The set of pure-strategy equilibria in max–min two-group contests with a private good prize

IF 0.7 4区经济学 Q4 ECONOMICS

Mathematical Social Sciences Pub Date : 2025-10-15 DOI:10.1016/j.mathsocsci.2025.102471

Mario Gilli, Andrea Sorrentino

引用次数: 0

Abstract

We characterize the set of pure-strategy equilibria in a deterministic group contest with the weakest-link impact function and a private good prize, complementing the results obtained by Lee (2012) and Chowdhury et al. (2016). We consider a two-stage two-group model, where in the first stage the agents simultaneously choose the sharing rule, while in the second stage they choose efforts. We find that there are continua of subgame perfect equilibria, which means that in equilibrium players’ behavior is indeterminate. By additional restrictions on the effort levels of each class of effort equilibria, we are able to computationally characterize the set of subgame perfect Nash equilibria in pure strategies.

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具有私有商品奖励的最大最小两组竞争的纯策略均衡集

我们用最弱链接影响函数和私人商品奖励来描述确定性群体竞争中的纯策略均衡集，补充了Lee（2012）和Chowdhury等人（2016）的结果。我们考虑一个两阶段的两群体模型，在第一阶段，agent同时选择共享规则，在第二阶段，agent同时选择努力。我们发现了子博弈完全均衡存在连续，这意味着在均衡状态下参与者的行为是不确定的。通过对每一类努力均衡的努力水平的附加限制，我们能够计算表征纯策略下的子博弈完美纳什均衡集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Social Sciences 数学-数学跨学科应用

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

59 days

期刊介绍： The international, interdisciplinary journal Mathematical Social Sciences publishes original research articles, survey papers, short notes and book reviews. The journal emphasizes the unity of mathematical modelling in economics, psychology, political sciences, sociology and other social sciences. Topics of particular interest include the fundamental aspects of choice, information, and preferences (decision science) and of interaction (game theory and economic theory), the measurement of utility, welfare and inequality, the formal theories of justice and implementation, voting rules, cooperative games, fair division, cost allocation, bargaining, matching, social networks, and evolutionary and other dynamics models. Papers published by the journal are mathematically rigorous but no bounds, from above or from below, limits their technical level. All mathematical techniques may be used. The articles should be self-contained and readable by social scientists trained in mathematics.