately observes the true value of the prize. We derive the conditions under which, respectively, no player, only one player, or both players delegate in equilibrium. (JEL D7)     

Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium.  It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function. Received: 24 June 1999/Accepted: 20 September 2000     

ENDOGENOUS TIMING IN CONTESTS WITH DELEGATION

We study two‐player contests in which each player hires a delegate, and the delegates decide endogenously when to expend their effort. First, we look closely at the delegates' decisions on when to expend their effort, given contracts between the players and the delegates, and look at the players' decisions on their contracts. Then, we compare the outcomes of the endogenous‐timing framework with those of the simultaneous‐move framework. We show that the higher‐valuation player offers her delegate greater contingent compensation than her opponent, the delegate of the higher‐valuation player chooses his effort level after observing his counterpart's, the equilibrium expected payoff of the delegate of the higher‐valuation player is greater than that of his counterpart, and economic rent for each delegate exists. We show that, in the endogenous‐timing framework, each player offers her delegate better contingent compensation, each delegate's expected payoff is greater, and each player's expected payoff is smaller, as compared with the simultaneous‐move framework. (JEL D72)     

BIDDING FOR TALENT IN SPORT

We present a novel microstructure for the market for athletes. Clubs simultaneously target bids at the players, in (Nash) equilibrium internalizing whether—depending on the other clubs' bids—a player not hired would play for the competition. When talent is either scarce or has low outside options, we support—and generalize to heterogeneous players—the Coasian results of Rottenberg (1956) and Fort and Quirk (1995): talent allocation is efficient and independent of initial “ownership” and revenue sharing arrangements. We also characterize equilibria when talent is abundant (or has a high outside option). The analysis uses a nonspecific club objective with an endogenously derived trade‐off between pecuniary and nonpecuniary benefits.(JEL J4, L1, L2)     

DO RENT‐SEEKING GROUPS ANNOUNCE THEIR SHARING RULES?

We study collective rent seeking between two groups in which each group has the option of releasing or not its sharing‐rule information. First, we show that the case where both groups release their sharing‐rule information never occurs in equilibrium; when the players are unevenly matched, one group releases its sharing‐rule information and the other does not. Then, we select the Pareto‐superior equilibrium when the players are unevenly matched. We show that, in this selected equilibrium, the underdog releases its sharing‐rule information, and the favorite does not; thus, the underdog becomes the leader, and the favorite the follower (JEL D72).     

THE OPTIMAL DEFENSE OF NETWORKS OF TARGETS

This paper examines a game‐theoretic model of attack and defense of multiple networks of targets in which there exist intranetwork strategic complementarities among targets. The defender's objective is to successfully defend all the networks and the attacker's objective is to successfully attack at least one network of targets. Although there are multiple equilibria, we characterize correlation structures in the allocations of forces across targets that arise in all equilibria. For example, in all equilibria the attacker utilizes a stochastic “guerrilla warfare” strategy in which a single random network is attacked. (JEL C72, D74)     

Agenda control in coalition formation

Theoretical models of government formation in political science usually assume that the head of state is non-strategic. In this paper, we analyze the power of an agenda setter who chooses the order in which players are recognized to form coalitions in simple games. We characterize those sets of players which can be imposed in the equilibrium coalition and show that the only decisive structures where the agenda setter can impose the presence of any minimal winning coalition are apex games, where a large player forms a winning coalition with any of the small players. Keywords: Government Formation, Agenda Control, Coalitional Bargaining, Finite Bargaining Rules. Received: 26 January 2001/Accepted: 31 July 2001     

PRIZE SCARCITY AND OVERDISSIPATION IN ALL‐PAY AUCTIONS

We compare bidding behavior in complete information all‐pay auction experiments that vary in the prizes and number of players. We confirm the observation from prior single‐prize experiments that there is overbidding relative to equilibrium predictions. Our primary results are that increasing the number of prizes and players proportionally does not reduce overbidding but increasing the number of prizes with a fixed number of players eliminates overbidding. We conclude that the overbidding phenomenon is related to the scarcity of the prize. We provide new theoretical results on the multi‐prize logit equilibrium, and our experimental results are qualitatively consistent with logit equilibrium predictions. (JEL D72, D91, C91, D44)     

Implementation in perfect equilibria

This paper considers implementation when the feasible outcomes are lotteries over a finite set of alternatives. The following weak condition is sufficient for implementation in trembling hand perfect equilibria (with three or more players): if all but one player agree on which alternative is the best, this alternative is (among those that are) chosen by the social choice rule, and if all but one player agree on which alternative is the worst, this alternative is not chosen. Many interesting social choice rules that are not Nash implementable satisfy this condition. On the other hand, there are social choice rules that are implementable in Nash equilibria but not in perfect equilibria.I am grateful to Luis Corchón, Eric Maskin, William Thomson, seminar participants at Harvard and Rochester, and two anonymous referees for helpful comments and suggestions. This research was supported by grants from the Royal Swedish Academy of Sciences and the Bank of Sweden Tercentenary Foundation.     

