Terminal Ranking Games

Bayraktar, Erhan; Zhang, Yuchong

doi:10.2139/ssrn.3409540

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…, k are positive and strictly concave; in particular, they are not equal. In the mean field game limit with an infinite number of competing players, the effect of reward inequality and several contest design problems are analyzed in [3] and [2]. Here players exert effort to maximize rewards based on the ranking of their terminal position and completion time of drifted Brownian motions, respectively, but analytical results are not available for the associated finite-player games.…”

Section: Introductionmentioning

confidence: 99%

Reward Design in Risk-Taking Contests

Nutz¹,

Zhang²

2021

Preprint

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Following the risk-taking model of Seel and Strack, n players decide when to stop privately observed Brownian motions with drift and absorption at zero. They are then ranked according to their level of stopping and paid a rank-dependent reward. We study the problem of a principal who aims to induce a desirable equilibrium performance of the players by choosing how much reward is attributed to each rank. Specifically, we determine optimal reward schemes for principals interested in the average performance and the performance at a given rank. While the former can be related to reward inequality in the Lorenz sense, the latter can have a surprising shape.

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Section: Introductionmentioning

confidence: 99%

Reward Design in Risk-Taking Contests

Nutz¹,

Zhang²

2021

Preprint

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Teamwise Mean Field Competitions

Zhang

Zhou

2021

Appl Math Optim

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This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of teamwise competition game, three optimization problems are introduced when the team size is determined by: (i) the team manager; (ii) the central planner; (iii) the team members' voting as partnership. We propose a relative performance criteria for each team member to share the team's reward and formulate some special cases of mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

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Reward Design in Risk-Taking Contests

Nutz

Zhang

2021

SSRN Journal

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Terminal Ranking Games

Cited by 4 publications

References 25 publications

Reward Design in Risk-Taking Contests

Reward Design in Risk-Taking Contests

Teamwise Mean Field Competitions

Reward Design in Risk-Taking Contests

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