Individual strategies in complementarity games and population dynamics

We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of them pushes too hard, no deal at all can be concluded, and they both lose. The game has many equilibria, and which of them is reached depends on the history of the interactions as the players evolve according to a fitness function that measures their gains across the interactions. We can then break the symmetry by assigning different strategy spaces to the populations, varying in particular with respect to the information available to the agents. The agents can, for example, adapt to the behavior of their opponents met in previous rounds, or they can try to copy the strategies of their successful friends. It turns out that, in general, the more restricted strategy spaces, that is, those which utilize less information, are more advantageous for a population as a whole as their adoption drives the equilibrium in a direction advantageous to that population. One reason is that a simpler strategy can be learned faster in an evolutionary setting, another is that it is good for a population to have some individuals that are unfit in the sense that they make offers that are individually unsuccessful, but have a systematic effect on the strategies of their opponents. All these effects are demonstrated through systematic simulations.