Fig. 3: Linked games favor partner strategies.
To understand how linking promotes cooperation, we distinguish between different strategy classes, representing different kinds of Nash equilibria. Partners mutually cooperate in both games; Game-k semi-partners cooperate in game k but defect in the other; and Defectors defect in both games. Each strategy class can be characterized analytically. In addition, we consider the class of “others”, which includes all remaining strategies. a, d Partners, semi-partners, and defectors only make up a minor fraction of the entire strategy space. b, e However, when strategies result from an evolutionary process that favors strategies with high payoffs, these strategies account for >72% (unlinked) and for >95% (linked) of the observed behaviors. c, f For each resident strategy that emerged during the simulation, we classified its type, recorded the time t (number of mutants) until invasion, and classified the successful mutant. In the unlinked case, partners and game-1 semi-partners are most robust to invasion. In addition, other strategies are frequently played despite their poor robustness. In the linked case, partners are clearly favored. The figure is based on the same parameters as in Fig. 2, but simulations are run for longer (during each simulation, we consecutively introduce 2 × 107 mutants; the figure shows data from eight independent simulations). Because the first four strategy classes have measure zero, we have recorded how often players are in a small neighborhood of the respective strategy class (see Supplementary Note 3).
