Games between Diversely Sophisticated Players

传统的博弈均衡分析假设所有玩家都是理性的决策者，对博弈及其对手的均衡行为有充分的了解。然而，让战略互动变得有趣的部分原因是玩家理解游戏规则的能力有限，通常是不对称的。传统博弈论对这一重要维度保持沉默。在过去的二十年里，我们看到了一些对有限战略复杂性建模的尝试，以脱离传统纳什均衡的新颖“均衡概念”的形式，捕捉诸如一次性互动中有限深度推理的现象，或者从游戏均衡分布中提取的小的、选择性的或粗粒度的样本进行天真的外推。在这种情况下，游戏中的“有限理性预期”被不同的均衡概念所捕获，这是不令人满意的。首先，它将游戏中的有限理性模型变成了一系列看似特别的工具，从而抑制了经济应用。第二，这些方面不应被视为相互排斥的。它们通常是玩家在学习平衡时收到的反馈的产物，就像传统的信息约束不是内在的个人特征，而是在不同的情况下有所不同。在这个项目中，我的目标是从Harsanyi（1967-8）的“不完全信息博弈”教科书理论中汲取灵感，制定一个通用的博弈论模型，可以适应多种形式的有限战略复杂性。我计划用一些经济应用来证明这个模型的有用性。如果获得成功，该项目将推动具有不同战略复杂性的玩家之间的战略互动的理论和应用工作。

Conventional equilibrium analysis of games presumes that all players are rational decision makers with full understanding of the game and the equilibrium behaviour of their opponents. Yet part of what makes strategic interactions interesting is players' limited, often asymmetric ability to understand the game's regularities. Conventional game theory is silent over this important dimension. The last twenty years saw a few attempts to model limited strategic sophistication, in the form of novel "equilibrium concepts" that depart from conventional Nash equilibrium, capturing phenomena such as limited depth of reasoning in one-shot interactions, or naive extrapolation from small, selective or coarse-grained samples drawn from the equilibrium distribution of play. This state of affairs, in which aspects of "boundedly rational expectations" in games are captured by distinct equilibrium concepts, is unsatisfactory. First, it turns modeling bounded rationality in games into a collection of seemingly ad-hoc tools, thus inhibiting economic applications. Second, these aspects should not be viewed as mutually exclusive. They are often artifacts of the feedback players receive when learning the equilibrium, just as conventional informational constraints are not intrinsic personal characteristics but vary from one situation to another. My objective in this project is to formulate a general game-theoretic model that can accommodate many forms of limited strategic sophistication, drawing inspiration from the textbook theory of "games with incomplete information" due to Harsanyi (1967-8). I plan to demonstrate the usefulness of this model with a number of economic applications. If successful, the project can give a major boost to theoretical and applied work on strategic interactions between players with diverse strategic sophistication.