EQUILIBRIUM STRUCTURE IN AN ECONOMIC MODEL OF CONFLICT

Four different types of equilibrium are possible within a two-player model of society where only armed self-enforcement of property rights is possible. The main underlying parameters are the total resource endowment and the initial distribution of this endowment between the players. The parameter space is partitioned into regions in which the respective types of equilibrium occur The equilibrium types involve positive arms expenditure by, respectively, neither player the richer player, and both players; the latter case involves a sub-type in which the poorer player's entire endowment is expended on arms. (JEL D30, D72, D74)     

Modeling resource flow asymmetries using condensation networks

This paper examines strict Nash networks in the noncooperative directed flow model of Bala and Goyal (Econometrica 68(5):1181–1230, 2000) with partner heterogeneity (payoff of a player in a link depends on the identity of her link partner). We focus on the asymmetries with regard to the resources obtained by players. Using the notion of condensation networks, we partition the population into groups of players who obtain the same resources and order these groups according to the resources they obtain. We show that the partner heterogeneity assumption impacts the strict Nash networks asymmetries in a different way than Galeotti (Econ Theory 29(1):163–179, 2006) player heterogeneity assumption (the payoff of a player in a link depends on her own identity).     

CONTESTS WITH DRAWS: AXIOMATIZATION AND EQUILIBRIUM

We introduce and axiomatize a class of single‐winner contest success functions that embody the possibility of a draw. We then analyze the game of contest that our success functions induce, having different prizes delivered in the occurrence of a win and a draw. We identify conditions for the existence and uniqueness of a symmetric interior Nash equilibrium and show that equilibrium efforts and equilibrium rent dissipation can be larger than in a Tullock contest (with no possibility of a draw) due to increased competition even if the draw‐prize is null. These results suggest that a contest designer may profit from introducing the possibility of a draw. Finally, we show that this approach naturally extends to multiprize contests with multiple draws across different subsets of the set of players. (JEL C72, D72, D74)     

CHAOTIC DYNAMICS IN CONTESTS

Under a myopic best‐reply dynamic, efforts in repeated contests may exhibit chaotic behavior. This may help explain, for example, why experimental data often show nonconvergence to one‐shot equilibrium efforts. (JEL C61, C72, D72, D74, D83)     

Barreras del Lenguaje: Children's Negotiation of Adult‐Created Exclusionary Practices*

This article explores the effects of language differences on dynamics among youth athletes. Fifteen hours of participant observation were conducted with a youth soccer team, supplemented by five interviews with the coach and with players’ parents. With a cohort consisting of a Spanish‐ and English‐speaking bilingual coach, one fully bilingual player and another partly bilingual player, two Spanish‐only‐speaking players, and four English‐only‐speaking players, there were opportunities for many different types of interactions. This article specifically focuses on how language differences served as a catalyst for the creation of exclusionary practices by the adults surrounding the team. However, these practices did not determine the team's culture; rather, there was both accommodation and resistance on the part of the players to those practices of exclusion that the adults had introduced.     

ON EQUILIBRIUM PLAYER ORDERING IN DYNAMIC TEAM CONTESTS

We study equilibrium player ordering in a dynamic all-pay contest between two teams. The contest lasts two periods, and each team consists of two players who perform in different periods on behalf of their teams. The team with the higher aggregate output wins the prize, which is a public good to its players. Each team has one stronger player and one weaker player, and the two teams can differ in their values of the prize. The teams maximize their winning odds by strategically assigning their players to different periods. We find that when the intrateam heterogeneity in player ability is not excessive, the teams would allocate their stronger players to the late positions as the “anchormen.” When both the intrateam ability gap and interteam heterogeneity in teams' values become excessively large, the team with high value always places its stronger player in the early position, who will place a large bid to preempt late competition. (JEL C7, D7, D8)     

CAPS IN SEQUENTIAL CONTESTS

We study a sequential two‐stage all‐pay auction with two identical prizes. In each stage, the players compete for one prize and each player can win either one or two prizes. The designer may impose a cap on the players' bids in each of the stages. We analyze the equilibrium in this sequential all‐pay auction with bid caps and show that capping the players' bids is profitable for a designer who wishes to maximize the players' expected total bid. (JEL D44, D82, J31, J41)