Characterization of Stable Manea Bargaining Networks

Abstract

We set up a model of endogenous network formation that extends the work of Mihai Manea (American Economic Review, Vol. 101, pp.2042-2080, 2011). Rubinstein and Wolinsky (Econometrica, Vol. 53, pp.1133-1150, 1985) looked at bargaining in markets with two populations. They found that in a model of markets with noncooperative foundations, the market equilibrium was not the competitive equilibrium. Gale (Journal of Economic Theory, Vol.43, pp.20-54, 1987) sets up a model that is similar to Rubinstein and Wolinsky but find a result that is in direct conflict with this finding. Manea (2011) extends Rubinstein and Wolinsky to look at multiple populations of agents. Manea introduces a reasonably realistic way of measuring bargaining power for agents in the network that is able to take in to account the entire network structure. We study Manea's network bargaining game and examine the set of stable networks using the notion of pairwise link stability as defined by Jackson and Wolinsky (Journal of Economic Theory, 1996). We completely characterise the set of Manea's link stable networks for all positive fixed costs per link. We show for all positive costs all link stable Manea bargaining networks are of degree two or less. This means that link stable Manea networks are circles and line segments. We also characterise the structure of the link stable networks at all costs. For high enough costs, below autarky levels, the only link stable networks involve bilateral bargaining. We extend the analysis to Nash stable and strongly Nash stable networks. JEL Classification: D85