Learning to Cooperate in Repeated Games

学习在重复博弈中合作

• 批准号: 9602082
• 负责人: In-Koo Cho
• 金额: $ 18.2万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1998-11-09
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9602082&HistoricalAwards=false
• 关键词: Learning; Cooperate; Repeated; Games

A primary reason for studying repeated games is to understand how selfish players can coordinate their actions to achieve improvements without a collusive agreement. Unfortunately existing game-theoretic models admit so many outcomes that it is impossible to predict whether coordination will emerge. Also analysis postulates a rational agent who has unbounded computational capability and perfect foresight. These assumptions are critical for equilibrium models but also rather unrealistic. This project explores alternative models in which perfectly rational agents are replaced by `boundedly rational` agents who have only limited computational capabilities, and who cannot perfectly foresee the strategy of other players, which they have to learn from the past experiences. This approach is shown to capture learning dynamics and to permit applications to a wide class of repeated and dynamic games which have a `big` player who can influence the long run outcome of the model. Applications include international debt and optimal growth with moral hazard. More specifically, the project examines two person repeated games where each player learns the opponent's strategy according to the gradient method by assuming that the opponent is playing according to a linear strategy. In addition, each player artificially adds random noise that disappears slowly in order to experiment against the opponent's strategy. No restrictions are imposed on feasible strategies, but the forecast of each player must be a linear function of past observations. The reason for selecting this particular class of strategies is that these strategies are simple enough to be parameterized easily. Then, each player can learn the opponent's strategy using least squares estimation. The agent's preference is also modified slightly so that he is selecting a best response while minimizing the complexity of the decision making process. then, a recursive least squares learning model is obtained, where each player updates his belief as well as his operated game strategy as the game proceeds. The learning dynamics converges with probability 1 and in the limit, both players have an identical estimator. Consequently the behavior of the two players is highly correlated, and the limit frequency of outcomes can be sustained by some Nash equilibrium in linear strategies. In the prisoner's dilemma game, for example, the limit frequency of outcomes must be a strict convex combination of cooperation and defection, which implies that the players must learn to cooperative with positive probability.

研究重复游戏的一个主要原因是理解自私的玩家如何在没有串通协议的情况下协调他们的行动以实现改进。不幸的是，现有的博弈论模型承认了太多的结果，以至于不可能预测是否会出现协调。此外，分析还假定理性代理人具有无限的计算能力和完美的远见。这些假设对均衡模型至关重要，但也相当不切实际。这个项目探索了另一种模型，在这种模型中，完全理性的代理被“有限理性”的代理所取代，这些代理只有有限的计算能力，并且无法完美地预见其他参与者的策略，他们必须从过去的经验中学习。这种方法被证明可以捕捉学习动态，并允许应用到广泛的重复和动态游戏中，这些游戏有一个可以影响模型长期结果的“大”玩家。适用范围包括国际债务和带有道德风险的最优增长。更具体地说，该项目考察了两个人重复的游戏，其中每个玩家通过假设对手是按照线性策略玩的，根据梯度法学习对手的策略。此外，每个玩家都会人为地添加随机噪音，这些噪音会慢慢消失，以对抗对手的策略。对可行的策略没有任何限制，但每个玩家的预测必须是过去观察到的线性函数。之所以选择这类特定的策略，是因为这些策略足够简单，易于参数化。然后，每个玩家可以使用最小二乘估计来学习对手的策略。代理的偏好也会稍作修改，以便他在选择最佳响应的同时将决策过程的复杂性降至最低。然后，得到递归最小二乘学习模型，在该模型中，随着游戏的进行，每个玩家更新他的信念以及他操作的游戏策略。学习动力学以概率1收敛，并且在极限情况下，两个参与者具有相同的估计器。因此，两个参与者的行为高度相关，结果的有限频率可以通过线性策略中的某些纳什均衡来维持。例如，在囚徒困境博弈中，结果的极限频率必须是合作和叛逃的严格凸组合，这意味着参与者必须学会以正概率合作。