A three player network formation game

Official URL: http://risc01.sabanciuniv.edu/record=b1606669 (Table of Contents)

Efficiency and stability are the two most widely discussed issues in the networks literature. Desirable networks are such that they combine efficiency and stability. In Currarini and Morelli's (2000) non-cooperative game-theoretic model of sequential network formation, in which players propose links and demand payoffs, if the value of networks satisfy size monotonicity (i.e. the efficient networks connect all players in some way or another), then each and every equilibrium network is efficient. Our sequential game is not endogenous in terms of payoff division. The setting is such that players prefer being part of a two player network, although three player networks generate the greatest total value. However, we present our result that, the efficient complete graph is sustainable as a subgame perfect equilibrium as well as a trembling{hand perfect equilibrium. We further our analysis by examining various repeated game formulations that are most frequently used in the literature. We focus on "zero{memory" (Markov) strategies and show that our conclusion still holds under "zero{memory" (Markov) subgame perfection. Keywords: Network Formation, complete graph, efficiency, dynamic game, markov equilibrium.