Direct reciprocity between individuals that use different strategy spaces
Fig 5
Evolutionary dynamics of memory spaces for different game structures.
We explore whether memory dilemmas are present in games beyond the repeated Prisoner’s Dilemma by repeating our previous simulations for various game matrices. a, We consider matrices parametrized by v and u. The parameter v varies in the interval [0, 2], and the parameter u varies in [−1, 1]. We can partition the resulting two dimensional space of game matrices into four quadrants. The lower right quadrant contains games with a Prisoner’s Dilemma (PD) structure like the donation game, whereas the other quadrants contain the other fundamental social dilemmas Snowdrift (SG), Harmony (HG), and Stag Hunt (SH) games. For each of these games, we do the same kind of analysis as for the donation games studied earlier. b, First, we depict the Nash equilibria of the 3 × 3 payoff matrices when the spaces ,
and
compete. For each strategy space, we find parameter regions where this space is an equilibrium. Additionally, we identify regions in which more than one space is stable. c, Here, we show the strategy space with the highest self-payoff. Memory-1 strategies tend to get the highest self-payoff in the PD and SH. In the other two game classes, strategy spaces of lower complexity can be more effective. d, We distinguish two kinds of memory dilemma. In the “classic” one, the strategy space with highest complexity gives the highest self-payoff, but is not a Nash equilibrium. In the “reverse” one, it is a less complex strategy space that yields the higher self-payoff without being an equilibrium. Both dilemmas also appear in their “weak” forms when bistabilities occur. Parameters: β = 100, simulations run for T = 109.