Network Formation with Asymmetric Players and Chance Moves

We propose a model of network formation as a two-stage game with chance moves and players of various types. First, the leader suggests a connected communication network for the players to join. Second, nature selects a type vector for players based on the given probability distribution, and each player decides whether or not to join the network keeping in mind only his own type and the leader’s type. The game is of incomplete information since each player has only a belief over the payoff functions of others. As a result, the network is formed, and each player gets a payoff related to both the network structure and his type. We prove the existence of the Bayesian equilibrium and propose a new definition of the stable partially Bayesian equilibrium defining the network to be formed and prove its existence. The connection between the stable partially Bayesian equilibrium and the Nash equilibrium in the game is examined. Finally, we investigate the characteristics of the network structures under the stable partially Bayesian equilibrium in a three-player game with the major player as well as in the n -player game with a specific characteristic function.