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.     

Implementing cooperative solution concepts: a generalized bidding approach

This paper provides a framework for implementing and comparing several solution concepts for transferable utility cooperative games. We construct bidding mechanisms where players bid for the role of the proposer. The mechanisms differ in the power awarded to the proposer. The Shapley, consensus and equal surplus values are implemented in subgame perfect equilibrium outcomes as power shifts away from the proposer to the rest of the players. Moreover, an alternative informational structure where these solution concepts can be implemented without imposing any conditions of the transferable utility game is discussed as well. The authors thank Yukihiko Funaki, Andreu Mas-Colell, David Pérez-Castrillo and Jana Vyrastekova for helpful discussions. We also appreciate the comments from the seminar and conference participants at Keele University, Tilburg University, University of Haifa, University of Warwick, CORE at Louvain-la-Neuve, Catholic University Leuven, Pablo de Olavide University in Seville, University of Vigo, the 2006 Annual Conference of the Israeli Mathematical Union in Neve Ilan, Israel, and the 61st European Meeting of the Econometric Society in Vienna, Austria in 2006. In particular, we are grateful to the associate editor and an anonymous referee. Their valuable comments and constructive suggestions contributed to a significant improvement of the paper. Wettstein acknowledges the financial support of the Pinchas Sapir Center for Development in Tel Aviv University.     

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.     

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.     

Green auctions: A biodiversity study of mechanism design with externalities

This paper uses a mechanism design approach to study the biodiversity improvement in a territory, where the government is the principal and the landholders are the agents. In particular, I analyze an optimal mechanism that considers multidimensional bid which includes both the biodiversity improvement of the project and its cost. Additionally, this mechanism incorporates the externality (either positive or negative) that a biodiversity project causes in the surrounding agents who decided not to participate. Specifically, I assume that externalities enter in the cost function of the nonparticipating landholders. I show that, in the case of negative externalities, the government will implement a transfer function which is decreasing in the landholder's efficiency level. On the other hand, in the case of a positive externality, paradoxically the government may be interested in the nonparticipation of the most efficient landholders.     

Modeling production externalities in the maquila industry

In the past decade, the maquiladora export industry surpassed both tourism and petroleum products to become the number one source of earned foreign exchange for Mexico. The continued growth of the maquila industry suggests that there may be significant production spillovers into the local environments. Dynamic modeling, using STELLA, provides a framework for quantifying the environmental impacts emanating from the growth of the maquila industry, focusing on wastewater treatment consequences and resulting infrastructural policy considerations. Such detailed modeling of industrial, infrastructural, and ecological linkages has not yet been a feature of research on this region, despite the potential for significant human health ramifications. An environmental model is therefore developed for two focal urban communities, Nogales and Mexicali, facing potential wastewater treatment concerns due to the growth of nearby maquila factories. In the former case, the analysis revealed the inadequacy of the capacity planning for the treatment of effluent; in the latter case, conservative projections reveal that the system upgrades should be able to handle demands through 2020.     

Optimality of the competitive equilibrium in the Uzawa-Lucas model with sector-specific externalities

Summary. In this paper, we show that the competitive equilibrium is optimal in the Uzawa-Lucas model with sector-specific externalities associated to human capital in the goods sector. Thus, these external effects do not provoke a market failure and do not provide a rationale for government intervention.Received: 1 November 2002, Revised: 3 June 2003, JEL Classification Numbers: E62, H21, O41.I wish to thank Sandra López Calvo and an anonymous referee for their valuable comments. Financial support from the Spanish Ministry of Science and Technology and FEDER through Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+D+I) Grant SEC2002-03663 is gratefully acknowledged.     

