Network Formation, Cost-Sharing And Anti-Coordination

The objective of this work is to analyze how social networks coevolve with other dimensions of agents' choice. We present a model where agents choose their neighbors as well as a mode of behavior in 2 × 2 anti-coordination games, i.e. games where an individual's best response is to behave differently than the opponent. Links are costly. The cost of a link is shared between the two individuals involved in it, but not necessarily in a symmetric way. We characterize the set of Nash equilibria of the resulting social game and show how this set shrinks as the shares of the link cost are more equal. In the extreme case in which each agent pays half of the cost, there is a unique equilibrium. We also show that, as usual in the literature of network formation, there is a general misalignment between the stable and efficient states of the game.