英文标题：
《Best reply structure and equilibrium convergence in generic games》
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作者：
Marco Pangallo, Torsten Heinrich, J Doyne Farmer
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最新提交年份：
2018
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英文摘要：
  Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in terms of best reply dynamics, in which each player myopically uses the best response to her opponent\'s last move. Existing research shows that convergence can be problematic when there are best reply cycles. Here we calculate how typical this is by studying the space of all possible two-player normal form games and counting the frequency of best reply cycles. The two key parameters are the number of moves, which defines how complicated the game is, and the anti-correlation of the payoffs, which determines how competitive it is. We find that as games get more complicated and more competitive, best reply cycles become dominant. The existence of best reply cycles predicts non-convergence of six different learning algorithms that have support from human experiments. Our results imply that for complicated and competitive games equilibrium is typically an unrealistic assumption. Alternatively, if for some reason \"real\" games are special and do not possess cycles, we raise the interesting question of why this should be so.
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中文摘要：
博弈论在生物学和社会科学中被广泛用作战略互动的行为模型。通常的做法是假设参与者迅速收敛到一个均衡，例如纳什均衡。这可以从最佳回应动力学的角度来研究，在最佳回应动力学中，每个玩家都会对对手的最后一步做出最佳反应。现有研究表明，当存在最佳回复周期时，收敛可能会出现问题。在这里，我们通过研究所有可能的两人正常形式博弈的空间并计算最佳回复周期的频率来计算这是多么典型。这两个关键参数是移动次数，它定义了游戏的复杂程度，以及收益的反相关性，它决定了游戏的竞争程度。我们发现，随着游戏变得越来越复杂，竞争也越来越激烈，最佳回复周期占据主导地位。最佳回复周期的存在预示着六种不同学习算法的不收敛性，这些算法得到了人类实验的支持。我们的结果表明，对于复杂的竞争性博弈，均衡通常是不现实的假设。或者，如果出于某种原因，“真实”游戏是特殊的，并且没有循环，我们会提出一个有趣的问题，即为什么会这样。
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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：Adaptation and Self-Organizing Systems        自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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