Punishment in a complementarity game

We study the effects arisen from the punishment in an evolutionary complementarity game. Each round one member of population “buyers” deals with a randomly chosen member of population “sellers”. When the buyerʹs offer is greater than the sellerʹs, a deal is done and both players are rewarded by gaining some points. Otherwise the transaction is not successful and both will lose certain points as punishment. Our simulations indicate that the resulting equilibrium of the game with punishment embedded is remarkably time-delayed compared to the counterpart of the non-punishment game. However, the median fee and the success rate of deals at the equilibrium remain nearly unchanged in various cases of games with different degrees of punishment, whether severe or not. Symmetry, between the two populations, and the equilibrium value can still be maintained when the members of both of them are punished fairly in any failed transaction. If they are done in a different manner, namely, the members of one population are subject to very severe punishment whereas their opponents receive less or no punishment at all, the latter in most cases will be better off.