Group contest success functions

This paper extends the axiomatic characterization of contest success functions of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998) to contests between groups. Comments by Dan Kovenock significantly improved the paper and are gratefully acknowledged. I would also like to thank Pavlo Blavatskyy, Aron Kiss, Kai Konrad, Florian Morath, Dana Sisak, participants of the SFB/TR 15 meeting in Gummersbach 2004, the 2004 meeting of the Verein für Socialpolitik in Dresden, and two anonymous referees. Any errors are mine. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged.     

Optimal contest design: volume and timing of rent seeking in contests

This paper undertakes a comparative analysis of rent-seeking contests in terms of the amount and the timing of effort they elicit from the participants. The optimal contest structure—the one that maximizes the discounted sum of efforts—is found to hinge on the degree of impatience of the contest organizers, the more patient of whom prefer longer contests consisting of pairwise matches among the contestants. Heterogeneity of the contestants' quality also turns out to play an important role in the comparison.     

Foundations for contest success functions

In the literature, the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions (CSFs). In the first, we analyze the implications of contestants’ incomplete information concerning the ‘type’ of the contest administrator. While in the case of two contestants this approach can rationalize prominent CSFs, we show that it runs into difficulties when there are more agents. Our second approach interprets CSFs as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular CSFs and guidelines for the definition of new ones.

“The strategic approach also seeks to combine axiomatic cooperative solutions and non-cooperative solutions. Roger Myerson recently named this task the ‘Nash program’.”(Rubinstein 1985, p. 1151)

     

Total effort, competitive balance and the optimal contest success function

This paper shows that, in the constrained case, the value weighted contest success function (CSF) maximizes not only total effort, but every objective function which is increasing in total effort and competitive balance. In the unconstrained case, a first price all-pay auction with a reserve price is optimal only if the impact of competitive balance on the objective is small. Otherwise, a modified value weighted CSF is optimal.     

Bidding in hierarchies

This paper reconsiders the comparison between hierarchical contests and single-stage contests. A condition is given that characterizes whether and when the aggregate equilibrium payoff of contestants is higher in the single-stage contest, and when the single-stage contest is more likely to award the prize to the contestant who values it most highly. The outcome depends on inter- and intra-group heterogeneity, and is not driven by free-rider incentives.     

Difference-form contest success functions and effort levels in contests

We examine players' equilibrium effort levels in a contest with difference-form contest success functions in which two players compete with each other to win a prize. We show the following. At the pure-strategy Nash equilibrium of a simultaneous-move game, and in the subgame-perfect equilibrium of a sequential-move game, only one of the players expends effort or neither player expends effort. If one player's composite strength is far greater than the other player's, only the player with greater composite strength expends effort whether they move simultaneously or sequentially. If the players' valuations for the prize and their marginal probabilities of winning at (0, 0) are sufficiently small, neither player expends effort whether they move simultaneously or sequentially.     

Endogenous contest success functions: a mechanism design approach

We describe optimal contest success functions (CSF) which maximize expected revenues of an administrator who allocates under informational asymmetry a source of rent among competing bidders. It is shown that in the case of independent private values rent administrator’s optimal mechanism can always be implemented via some CSFs as posited by Tullock. Optimal endogenous CSFs have properties which are often assumed a priori as plausible features of rent-seeking contests; the paper therefore validates such assumptions for a broad class of contests. Various extensions or optimal CSFs are analyzed.     

Designing an optimal contest

The paper brings a mechanism design perspective to the study of contests. We consider the problem of selecting a contest success function when the contest designer may also value the prize. We show that any equilibrium outcome that can be achieved by a concave increasing contest success function can be replicated by a linear contest success function. An expected utility maximizing designer should employ a linear homogeneous contest success function. We explicitly derive the optimal contest for a risk-neutral designer and present comparative statics results. Tullock's contest is optimal only when the designer's valuation for the prize is low.     

An investment contest to influence environmental policy

In an investment contest for environmental policy, polluters and victims of pollution invest in an increase of their marginal benefits of pollution and environmental quality, respectively. These investments influence time-consistent environmental policy. Investments will exceed their optimal level. The more victims there are, the lower aggregate investment, the lower payoffs for the victims and the higher payoffs for the polluters. The more polluters there are, the higher aggregate investment and the lower payoffs for polluters and victims. Asymmetries between polluter and victim result in less overinvestment and bias environmental policy in favour of the less productive side.     

Cooperation by way of support in a rent seeking contest for a public good

This paper analyzes the efforts made to influence a decision that can have two outcomes. First, the agents on the same side designate an agent to play the contest for them. The inactive agents can then decide to support this active agent, i.e. pay a percentage of his effort. It is optimal to designate either the agent with the lowest stake (who will receive support from everyone else) or the agent with the highest stake (who will not receive support) as the active agent. We find that the side with the higher aggregate stake may have the lower success probability.     

The value of rents and the likelihood of conflicts

This paper extends the prey–predator model of Grossman and Kim (J Political Econ 103:1275–1288, 1995) to analyze the relation between the value of a contested rent and the emergence of conflict. We show that an increase in the value of the rent makes a conflict equilibrium more likely. We also analyze the case where the valuation of the rent is different for the two players. We find, for example, that a conflict equilibrium may occur even though the predator has an important disadvantage in warfare. That is when his valuation of the rent is sufficiently high compared to that of the prey.

