Abstract
To improve the network interaction step-wise process, a genetic algorithm is suggested for finding more stable solutions in bimatrix games. The algorithm is based on using an approach of successive approximation to an equilibrium situation within a finite space of actions whose size directly depends on the number of game repetitions (network interactions). The algorithm has seven input parameters: the population size, the maximum number of generations, the number of generations for the early stop, the mutation rate, the number of bits per pure strategy, the number of maximum network interactions, and the number of the best chromosomes selected. The algorithm is more efficient for fewer network interactions, when the network peers obtain more stable and consistent strategies that encourage interaction itself rather than resigning from sending any information due to instability. The equilibrium concept is strengthened by introducing a criterion of mutual profitability, which is clearly a good tone and respect in network interactions (particularly, in P2P file-sharing networks). This criterion, expressed as a fitness value equal to negative maximum of potential losses, can be varied to alternatively evaluate the consequence of swerving from a given mixed strategy.