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Abstract:
We develop a model of friendship formation that sheds light on segregation patterns observed in social and economic networks. Individuals come in different types and have type-dependent benefits from friendships; we examine the properties of a steady-state equilibrium of a matching process of friendship formation. We use the model to understand three empirical patterns of friendship formation: (i) larger groups tend to form more same-type ties and fewer other-type ties than small groups, (ii) larger groups form more ties per capita, and (iii) all groups are biased towards same-type relative to demographics, with the most extreme bias coming from middle-sized groups. We trace each of these empirical observations to specific properties of the theoretical model and highlight the role of choice and chance in generating homophilous behavior. Finally we discuss welfare implications of the model.

Networks, Homophily, Segregation, Friendships, Social Networks, Integration, Diversity, Minorities

Abstract:
We study the stability properties of organizations in partition function games, describing cooperative situations with externalities. An organization is defined as a group of agents, together with a set of bilateral relations, formally, a connected graph. Because of the presence of externalities, the profitability of coalitional threats to an organization depend on the reaction of non coalitional members. This reaction is likely to depend on the links that non coalitional members maintain in the organization. We show that this directly implies that minimally connected organizations emerge under positive externalities, while the fully connected organization emerges under negative. This result is shown to hold independently of the adopted payoff imputation rule. Sharper predictions are possible for the specific case of the egalitarian rule. Here, if only coalitions that are connected in the organization can effectively object to it, the star organization prevails under positive externalities, and the wheel, a non fully connected organization, prevails under negative.

Organizations, Graphs, Networks, Cooperation, Coalitions, Externalities

Abstract:
This paper proposes a formulation of coalitional payoff possibilities in games with externalities, based on the assumption that forming coalitions can exploit a first mover advantage. We derive a characteristic function and show that when outside players play their best response noncooperatively, the core is always nonempty when the game has strategic complementarities. We apply this result to cartel formation in Bertrand oligopoly and in Shapley-Shubik (1977) strategic market games.

core, cooperative games, externalities

Abstract:
In this paper we study the welfare effects of monetary policy in a simple overlapping generation economy in which agents voluntarily contribute to a public good. Inflation has two effects at equilibrium: it increases voluntary contributions and it misallocates private consumption across time. We show that the aggregate effect is welfare-improving for not too large inflation rates. Moreover, there exists an optimal inflation rate.

Optimal inflation, public goods, voluntary contributions

Abstract:
This paper establishes sufficient conditions for the existence of a stable coalition structure in the "coalition unanimity" game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2000). Our conditions are defined on the strategic form game used to derive the payoffs the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions. We illustrate the role of synergies in a Cournot oligopoly example with cost reducing R&D.

coalition formation, synergies, strong nash equilibrium

Abstract:
We study a simple contracting game with a principal and two agents. Contracts exert an externalities on non contractors. The principal can either contract both agents in a centralized manner, or delegate one agent to contract the other. We show that the choice of the principal depends on the sign of the externality. If this is positive, the principal prefers to delegate as long as the agency costs are not too high; if the externality is negative, the principal prefers to centralize for all sizes of agency costs.

Contracts, Externalities, Centralization, Delegation

Abstract:
We study the problem of information sharing in oligopoly, when sharing decisions are taken before the realization of private signals. Using the general model developed by Raith (1996), we show that if firms are allowed to make bilateral exclusive sharing agreements, then some degree of information sharing is consistent with equilibrium, and is a constant feature of equilibrium when the number of firms is not too small. Our result is to be contrasted with the traditional conclusion that no information is shared in common values situations with strategic substitutes - such as Cournot competition with demand shocks - when firms can only make industry-wide sharing contracts (e.g., a trade association).

Information sharing, oligopoly, networks, Bayesian equilibrium

Abstract:
We study the group stability of collective decision making when society is organized according to a non directed graph, and groups' payoff possibilities are given by a partition function. We focus on the stability properties of hierarchical organizations, formally described by minimally connected graphs (or trees). Building on previous works by Greenberg and Weber (1986, 1993) and by Demange (1994, 2001), we restrict the ability of raising objections to proposed payoff imputations to coalitions that are connected in the organization. We show that the stability properties of hierachical organizations, proved in Demange (1994, 2002), extend to partition function games with negative externalities. Under positive externalities, although not ensuring social stability, hierarchies are the "most stable" organizational forms for society.

Abstract:
This paper presents a new cooperative equilibrium for strategic form games, denoted Conjectural Cooperative Equilibrium (CCE). This concept is based on the expectation that joint deviations from any strategy profile are followed by an optimal and noncooperative reaction of non deviators. We show that CCE exist for all symmetric supermodular games. Furthermore, we discuss the existence of a CCE in specific submodular games employed in the literature on environmental agreements.

Cooperative Equilibrium, Coalitions

Abstract:
How should an organization be designed in order to provide its members with minimal incentives to defect? And how does the optimal design depend on the type of strategic interaction between defectors and remaining organizational members? This paper addresses such issues in a game theoretic model of cooperation, in which an organization is formally represented by a connected network, and where gains from cooperation are given by a partition function. We show that critical structural features of the organization depend in a clear-cut way on the sign of spillovers. In particular, positive spillovers favor the adoption of dispersed and centralized forms, while negative spillovers favor cohesive and horizontal ones. Moreover, if the organizational form determines all the communication possibilities of members, a highly centralized organization - the star - emerges under positive spillovers, whereas two horizontal architectures - the circle and the complete - emerge under negative spillovers.

Organizational design, networks, group stability, spillovers

Abstract:
In a recent paper, Demange (2004) has shown that hierarchical organizations can guarantee the existence of stable cooperative outcomes by appropriately allocating the blocking power to a subset of coalitions, the "teams". This paper extends the analysis of Demange to cooperative problems with spillovers. We show that if blocking coalitions have "pessimistic expectations" on the reaction of outsiders, in all cooperative problems there exists an allocation which is blocked by no team. We also study the case of "passive expectations", for which the same result holds in all games with negative spillovers, while stable allocations may fail to exist in games with positive spillovers. In the latter class of games, however, hierarchies are shown to be the most stable organizational forms.

Hierarchies, Coalitions, Stability, Spillovers, Cooperative Games, Networks

Abstract:
We study the incentives of oligopolistic firms to share private information on demand parameters. Differently from previous studies, we consider bilateral sharing agreements, by which firms commit at the ex-ante stage to truthfully share information. We show that if signals are i.i.d., then pairwise stable networks of sharing agreements are either empty or made of fully connected components of increasing size. When linking is costly, non complete components may emerge, and components with larger size are less densly connected than components with smaller size. When signals have different variances, incomplete and irregular network can be stable, with firms observing high variance signals acting as "critical nodes". Finally, when signals are correlated, the empty network may not be pairwise stable when the number of firms and/or correlation are large enough.

Information sharing, oligopoly, networks, Bayesian equilibrium

Abstract:
This paper revisits a particular behaviour for firms competing in imperfect competitive markets, underlying the well known model of kinked demand curve. We show that under some symmetry and regularity conditions, this asymmetric behaviour of firms sustains monopoly pricing, and possesses therefore some "rationality" interpretation. We also show that such a behaviour can be generalized and interpreted as a norm of behaviour that sustains efficient outcomes in a more general class of symmetric games.

kinked demand, symmetric games, norms of behaviour