In the study of social networks, the interplay between network games and network formation is significant yet not well understood. Research in network games seeks to explain strategic interactions between neighbors, whereas research in network formation explores the evolution of link patterns. Our work combines these approaches. We show how cooperative behavior in prisoners' dilemma (PD) interactions can be sustained via the endogenous structure of the social network, demonstrating that the co-evolution of network games and network formation results in new phenomena. Early research explained cooperation in static infinitely repeated settings via an application of the Folk Theorem where agents use the threat of defection to sustain cooperation [2]. When agents change partners over time, community enforcement procedures can sustain cooperation through public reputations [4, 6]. If agents are anonymous (no reputation), the community can enforce cooperation by defecting with all partners as soon as any defection is observed [1], thereby punishing defection through a costly contagion. In these models, partnerships are determined exogenously. More recent literature explores the effect of allowing agents to choose partners via buildup of trust [3, 5]. We also allow discretion over partners. The novel feature of our model is that it sustains cooperation through the emergence of social capital and holds when agents are anonymous, without the use of potentially costly social enforcement protocols. Model: There is a countable set of agents interacting through a directed network. The network is dynamic: nodes are removed at a fixed rate and replaced by new agents. Each agent sponsors a finite number of connections to others, each of which persists until one partner dies or chooses to break it. When a connection is broken, the agent who sponsored it randomly re-matches with another agent at the next time period. In each round, an agent plays a PD with each neighbor, choosing the same action for all neighbors.
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