Research on Generation of Internal Models in Games and Their Dynamics

本研究的目的是提出一个新的模型框架来研究游戏的动态方面，并通过对模型的模拟来讨论游戏参与者的合理性和社会规范。以下是本项目的结果。(A)我们研究了认知参与者玩的迭代囚犯困境博弈，其中每个参与者通过建立对手行为的内部模型来优化自己未来的行动。一种被称为动态识别器(DR)的递归神经网络被用来建立这些内部模型，其优点是对手的图像在动态识别器的上下文空间中被表示为复杂的几何模式。这些几何模式的动态行为将通过改变其维度来给出新的混沌动力学。(B)每个玩家的行为的内部模型是从有限的历史构建的，并且可以从每个历史生成各种可能的模型。也就是说，许多内部型号都具有同等的…在模仿对手的行为时，尿酸含量更高。如果优化的未来行动根据选择的模型而不同，我们在世界线上构建分支来表示几个可能的未来世界。根据博弈情况(例如，收益结构、要考虑的过去序列的长度、选择模型时的不确定性水平等)，世界线的分支的结构(即，可能世界的分支)将有所不同。在某些情况下，世界线被许多可能的世界包围，每个世界都有不同的行为。(C)同样的方法也适用于Rashevskyan游戏，玩家沿着自己的空间轴移动，以获得比其他玩家更有利的位置。虽然这些参与者原则上是以自我为中心的，但研究表明，某些利他行为将作为一个动态吸引子阶段来执行。利他主义的行为不再是仅仅让对手球员的模型作为针锋相对的球员来实现的。相反，玩家必须动态地改变他的模仿模式，以实现相互合作。否则，他们将使用静态的非合作Nash解决方案。较少

The purpose of this research is to propose a new modeling framework to study dynamical aspects of games and to discuss rationality of game players and social norms through the simulations of the model. The followings are the results from this project.(a) We study the iterated prisoner's dilemma game as played by cognitive players, where each player optimizes his or her own future actions by making an internal model of the opponent's behavior. A kind of recurrent neural network called a dynamical recognizer (DR) is used to make these internal models, providing the advantage that the opponent's images are represented by complicated geometrical patterns in a context space of the DR.The dynamical behavior of these geometrical patterns will give a new chaotic dynamics by varying its dimensionality.(b) The internal model of each player's behavior is constructed from a finite history, and various possible models can be generated from each history. That is, many internal models are equally acc … More urate in mimicking the opponent's behavior. If the optimized future action varies depending on which of the models is chosen, we construct branches in the world line to represent several possible future worlds. Depending on the game situation (e.g. the payoff structures, the length of past sequences to be considered, the uncertainty level in choosing models, etc.), the structures of the branching of world lines (i.e., of possible worlds) will vary. In some situations, the world line is surrounded by many possible worlds, each with different behaviors.(c) The same approach is applied to the Rashevskyan game, where players move along his own spatial axis to take an advantageous position over the other player. Though those players are egocentric in principle, it is shown that some altruistic behavior will be performed as a dynamical attractor phase. The altruistic behavior is no longer attainable by merely having the opponent player's model as a Tit for Tat player. Rather players have to dynamically change his model of imitation to achieve mutual cooperation. Otherwise they go to a static noncooperative Nash solution. Less