Existence of Nash networks and partner heterogeneity

In this paper, we pursue the work of H. Haller and al. (2005, [10]) and examine the existence of equilibrium networks, called Nash networks, in the noncooperative two-way flow model (Bala and Goyal, 2000, [1]) with partner heterogeneous agents. We show through an example that Nash networks do not always exist in such a context. We then restrict the payoff function, in order to find conditions under which Nash networks always exist. We give two properties: increasing differences and convexity in the first argument of the payoff function, that ensure the existence of Nash networks. It is worth noting that linear payoff functions satisfy the previous properties.