Mixed equilibria in Tullock contests

Ewerhart, Christian

doi:10.1007/s00199-014-0835-x

Cited by 56 publications

(21 citation statements)

References 23 publications

(16 reference statements)

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“…In particular, the denominator of the ratio in equation 22does not vanish on S, which proves the claim. Hence, we may argue as in Ewerhart (2015a) to see that…”

Section: Appendix Proofsmentioning

confidence: 98%

The n-Player Hirshleifer Contest

Ewerhart

Sun

2020

SSRN Journal

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We characterize the equilibrium set of the n-player Hirshleifer contest with homogeneous valuations. A symmetric equilibrium always exists. It necessarily corresponds to multilateral peace for su¢ cient noise and uses …nitesupport randomized strategies otherwise. Asymmetric equilibria are feasible for n 3 contestants only, and only for su¢ ciently small noise. In pure strategies, any asymmetric equilibrium corresponds to one-sided dominance, but there is also a variety of payo¤-inequivalent mixed-strategy equilibria for small noise. For arbitrarily small noise, at least two contestants engage in cut-throat competition, while any others become ultimately inactive. Of some conceptual interest is the observation that, for n su¢ ciently large, the unique equilibrium is multilateral peace.

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“…In particular, the denominator of the ratio in equation 22does not vanish on S, which proves the claim. Hence, we may argue as in Ewerhart (2015a) to see that…”

Section: Appendix Proofsmentioning

confidence: 98%

The n-Player Hirshleifer Contest

Ewerhart

Sun

2020

SSRN Journal

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“…First, when impact functions are convex, a pure‐strategy equilibrium does not often exist. Although mixed‐strategy equilibria exist, they generally are not unique and their properties remain elusive in the literature (e.g., Ewerhart 2015, 2017). Second, the condition alludes to the usual production technology with nonincreasing marginal output.…”

Section: Setup and Preliminariesmentioning

confidence: 99%

On the optimal design of biased contests

2020

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This paper explores the optimal design of biased contests. A designer imposes an identity‐dependent treatment on contestants that varies the balance of the playing field. A generalized lottery contest typically yields no closed‐form equilibrium solutions, which nullifies the usual implicit programming approach to optimal contest design and limits analysis to restricted settings. We propose an alternative approach that allows us to circumvent this difficulty and characterize the optimum in a general setting under a wide array of objective functions without solving for the equilibrium explicitly. Our technique applies to a broad array of contest design problems, and the analysis it enables generates novel insights into incentive provisions in contests and their optimal design. For instance, we demonstrate that the conventional wisdom of leveling the playing field, which is obtained in limited settings in previous studies, does not generally hold.

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“…14 The properties of the symmetric Nash equilibrium of the Tullock contest are fairly well-understood. See, e.g., Pérez-Castrillo and Verdier (1992), Baye et al (1994), and Ewerhart (2014). g(X i ) = X R i for R > 0, and by g(X i ) = 1 for R = 0.…”

Section: The Tullock Contestmentioning

confidence: 99%

Contest Success Functions: The Common-Pool Perspective

Ewerhart

2015

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. The axiomatic route to the foundation of contest success functions (CSF) has proved to be both useful and proli…c. The standard approach in the literature is based on the decision-theoretic notion that choice probabilities should be independent of irrelevant alternatives (Skaperdas, Economic Theory 1996). The present paper develops an alternative approach that suggests itself once the contest is re-interpreted as a common-pool resource problem. Proceeding along these lines, new axiomatizations are obtained for a variety of popular classes of CSFs, including the logit, Tullock, and di¤erence-form CSFs. The axiomatizations provided are particularly parsimonious in the important special case of two contestants. Terms of use: Documents in EconStor may

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Mixed equilibria in Tullock contests

Cited by 56 publications

References 23 publications

The n-Player Hirshleifer Contest

The n-Player Hirshleifer Contest

On the optimal design of biased contests

Contest Success Functions: The Common-Pool Perspective

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