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.Nash networks; two-way flow models; partner heterogeneity

Existence of Nash Networks and Partner Heterogeneity

Working paper GATE 2011-11In 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

Public Goods in Endogenous Networks

In this paper, we study a local public good game in an endogenous network with heterogeneous agents. We consider two specifications in which different networks arise. When agents differ in the cost of acquiring the public good, active agents form hierarchical complete multipartite graphs; yet, better types need not have more neighbors. When agents' benefits from the public good are heterogeneous, nested split graphs emerge in which investment need not be monotonic in type. In large societies, few agents produce a lot and networks dampen inequality for most agents under cost heterogeneity and increase it under heterogeneity in benefits

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.Nash networks, two-way flow models, partner heterogeneity