Connections Among Farsighted Agents

We study the stability of social and economic networks when players are farsighted. In particular, we examine whether the networks formed by farsighted players are different from those formed by myopic players. We adopt Herings, Mauleon and Vannetelbosch’s (Games and Economic Behavior, forthcoming) notion of pairwise farsightedly stable set. We first investigate in some classical models of social and economic networks whether the pairwise farsightedly stable sets of networks coincide with the set of pairwise (myopically) stable networks and the set of strongly efficient networks. We then provide some primitive conditions on value functions and allocation rules so that the set of strongly efficient networks is the unique pairwise farsightedly stable set. Under the componentwise egalitarian allocation rule, the set of strongly efficient networks and the set of pairwise (myopically) stable networks that are immune to coalitional deviations are the unique pairwise farsightedly stable set if and only if the value function is top convex.Farsighted Players, Stability, Efficiency, Connections Model, Buyerseller Networks

Farsightedly stable networks

We propose a new concept, the pairwise farsightedly stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pairwise farsightedly stable (i) if all possible pairwise deviations from any network g E G to a network outside G are deterred by the threat of endind worse off or equally well off, (ii) if there exists a farsightedly improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying (i) and (ii). We show that a non-empty pairwise farsightedly stable set always exists and we provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsightedly yields a Pareto dominating betwork, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsightedly stability and other concepts such as the largest consistent set.Networks, Farsighted, Stability, Pairwise, Efficiency

Farsightedly Stable Networks

We propose a new concept, the pairwise farsightedly stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pairwise farsightedly stable (i) if all possible pairwise deviations from any network g ∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsightedly improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying (i) and (ii). We show that a non-empty pairwise farsightedly stable set always exists and we provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominating network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest consistent set.Economics ;

Connections among farsighted agents

farsighted players, stability, efficiency, connections model, buyer-seller networks

Risk-sharing networks and farsighted stability

Evidence suggests that in developing countries, agents rely on mutual insurance agreements to deal with income or expenditure shocks. This paper analyzes which risk-sharing networks can be sustained in the long run when individuals are far- sighted, in the sense that they are able to forecast how other agents would react to their choice of insurance partners. In particular, we study whether the farsightedness of the agents leads to a reduction of the tension between stability and efficiency that arises when individuals are myopic. We find that for extreme values of the cost of establishing a mutual insurance agreement, myopic and farsighted agents form the same risk-sharing networks. For intermediate costs, farsighted agents form efficient networks while myopic agents don't.risk-sharing, networks, farsighted agents, stability, efficiency

Networks and Farsighted Stability

We make two main contributions to the theory of economic and social network formation. First, we introduce the notion of a network formation network or a supernetwork. Supernetworks provide a framework in which we can formally define and analyze farsightedness in network formation. Second, we introduce a new notion of equilibrium corresponding to farsightedness. In particular, we introduce the notion of a farsightedly basic network, as well as the notion of a farsighted basis, and we show that all supernetworks possess a farsighted basis. A farsightedly basic network contained in the farsighted basis of a given supernetwork represents a possible final resting point (or absorbing state) of a network formation process in which agents behave farsightedly. Given the supernetwork representation of the rules governing network formation and the preferences of the individuals, a farsighted basis contains networks which are likely to emerge and persist if individuals behave farsightedlynetwork formation ; supernetworks ; farsighted stability

Networks and farsighted stability

We make two main contributions to the theory of economic and social network formation. First, we introduce the notion of a network formation network or a supernetwork. Supernetworks provide a framework in which we can formally define and analyze farsightedness in network formation. Second, we introduce a new notion of equilibrium corresponding to farsightedness. In particular, we introduce the notion of a farsightedly basic network as well as the notion of a farsighted basis, and we show that all supernetworks possess a farsighted basis. A farsightedly basic network contained in the farsighted basis of a given supernetwork represents a possible final resting point (or absorbing state) of a network formation process in which agents behave farsightedly, Given the supernetwork representation of the rules governing network formation and the preferences of the individuals, a farsighted basis contains networks which are likely to emerge and persist of individuals behave farsightedly

Myopic or Farsighted? An Experiment on Network Formation

Pairwise stability (Jackson and Wolinsky, 1996) is the standard stability concept in network formation. It assumes myopic behavior of the agents in the sense that they do not forecast how others might react to their actions. Assuming that agents are farsighted, related stability concepts have been proposed. We design a simple network formation experiment to test these theories. Our results provide support for farsighted stability and strongly reject the idea of myopic behavior.Network Formation, Experiment, Myopic and Farsighted Stability

Stability of Networks under Limited Farsightedness

We provide a tractable concept that can be used to study the influence of the degree of farsightedness on network stability. A set of networks G K is a level-K farsightedly stable set if three conditions are satisfied. First, external deviations should be deterred. Second, from any network outside of G K there is a a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in G K . Third, there is no proper subset of G K satisfying the first two conditions. We show that a level-K farsightedly stable set always exists and we provide a sufficient condition for the uniqueness of a level-K farsightedly stable set. There is a unique level-1 farsightedly stable set G 1 consisting of all networks that belong to closed cycles. Level-K farsighted stability leads to a refinement of G 1 for generic allocation rules. We then provide easy to verify conditions for a set to be level-K farsightedly stable and we consider the relationship between limited farsighted stability and efficiency of networks

Coalition Formation among Farsighted Agents

A set of coalition structures P is farsightedly stable (i) if all possible deviations from any coalition structure p belonging to P to a coalition structure outside P are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any coalition structure outside the set leading to some coalition structure in the set, and (iii) if there is no proper subset of P satisfying the first two conditions. A non-empty farsightedly stable set always exists. We provide a characterization of unique farsightedly stable sets of coalition structures and we study the relationship between farsighted stability and other concepts such as the largest consistent set and the von Neumann-Morgenstern farsightedly stable set. Finally, we illustrate our results by means of coalition formation games with positive spillovers.microeconomics ;