Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule satisfying efficiency, linearity, dummy player and a strong symmetry axioms can be obtained through an average game. Adding an additional axiom, we identify one unique rule satisfying these properties.     

Efficiency in coalition games with externalities

A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition formation games and characterizes the resulting payoff division.     

Efficiency in coalition games with externalities

A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition formation games and characterizes the resulting payoff division.     

Consistent solutions for cooperative games with externalities

In order to calculate the worth of a coalition of players, the coalition needs to predict the actions of outsiders. We propose that, for a given solution concept, such predictions should be made by applying the solution concept to the “reduced society” consisting of the non-members. We illustrate by computing the r-core for the case of Bertrand competition with differentiated commodities.     

Network externalities in consumer spending on lottery games: evidence from Spain

We use data from two nationally representative Spanish surveys in 2005 and 2006 to investigate spending on lottery games. Estimates from Tobit and double hurdle models of participation in lottery markets and spending on lottery tickets find that frequent participation in one game is not associated with an increased or decreased probability of participating in other games, but is associated with increased spending on other games. Consumer spending on different lottery games exhibits inter-related consumption decisions. Also, the assumptions underlying the double hurdle model, but not the Tobit model, better describe consumer spending on lottery tickets in Spain.     

Fair allocation in networks with externalities

I prove existence and uniqueness of a component efficient and fair allocation rule when the value of the network is allowed to exhibit any type of externalities across its components. This is done by means of a new specification of the value function, generalizing partial results appearing in Myerson [Myerson, R.B., 1977a. Graphs and cooperation in games. Math. Operations Res. 2, 225–229], Feldman [Feldman, B.E., 1996. Bargaining, coalition formation and value. PhD dissertation. State University of New York at Stony Brook] and Jackson and Wolinsky [Jackson, M.O., Wolinsky, A., 1996. A strategic model of social and economic networks. J. Econ. Theory 71, 44–74]. This component efficient and fair allocation rule is found closely related to an extension of the Shapley value to TU-games in partition function form proposed by Myerson [Myerson, R.B., 1977b. Values of games in partition function form. Int. J. Game Theory 6 (1), 23–31].     

Stationary equilibria in bargaining with externalities

This paper studies infinite-horizon bargaining between a seller and multiple buyers when externalities are present. We extend the analysis in Jehiel and Moldovanu by allowing for both pure and mixed equilibria [Jehiel, P., Moldovanu, B., 1995a. Cyclical delay in bargaining with externalities. Rev. Econ. Stud. 62, 619–637]. A characterization of the stationary subgame perfect equilibria in generic games is presented. Equilibria with delay exist only for strong positive externalities. Since each buyer receives a positive payoff when the seller makes an agreement with some other buyer, positive externalities induce a war of attrition between buyers.     

Contracting with externalities and outside options

This paper proposes a model of multilateral contracting where players are engaged in two parallel interactions: they dynamically form coalitions and play a repeated normal form game with temporary and permanent decisions. We show that when outside options are independent of the actions of other players all Markov perfect equilibrium without coordination failures are efficient, regardless of externalities created by interim actions. Otherwise, in the presence of externalities on outside options, all Markov perfect equilibrium may be inefficient. This formulation encompasses many economic models, and we analyze the distribution of coalitional gains and the dynamics of coalition formation in four illustrative applications.     

Coordination and bargaining power in contracting with externalities

Building on Genicot and Ray [G. Genicot, D. Ray, Contracts and externalities: How things fall apart, J. Econ. Theory 131 (2006) 71-100] we develop a model of non-cooperative bargaining that combines the two main approaches in the literature of contracting with externalities: the offer game (in which the principal makes simultaneous offers to the agents) and the bidding game (in which the agents make simultaneous offers to the principal). Allowing for agent coordination, we show that the outcome of our bargaining procedure may differ remarkably from those of the offer and the bidding games. In particular, we find that bargaining can break agents' coordination and that the principal's payoff can be decreasing in his own bargaining power.     

