Alternative evolution of strategies with memory

Abstract

Within the generalized prisoner's dilemma, the evolution of a population with a complete set of behavioral strategies limited only by memory depth has been examined. Evolution considers the pairing of strategies, in accordance with the iterated prisoner's dilemma. In doing so, each strategy interacts with each, including itself. Each subsequent generation of the population consistently loses the most profitable behavior strategies of the previous generation. Increasing population memory has been shown to be evolutionarily beneficial. The winners of evolutionary selection consistently are the agents with maximum memory. The concept of strategy complexity has been introduced. Collective variables are introduced to obtain the average of the family of strategies and their changes over time are studied. Strategies that succeed in natural selection have been shown to have maximum or near maximum complexity. An alternative evolution of a family of strategies limited only by memory depth is considered. In each generation, a strategy that maximizes the point of evolutionary benefits is removed from the family. Such an alternative evolution leads to significant changes in the family compared to the normal evolution. In some ways, alternative evolution maintains maximum memory depth and complexity even more than normal evolution. The main difference is the stationary strategies being absolute aggressive against each other. The stationary family is formed by the strategies being the most aggressive towards each other. Memory depth and complexity of strategies, as in normal evolution, are evolutionarily beneficial properties. The universal relation between the aggressiveness of the population and the number of points of evolutionary advantages that the strategy receives on average per turn is considered. On the whole, the universal link between average aggression and the number of strategy payoffs per turn is maintained.