Existence of Nash Networks in One-Way Flow Models

Abstract

This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. First, we provide conditions for he existence of Nash networks in models where costs and values of links are heterogenous and players obtain resources from others only through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks. Next we examine the existence of Nash networks when there are congestion effects in the model. Then, we provide conditions for the existence of Nash networks in a model where a player’s payoff depends on the number of links she has established as well as on the number of links that other players in the population have created. More precisely, we show that convexity and increasing (decreasing) differences allow for the existence of Nash networks.