Revision game is a very new model formulating the real-time situation where players dynamically prepare and revise their actions in advance before a deadline when payoffs are realized. It is at the cutting edge of dynamic game theory and can be applied in many real-world scenarios, such as eBay auction, stock market, election, online games, crowdsourcing, etc. In this work, we novelly identify a class of strategies for revision games which are called Limited Retaliation strategies. An limited retaliation strategy stipulates that, (1) players first follow a recommended cooperative plan; (2) if anyone deviates from the plan, the limited retaliation player retaliates by using the defection action for a limited duration; (3) after the retaliation, the limited retaliation player returns to the cooperative plan. A limited retaliation strategy has three key features. It is cooperative, sustaining a high level of social welfare. It is vengeful, deterring the opponent from betrayal by threatening with a future retaliation. It is yet forgiving, since it resumes cooperation after a proper retaliation. The cooperativeness and vengefulness make it constitute cooperative subgame perfect equilibrium, while the forgiveness makes it tolerate occasional mistakes. limited retaliation strategies show significant advantages over Grim Trigger, which is currently the only known strategy for revision games. Besides its contribution as a new robust and welfare-optimizing equilibrium strategy, our results about limited retaliation strategy can also be used to explain how easy cooperation can happen, and why forgiveness emerges in real-world multi-agent interactions. In addition, limited retaliation strategies are simple to derive and computationally efficient, making it easy for algorithm design and implementation in many multi-agent systems.
翻译:修订游戏是一个非常新的模式,它展示了实时局面,让玩家在付款实现的最后期限到来之前积极准备和修改其行动;它处于动态游戏理论的前沿,可以应用于许多现实世界情景,例如eBay拍卖、股票市场、选举、在线游戏、众包等。在这项工作中,我们新确定了一套修订游戏的战略,称为有限报复战略。一个有限的报复战略规定,(1) 玩家首先遵循建议的合作计划;(2) 如果任何人偏离计划,有限的报复玩家通过使用有限期限的脱节行动进行报复;(3) 在报复后,有限的报复玩家返回合作计划。一个有限的报复策略有三个关键特征:合作,维持高水平的社会福利。这是有求必应的,通过威胁未来报复来阻止对手背叛。由于在适当报复之后恢复了合作。许多合作和报复策略的增加使得它构成合作的次平衡,而宽恕行动则使得它能够容忍偶然的错误设计。有限的报复策略显示了显著的优势,它用来解释它是如何稳健的报复战略。