Micro to Macro Game Theory in a Multi-Agent System

Recently there has been interest in the study of multi-agent systems where these systems can be described using the principles of game-theory. In particular the minority game has been used to study the relationship between trading behaviour and volatility of financial markets while micro-economic games have been studied in order to understand how agents adapt to each others behaviour at the level of agent-agent interactions. This paper introduces a model which enables the numerical study of the collective adaptation of agents when a parameter phi is adjusted, varying the relative contribution of local and global interactions to the adaptive dynamics of the agents. The model also allows for the variation in a memory parameter which attenuates an agents history. It is demonstrated that for two different types of local interaction between the agents, co-operative and non-co-operative, there are significant memory dependent differences in the volatility of the system.