(Non-)Existence and Scope of Nash Networks

For the connections model of strategic network formation, with two-way flow of information and without information decay, specific parameter configurations are given for which Nash networks do not exist. Moreover, existence and the scope of Nash network architectures are briefly discussed.

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

Network connectivity under node failure

We examine a non-cooperative model of network formation where players may stop functioning. We identify conditions under which Nash and efficient networks will remain connected after the loss of kk nodes by introducing the notion of kk-Node Super Connectivity

Existence of Nash Networks in One-Way Flow Models

This paper addresses the existence of Nash equilibria in one-way flow or directed network models in a number of different settings. In these models players form costly links with other players and obtain resources from them through the directed path connecting them. We find that heterogeneity in the costs of establishing links play a crucial role in the existence of Nash networks. We also provide conditions for the existence of Nash networks in models where costs and values of links are heterogeneous.Network Formation, Non-cooperative Games

Network Formations among Immigrants and Natives

In this paper we examine possible network formations among immigrants and natives with endogenous investment. We consider a model of a network formation where the initiator of the link bears its cost while both agents benefit from it. We present the model by considering possible interactions between immigrants and the new society in the host country: assimilation, separation, integration and marginalization. The paper highlights different aspects of immigrants’ behavior and their interaction with the members of the host country (society) and their source country (society). We found that when the stock of the immigrants in the host country increases, the immigrants' investment in the middlemen increases and the natives may bear the cost of link formation with the middlemen.assimilation and separation, social networks, network formations

Interaction on Hypergraphs

Interaction on hypergraphs generalizes interaction on graphs, also known as pairwise local interaction. For games played on a hypergraph which are supermodular potential games, logit-perturbed best-response dynamics are studied. We find that the associated stochastically stable states form a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest stochastically stable state. In the special case of networking games, we obtain comparative statics results with respect to investment costs, for Nash equilibria of supermodular games as well as for Nash equilibria of submodular games.

Modeling Resource Flow Asymmetries using Condensation Networks

This paper analyzes the asymmetries with regard to the resources obtained by groups of players in equilibrium networks. We use the notion of condensation networks which allows us to partition the population into sets of players who obtain the same resources and we order these sets according to the resources obtained. We establish that the nature of heterogeneity plays a crucial role on asymmetries observed in equilibrium networks. Our approach is illustrated by introducing the partner heterogeneity assumption into the one-way ow model of Bala and Goyal[1].

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