Network Design in Games with Spillovers

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.

Group Stability of Hierarchies in Games with Spillovers

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.Organizational design, networks, group stability, spillovers.

The Core of Games with Stackelberg Leaders

This paper considers cooperative game theoretic settings in which forming coalitions can act as Stackelberg leaders. We de�fine a value function which modi�fies the gamma-value function (Hart & Kurz, 1983, Chander & Tulkens, 1997) by letting members of deviating coalitions move �first in choosing a coordinated strategy. We accordingly defi�ne what we call the phi-core, and characterize the phi-core allocations of a cartel formation game and of a public goods economy.Core, Cooperative Games, Oligopoly, Public Goods

Bilateral Information Sharing in Oligopoly

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).Networks, Information sharing, oligopoly, networks, Bayesian equilibrium

Coalitional Approaches to Collusive Agreements in Oligopoly Games.

In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of firms are shown to yield a wide range of different results.Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Externalities, Endogenous Coalition Formation.

A conjectural cooperative equilibrium for strategic form games

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.Strong Nash Equilibrium, Cooperative Games, Public Goods

Coalition Formation in Games without Synergies

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

The Kinked Demand Model and the Stability of Cooperation

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.

Delegation Versus Centralization: The Role of Externalities

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.