Endogenous Network Dynamics

Games and Economic Behavior, 2009

Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from noncooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation defined on the feasible set of networks. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterization of equilibrium of well known models and their rules of network formation, such as those of and .

2009

We combine a network game introduced in Ballester et al. (2006), where the Nash equilibrium action of each agent is proportional to her Bonacich centrality (Bonacich, 1987), with an endogenous network formation process. Links are formed on the basis of centrality while the network is exposed to a volatile environment introducing interruptions in the connections between agents. Taking into account bounded rational decision making, new links are formed to the neighbors' neighbors with the highest centrality. The volatile environment causes existing links to decay to the neighbor with the lowest centrality. We show analytically that there exist stationary networks and that their topological properties completely match with features exhibited by social and economic networks. Moreover, we find that there exists a sharp transition in efficiency and network density from highly centralized to decentralized networks.

SSRN Electronic Journal, 2005

We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists at least one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis, and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model.

2001

I propose a recursive generalization of pairwise stability of social and economic networks. My notion applies to many kinds of networks, encompassing the cooperative and the non-cooperative approach, allowing for multiple dimensions of interaction and for links with different intensity. Moreover, it explores recursively how different degrees of rationality are required for certain structures to form. Preliminary results are presented, which show that this notion is indeed manageable and may provide interesting insights.

ArXiv, 2020

We study the problem of convergence to stability in coalition formation games in which the strategies of each agent are coalitions in which she can participate and outcomes are coalition structures. Given a natural blocking dynamic, an absorbing set is a minimum set of coalition structures that once reached is never abandoned. The coexistence of single and non-single absorbing sets is what causes lack of convergence to stability. To characterize games in which both types of set are present, we first relate circularity among coalitions in preferences (rings) with circularity among coalition structures (cycles) and show that there is a ring in preferences if and only if there is a cycle in coalition structures. Then we identify a special configuration of overlapping rings in preferences characterizing games that lack convergence to stability. Finally, we apply our findings to the study of games induced by sharing rules.

I survey the recent literature on the formation of networks. I provide definitions of network games, a number of examples of models from the literature, and discuss some of what is known about the (in)compatibility of overall societal welfare with individual incentives to form and sever links. JEL Classification Numbers: A14, C71, C72

2017

We consider a class of cooperative games with transferable utilities where the payoff to a coalition is a function of the overall coalition structure (externalities) and the payoff to a coalition is not deterministic (stochasticity). Externalities and stochasticity in the cooperative game theory literature have almost always been studied separately. We propose a theoretical framework to analyze a situation when both are present together. We introduce a notion of stability and propose a related solution concept, called “foresighted nucleolus”. We prove that the foresighted nucleolus always exists, but it may not be unique. We also provide a computational method and a numerical example to illustrate the solution concept.

Handbook of Social Economics, 2011

Economics Bulletin, 2010

This paper explores the formation of stable network structures in a model with public goods. The multiplicity of equilibria in the non-cooperative formulation of network formation games brings out further difficulties in analyzing stability of network structures. This contrasts with the cooperative game approach where payoffs for agents are predetermined and thereby the multiplicity of equilibrium issues are sidestepped. We took issue with the multiplicity of equilibrium effort levels exerted on a given network structure, and we suggested different stability definitions for such network structures under multiplicity of equilibria. We demonstrated how these stability notions work for the network structures with four agents where breaking and forming links is costless, and the cost of exerting effort level is linear.

Social Science Research Network, 2005

This paper considers a model of economic network characterized by an endogenous architecture and frictions in the relations among agents as described in Bala and Goyal (2000). We propose a similar network model with the difference that frictions in the relations among agents are endogenous. Frictions are modeled as dependent on the result of a coordination game, played by every pair of directly linked agents and characterized by 2 equilibria: one efficient and the other risk dominant. The model has a multiplicity of equilibria and we produce a characterization of those are stochastically stable.