Fig. 1: Cooperation in multichannel games.
a In a multichannel game, individuals repeatedly interact in several independent games. Here, we illustrate the case of two players who interact in two different prisoner’s dilemma games. In each game, players can either cooperate (C) or defect (D). A player’s payoff in each game k is either Rk, Sk, Tk, or Pk, depending on the player’s and the co-player’s decision. In the main text, we consider the case that the two games take the form of a donation game7, such that Rk = bk − ck, Sk = −c, Tk = bk, and Pk = 0, where bk and ck are the benefit and cost of cooperation. The effect of other payoffs is studied in the Supplementary Information. Players interact for infinitely many rounds. In each round, players simultaneously determine how to act in each game. We distinguish two different scenarios. b In the unlinked case, the two players are restricted to treat each game as independent. They only react to the co-player’s previous action in the very same game. c In the linked case, the two players are able to couple the two games—they are allowed to react to a co-player’s defection in one game by defecting in the other. In the above example, the first player defects in the first game in the second round (as indicated by the white D in the respective blue box). In response, the second player defects in both games in the third round.