要素市场扭曲对企业家寻租及创新的影响

Baumol认为企业家行为模式受到所在制度环境的影响,良好的制度环境会促进企业家从事增加社会福利的生产性活动,比如创新;而制度环境不佳会导致企业家从事攫取社会利益的非生产性活动,比如寻租。Baumol的企业家才能配置理论在中国具体情境中,是否有其适用性？以我国2009-2014年省级层面面板数据,利用各省份人均土地出让面积作为地区要素市场扭曲的工具变量,在有效控制内生性可能导致的模型估计偏误后,实证考察了要素市场扭曲对企业家寻租活动的作用效应。研究发现,转轨时期我国地区要素市场扭曲程度越深,企业家寻租活动就越多。进一步通过系数检验以及Bootstrap方法考察企业家寻租活动在地区要素市场扭曲和企业创新强度之间的中介效应,证实了“要素市场扭曲→企业家寻租活动增多→企业创新强度减弱”传导机制的存在,可为深化中国要素市场机制改革提供理论和实证支持。     

Is Talk Cheap?

For the steel import quota bill of 1999, each word in the Congressional Record costs $39 in campaign contributions from the steel industry. Consequently, our answer is "Yes, talk is cheap!"     

On the escalation and de-escalation of conflict

We introduce three extensions of the Hirshleifer–Skaperdas conflict game to study experimentally the effects of post-conflict behavior and repeated interaction on the allocation of effort between production and appropriation. Without repeated interaction, destruction of resources by defeated players can lead to lower appropriative efforts and higher overall efficiency. With repeated interaction, appropriative efforts are considerably reduced because some groups manage to avoid fighting altogether, often after substantial initial conflict. To attain peace, players must first engage in costly signaling by making themselves vulnerable and by forgoing the possibility to appropriate the resources of defeated opponents.     

The strategic equivalence of rent-seeking, innovation, and patent-race games

We establish the strategic equivalence of a variety of rent-seeking contests, innovation tournaments, and patent-race games. The results allow us to disentangle negative and positive externalities, and to apply theorems and results intended for rent-seeking games to other games, and vice versa. We conclude with several examples that highlight the practical utility of our results.     

Contest success functions

Summary Tournaments, conflict, and rent-seeking have been modelled as contests in which participants exert effort to increase their probability of winning a prize. A Contest Success Function (CSF) provides each player's probability of winning as a function of all players' efforts. In this paper the additive CSF employed in most contests is axiomatized, with an independence from irrelevant alternatives property as the key axiom. Two frequently used functional forms are also axiomatized: one in which winning probabilities depend on the ratio of players' efforts and the other in which winning probabilities depend on the difference in efforts.I am grateful to three anonymous referees, Jack Hirshleifer, Guillermo Owen, and especially Duncan Luce for their helpful comments, and to the UC Irvine Academic Senate and the NSF for financial support.     

A KKM-result and an application for binary and non-binary choice functions

Summary. By generalizing the classical Knaster-Kuratowski-Mazurkiewicz Theorem, we obtain a result that provides sufficient conditions to ensure the non-emptiness of several kinds of choice functions. This result generalizes well-known results on the existence of maximal elements for binary relations (Bergstrom [4]; Walker [16]; Tian [15]), on the non-emptiness of non-binary choice functions (Nehring [12]; Llinares and Sánchez [9]) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-finite sets. Received: December 29, 1999; revised version: October 18, 2001     

Contest success functions: an extension

Summary. This note extends the axiomatic characterization of the power success function in fair contests by Skaperdas (1996) to an unfair contest. We show that the results previously obtained are straightforward to generalize; the success function is uniquely characterized by Luces Choice Axiom (implying independence of irrelevant alternatives) and homogeneity of degree zero.Received: July 1, 1996; revised version: October 30, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Equilibria in rent-seeking contests with homogeneous success functions

Summary. We characterize pure-strategy Nash equilibria for symmetric rent-seeking contests in which the contest success function is homogeneous of degree zero. The equilibrium strategies have a simple form. We give sufficient conditions for existence of an equilibrium.Received: 11 February 2003, Revised: 27 August 2004, JEL Classification Numbers: D72. Correspondence to: Andrew J. YatesWe thank Douglas Nelson, Jac Heckelman, and two anonymous referees for helpful comments.     

Whether to attack a terrorist's resource stock today or tomorrow

A terrorist defends an asset which grows from the first to the second period and is attacked. With large asset growth, the terrorist's first period outcome is low caused by a large attack. With no expenditure constraint, the terrorist's total outcome is positive. With equal attack and defense inefficiencies, when the terrorist as defender requires his first period outcome to be positive, the attacker eliminates the asset in the first period when asset growth multiplied with the square roots of the terrorist's and attacker's discount parameters exceed . This gives maximum conflict in the first period. Growth and the two discount parameters are strategic complements. The range for the attack inefficiency divided by defense inefficiency, which causes negative first period outcome for the terrorist, increases with asset growth. The attacker refrains from asset elimination in the first period due to strength (weakness) if the ratio is below (above) the range.