Simple games as dynamic, coupled systems: randomness and other emergent properties

From a game theory perspective the ability to generate random behaviors is critical. However, psychological studies have consistently found that individuals are poor at behaving randomly. In this paper we investigated the possibility that the randomness mechanism lies not within the individual players but in the interaction between the players. Provided that players are influenced by their opponent’s past behavior, their relationship may constitute a state of reciprocal causation [Cognitive Science 21 (1998) 461], in which each player simultaneously affects and is affected by the other player. The result of this would be a dynamic, coupled system. Using neural networks to represent the individual players in a game of paper, rock, and scissors, a model of this process was developed and shown to be capable of generating chaos-like behaviors as an emergent property. In addition, it was found that by manipulating the control parameters of the model, corresponding to the amount of working memory and the perceived values of different outcomes, that the game could be biased in favor of one player over the other, an outcome not predicted by game theory. Human data was collected and the results show that the model accurately describes human behavior. The results and the model are discussed in light of recent theoretical advances in dynamic systems theory and cognition.