The iterated Prisoner’s Dilemma in societies of deterministic players

Two players engaged in the Prisoner’s Dilemma have to choose between cooperation and defection, the pay-off of the players is determined by a weight w = ( T , R , P , S ) . For deterministic strategies p 1 , … , p n we consider a society S = S ( u i : p i ∣ i = 1 , … , n ) formed by u = ∑ i = 1 n u i individuals playing at random the IPD with weight w . We introduce the concept of a w -successful society as one where all individuals have eventually a non-negative pay-off. We discuss success of individuals and societies by means of quadratic forms associated to the pay-off matrix of the given set of strategies.