摘要翻译：
我们研究了三agent博弈的动力学和由此产生的分数分布，其中每次比赛后，单个agent获胜并获得一分。单个比赛用三个数字$P$，$T$，$Q$来描述，表示累积得分最高、中或最低的球队获胜的概率。我们研究了在代理和竞争的数量都很大的情况下的全解族，这可以看作是一个流体力学极限。根据参数值$(p，q，t)$，我们发现了六个性质不同的渐近分数分布，并对这些结果提供了定性的理解。我们将我们的分析结果与微观模型的数值模拟进行了检验，发现这些结果非常吻合。三代理博弈可以被看作是一个社会模型，在这个模型中，一个玩家可以根据他/她的累积得分而被青睐或不被青睐。也可以通过一个由两个参与者组成的小型锦标赛来决定三agent博弈的结果，结果表明，所得的可能分数分布是一般三agent博弈所得分数分布的子集。我们讨论了如何在模型中加入一个稳定和民主的递减率，并给出了一个简单的几何结构，允许我们写下相应的$N$-agent博弈的分数演化方程。
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英文标题：
《Dynamics of Three Agent Games》
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作者：
Tonguc Rador and Muhittin Mungan
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games.
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PDF链接：
https://arxiv.org/pdf/706.1645