Optimal fiscal policy in the Uzawa-Lucas model with externalities

Summary. This paper devises a fiscal policy by means of which the first-best optimum equilibrium is attained as a market equilibrium in the Uzawa-Lucas model when average human capital has an external effect on productivity. The optimal policy requires the use of a subsidy to investment in human capital which can be financed by a tax on labor income. Lump-sum taxation is not required to balance the government budget either in the steady state or in the transitional phase. Physical capital income should not be taxed. Alternatively, the optimal growth path can be attained by means of a subsidy to human capital. Received: March 21, 2002; revised version: September 4, 2002 RID="*" ID="*" Financial support from the Spanish Ministry of Science and Technology through PNICDYIT grant SEC2002-03663 is gratefully acknowledged.     

Comparison of equilibrium actions and payoffs across players in games of strategic complements

This paper provides sufficient conditions for comparing the choices of different players in games of strategic complements. The main results require a weak ordering relation on the best responses of players in the game and their constraint sets. Under additional restrictions, we can also compare their relative payoffs. We offer three applications of our idea to industrial organization and new models of behavioral economics. Specifically, we study horizontal mergers in oligopolies, competition among firms with differentiated demands and costs of production, and a model of biased perceptions.     

Competition in telecommunication networks with call externalities

This paper describes a model involving two interconnected networks offering different degrees of quality. In these networks, there are call externalities enabling consumers to assess the quality of the calls they send and receive. Networks compete in two-part tariffs. Our aim is to show that the “profit neutrality” result no longer applies due to network asymmetry and call externalities. In the case of non reciprocal access charges, call externalities generate private incentives enabling each competitor to charge low access prices. This reduces the risk of tacit collusion as competitors are free to negotiate their access charges.      

Indeterminacy with no-income-effect preferences and sector-specific externalities

We examine a two-sector real business cycle (RBC) model with sector-specific externalities in which household utility exhibits no income effect on the demand for leisure. Unlike in the one-sector counterpart, indeterminacy can result with sufficiently high returns-to-scale in the investment sector. Moreover, the smaller the labor supply elasticity, the lower the level of externalities needed for indeterminacy. This finding is the opposite of that in all existing RBC-based indeterminacy studies. Finally, in contrast to previous sunspot-driven two-sector RBC models, our economy is able to match the stylized facts that sectoral labor inputs are positively correlated and consumption is procyclical.     

Endogenous timing in the switching of technology with Marshallian externalities

We analyze endogenous timing in the switching of technology. Each user chooses when to purchase a new product which embodies new technologies characterized by Marshallian externalities. The technological switch occurs when a large number of users purchase new products. Under complete information, multiple market equilibria exist, and one of the equilibria in which technological switching occurs is efficient. However, if we introduce even a small amount of uncertainty, the switch is delayed in the unique equilibrium under perfect competition, resulting in a loss of social welfare. The market power of a monopolistic supplier of new products alleviates this inefficiency.     

Technological standards with local externalities and decentralized behaviour

We model a situation in which agents must choose between two technologies that operate under local, positive network externalities. We find that decentralized behaviour can lead to the emergence of a technical standard, but can also result in a variety of other equilibria. Policy to eliminate non-standardized equilibria can be effected, but in some cases it may be very costly.     

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.     

Endogenous fluctuations in unionized economies with productive externalities

Summary. We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factors substitutability).Received: 16 January 2002, Revised: 18 March 2004, JEL Classification Numbers: E32, J51, D60, D62. Correspondence to: Leonor ModestoThis paper is a much revised version of our former working paper Unions, Increasing Returns and Endogenous Fluctuations. Financial support from Fundação para a Ciência e Tecnologia under the POCTI, is gratefuly acknowledged.     

Shapley and Scarf housing markets with consumption externalities

We introduce externalities into the classical model by Shapley and Scarf; that is, agents care about others and their preferences are defined over allocations rather than over single indivisible goods. After collecting some results about the nonexistence of several cooperative solutions, we focus on stable allocations and propose domains of preferences that can guarantee that they both exist and form a stable set à la von Neumann and Morgenstern.