![]() Importantly, however, these models take a static approach. The corresponding models suggest that multi-market contact may help, but only if there is sufficient heterogeneity between firms or markets 39, or if monitoring is imperfect 40. This work explores whether firms find it easier to reach collusive agreements when they are in contact in several distinct markets. An independent strand of literature related to our study is previous work on multi-market price competition 39, 40. They cannot explain how individuals optimally use one interaction to enhance cooperation in another. By focusing on one-shot games, however, these previous studies do not capture reciprocal exchanges. Evolutionary trajectories may yield persistent cycles even if each individual game has a unique absorbing state. This literature suggests that people find it more difficult to coordinate on an equilibrium when they interact in several games simultaneously. The previous evolutionary literature has shown that remarkable dynamical effects can already occur when two or more one-shot (non-repeated) games are coupled 35, 36, 37, 38. To capture such strategic spillovers between distinct interactions, we introduce an evolutionary framework for multichannel games (Fig. This added leverage can be used to force cooperative behaviors even in those games in which cooperation is particularly difficult to sustain. By conditioning behavior in one game on what happened in another, individuals can increase their bargaining power 34. In many scenarios, however, individuals have an incentive not to treat the different games as independent. If individuals treated all their different games as independent, each game could be analyzed in isolation, and the existing framework of direct reciprocity would continue to make correct predictions. Research teams routinely work on several concurrent projects 32, firms compete in distinct geographic locations 33, and political parties or entire nations need to collaborate on a whole range of different policy areas. ![]() In most applications, however, people are regularly involved in multiple repeated games in parallel. Much of the existing literature on reciprocity is based on the assumption that individuals only engage in one repeated game. Over the last decades, research on repeated games has identified which strategies can sustain cooperation 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, which conditions allow these strategies to spread in a population 21, 22, 23, 24, 25, 26, 27, and which of these strategies are used by human subjects 28, 29, 30, 31. This framework considers individuals who repeatedly engage in the same strategic interaction. To describe direct reciprocity mathematically, researchers use the framework of iterated games 7, 8. With these conditional strategies, cooperation can be enforced more effectively than would be possible in one-shot interactions. ![]() When individuals interact more than once, they can adopt conditional strategies that take into account the co-player’s past behavior 3, 4, 5, 6. Once there is a “shadow of the future”, people are more hesitant to free ride even if there are strong short run incentives to do so. Many of our social interactions occur in the context of repetition, which enables the evolution of cooperation by direct reciprocity 1, 2. When several interactions occur in parallel, people often learn to coordinate their behavior across games to maximize cooperation in each of them. Our results suggest that previous studies tend to underestimate the human potential for reciprocity. With analytical equilibrium calculations for the donation game and evolutionary simulations for several other games we show that such linkage facilitates cooperation. Strategic choices in one channel can affect decisions in another. Individuals interact with each other over multiple channels each channel is a repeated game. Here we introduce a general framework of multichannel games. Such models cannot account for strategic attempts to use the vested interests in one game as a leverage to enforce cooperation in another. Yet the existing theory of direct reciprocity studies isolated repeated games. Team members collaborate on several concurrent projects, and even whole nations interact with each other across a variety of issues, including trade, climate change and security. Humans routinely engage in many distinct interactions in parallel.
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