The Formation of Partnerships in Social Networks

Francis Bloch, Sttphane Robin, Min Zhu
2017 Social Science Research Network  
This paper analyzes the formation of partnerships in social networks. Agents randomly request favors and turn to their neighbors to form a partnership where they commit to provide the favor when requested. If favors are costly, agents have an incentive to delay the formation of the partnership. In that case, we show that for any initial social network, the unique Markov Perfect equilibrium results in the formation of the maximum number of partnerships when players become infinitely patient. If
more » ... avors provide benefits, agents rush to form partnerships at the cost of disconnecting other agents and the only perfect initial networks for which the maximum number of partnerships are formed are the complete and complete bipartite networks. The theoretical model is tested in the lab. Experimental results show that a large fraction of the subjects (75%) play according to their subgame perfect equilibrium strategy and reveals that the efficient maximum matching is formed over 78% of the times. When subjects deviate from their best responses, they accept to form partnerships too early. The incentive to accept when it is optimal to reject is positively correlated with subjects' risk aversion, and players employ simple heuristicslike the presence of a captive partner to decide whether they should accept or reject the formation of a partnership. Abstract This paper analyzes the formation of partnerships in social networks. Agents randomly request favors and turn to their neighbors to form a partnership where they commit to provide the favor when requested. If favors are costly, agents have an incentive to delay the formation of the partnership. In that case, we show that for any initial social network, the unique Markov Perfect equilibrium results in the formation of the maximum number of partnerships when players become infinitely patient. If favors provide benefits, agents rush to form partnerships at the cost of disconnecting other agents and the only perfect initial networks for which the maximum number of partnerships are formed are the complete and complete bipartite networks. The theoretical model is tested in the lab. Experimental results show that a large fraction of the subjects (75%) play according to their subgame perfect equilibrium strategy and reveals that the efficient maximum matching is formed over 78% of the times. When subjects deviate from their best responses, they accept to form partnerships too early. The incentive to accept when it is optimal to reject is positively correlated with subjects' risk aversion, and players employ simple heuristicslike the presence of a captive partnerto decide whether they should accept or reject the formation of a partnership. JEL Classification Numbers: D85, C78, C91 Keywords: social networks, partnerships, matchings in networks, non-stationary networks, laboratory experiments * We thank Yann Bramoullé, Gabrielle Demange, Matt Eliott, Sanjeev Goyal, Matt Jackson, Eva Tardos and seminar participants at different institutions for their comments on the paper. We are grateful to Quentin Thévenet for programming the experiment and to Yannick Boireaud for valuable research assistance.
doi:10.2139/ssrn.2898191 fatcat:j7mvzisqlba43a5ocajzo7ak5y