Institute for Theoretical Physics and Center for Complex Systems Studies, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands.
Sci Rep. 2019 Feb 20;9(1):2352. doi: 10.1038/s41598-018-36562-2.
In nature and society, problems that arise when different interests are difficult to reconcile are modeled in game theory. While most applications assume that the players make decisions based only on the payoff matrix, a more detailed modeling is necessary if we also want to consider the influence of correlations on the decisions of the players. We therefore extend here the existing framework of correlated strategies by giving the players the freedom to respond to the instructions of the correlation device by probabilistically following or not following its suggestions. This creates a new type of games that we call "correlated games". The associated response strategies that can solve these games turn out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and pure or mixed-strategy solutions and also gives better payoffs in certain cases. We here determine these Nash equilibria for all possible correlated Snowdrift games and we find these solutions to be describable by Ising models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.
在自然界和社会中，博弈论用于模拟当不同利益难以协调时出现的问题。虽然大多数应用程序都假设玩家仅根据收益矩阵做出决策，但如果我们还想考虑相关性对玩家决策的影响，就需要更详细的建模。因此，我们通过赋予玩家根据相关设备的指令自由决定是否遵循或不遵循其建议的方式，扩展了现有相关策略的框架。这创建了一种我们称之为“相关博弈”的新类型游戏。可以解决这些游戏的相关响应策略结果具有丰富的纳什均衡结构，超越了相关均衡和纯策略或混合策略解决方案，并且在某些情况下还能获得更好的收益。我们在这里确定了所有可能的相关雪堆博弈的纳什均衡，并发现这些解决方案可以通过热平衡的伊辛模型来描述。我们相信，我们的方法为研究游戏中的相关性铺平了道路，揭示了有趣的潜在相互作用机制的存在，同时又不影响玩家的独立性。
