Seeking Relationship Support: Strategic network formation and robust cooperation

With Xu Tan

Abstract: We study cooperation on social networks with private monitoring and communication. For arbitrary networks, we construct a class of equilibria that attain high cooperation on all supported links, in a way that is robust to social contagion, bilaterally renegotiation proof, and in which players need only local information about the network. In these equilibria, guilty players exert high effort for their innocent partners, and are willing to do so because they are compensated for their effort costs. Anticipating cooperation, players in a network formation game with random opportunities to form links will strategically form a network with realistic “small worlds” properties, including high “support” but relatively low clustering.

Draft available on request

Community enforcement with imperfect monitoring

With David Yilin Yang

Abstract: Contagion equilibria enable communities to enforce cooperation in simple strategies, if the monitoring that occurs privately within bilateral relationships is perfect and partners can adjust the stakes of their relationships. But if monitoring within relationships is imperfect, then punishments arise on the equilibrium path, and players' private information about the spread of contagion makes it difficult for them to coordinate their continuation play. We introduce a novel approach to constructing equilibria in private strategies that are not "belief-free" but are nonetheless tractable. In equilibrium, players who are aware of contagion always shirk, whereas players who are unaware of contagion shirk only if they become very pessimistic due to lack of data. Thus contagion may start in two ways along the equilibrium path: an incorrect monitoring signal may make an innocent player appear to have shirked, or a pessimistic player may spontaneously shirk. The equilibria we construct converge to ordinary contagion equilibria as monitoring imperfections vanish.

Project in progress