How altruism can pay in a collective game

We consider a collective version of Parrondo’s paradox, a game in which the re-distribution of capital between agents, who can play different strategies, creates a positive trend of increasing capital. In this framework, we insert two categories of players, altruistic and egoistic ones, and see how they interact and how their ini-tial capital changes, considering also different network topologies. In particular, we analyse the positive effects of the altruists ’ behaviour, but we also point out how the egoists take advantage of them. The general result is that the altruistic behaviour is discouraged, because egoists get richer while altruists get poorer. We consider also a smarter version of being altruistic, based on reputation, called ”selective altruism”, which prevents egoistic players from taking advantage of altruistic ones. In this new situation it is altruism, and not egoism, to be encouraged. Finally, we introduce a mechanism of imitation between players and study how it influences the composi-tion of the population of both altruistic and egoistic players as a function of time and for different initial conditions and network topologies adopted