Distributing cognitive resources in one-against-many strategy games

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Many real-world situations require an agent with limited cognitive resources to be engaged in multiple games simultaneously. In these circumstances, the agent is unable to devote infinite cognitive resources to represent the optimal strategy that needs to be played against each opponent. We investigate this type of game, where a player, called the focal player, playing concurrently against multiple opponents independent 2-player games. Nevertheless, these games are coupled through the shared memory resource available to the agent. Each opponent has a fixed strategy. While the history length may vary from one opponent to another, the focal player doesn't know the opponents' strategies or which history length is used by which opponent. All the focal player can observe is the opponents' actions. We use evolutionary computation to decide on an appropriate allocation of memory to opponents. We show - given that opponents are using fixed strategies - that the memory distribution relies on the number of active bits (i.e., bits which generates a repeated pattern with a favorable payoff) that the focal player needs to exploit its opponents' strategies. We show how our current results relate to the minimum required number of bits for a player to face a set of opponents with fixed strategies, and how the number of active bits increases as the richness of the opponent strategy - measured using entropy - increases.