Research on Generation of Internal Models in Games and Their Dynamics

本研究的目的是提出一个新的建模框架来研究游戏的动态方面，并通过模型的模拟来讨论游戏参与者和社会规范的合理性。以下是这个项目的结果。(a)我们研究了认知参与者所玩的迭代囚徒困境游戏，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的未来行动。利用一种称为动态识别器（DR）的递归神经网络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由复杂的几何模式来表示，这些几何模式的动态行为会通过改变其维数而产生新的混沌动力学。(b)每个玩家行为的内部模型是从有限的历史中构建的，并且每个历史可以生成各种可能的模型。也就是说，许多内部模型在模仿对手的行为时同样准确。如果优化的未来行为取决于选择的模型，我们在世界线上构建分支来表示几个可能的未来世界。根据游戏情境（游戏邦注：如收益结构、过去序列的长度、选择模式的不确定性等），世界线分支的结构（即可能世界）也会发生变化。在某些情况下，世界线被许多可能的世界所包围，每个世界都有不同的行为。(c)同样的方法也适用于Rashevskyan游戏，即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自我中心的，但研究表明，一些利他行为将作为一个动态吸引阶段进行。利他行为不再仅仅是通过对手玩家的模型来实现的。相反，玩家必须动态地改变自己的模仿模式，以实现相互合作。否则他们就会得到一个静态的非合作纳什解。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