Economics of externalities and public policy

In this paper we study a particular case of “multiple” externalities associated to the production of a good/activity, whose external effects can change from positive to negative depending on the level of output (intersecting externalities). To analyze their impact on the public policy we propose a very simple two-agent partial equilibrium model in the technological context of externalities. In a static framework, the centralized solution always implies an optimal policy, which may consist of taxation or subsidization depending on the individual optimum and on the technology parameters. In a dynamic model with local knowledge of the efficiency function and instantaneous output adjustments, such an optimal policy can be structurally stable or unstable. In the latter case, under small changes of the parameters the policy may switch from low taxation/subsidization to high taxation/subsidization or vice versa, or even jump discontinuously from taxation to subsidization or vice versa. Furthermore, the decentralized solution based upon “tradable rights” can be economically equivalent to the centralized solution in the form of taxation policy but the two solutions may be not politically equivalent.

Utility and production externalities, equilibrium efficiency and leisure specification

This paper analyzes the implications that the specification of the leisure activity has on the equilibrium efficiency in a two-sector endogenous growth model with human capital accumulation. We consider external effects of consumption and leisure in utility, and sector-specific externalities associated to physical and human capital in production. The optimal tax policy to correct for the distortions caused by the externalities is characterized under all the typical leisure specifications considered in the literature: home production, quality time and raw time. We show that the optimal policy depends markedly on the leisure specification.     

Innovation,externalities, and the state: a synergetic approach

A politicoeconomic model dealing with the interaction of private innovation and public regulation is presented. Causes and effects of this interdependence are investigated with special regard to the externalities which accompany innovations and make them into a partly public good. Our main hypothesis is that the collective character of inventive activity gives rise to synergetic effects. This hypothesis is supported by a microfoundation based on a nonlinear Markov process. Furthermore, the consequences of such synergetic innovation processes are examined: persistent disequilibrium, multiple equilibria, lock-in, path dependence, and chaos. Finally, some policy implications are derived concerning the effects of ageneral public promotion of innovations and of aselective industrial policy.     

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].     

Structural change in the presence of network externalities: a co-evolutionary model of technological successions

The paper uses a two-stage, multi-agent simulation model to examine the conditions under which technological successions can occur in the presence of network externalities. Data is used to identify a robust econometric model of the probability of succession. Four key factors are identified. First, the trade-off between higher direct utility from new technology goods and the network utility of old technology goods. Second, the relative innovative performance of new and old technology firms. Third, cost (price) differentials due to increasing returns in production. Fourth, the time old (new) firms have to develop their product designs prior to entry.JEL Classification: O30, C15 Correspondence to: Paul WindrumThe authors would like to thank Richard Nelson and Uwe Cantner for their helpful comments on an earlier draft of the paper, and for the comments provided by the anonymous referees. The usual disclaimers apply. The authors gratefully acknowledge supportive funding through SEIN-Project, European Commissions Framework 4 Programme (contract# SOEI-CT-98-1107) and through the Policy Regimes and Environmental Transitions (PRET) project funded by the Dutch Scientific Research Council (NWO).     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Watershed externalities, shifting cropping patterns and groundwater depletion in Indian semi-arid villages: The effect of alternative water pricing policies

Frequent droughts and groundwater depletion are critical constraints to improving agricultural productivity in the semi-arid tropics. India has been promoting integrated watershed management in drought-prone areas to address these constraints. Watershed communities are being assisted to invest in groundwater re-charging facilities. While communities and the public bear such costs, individual farmers capture irrigation benefits. Groundwater is a free common property resource and land users hold de-facto use rights. This has accelerated private irrigation investments and depletion of aquifers resulting in iniquitous distribution of irrigation water. Power subsidies and negligible pumping costs aggravate the problem. These policy failures and low irrigation costs to farmers are displacing water-efficient crops in favor of water-intensive crops in water-scare areas. The paper reviews the village-level externalities that aggravate groundwater depletion and evaluates potential policy options to enhance local collective action in water management. Using 3SLS, an econometric crop-water productivity model is used to evaluate alternative water policy instruments. The results indicate that different types of water user charges can be introduced with modest consequences on profitability and farm incomes. If properly implemented and managed by the local communities, pro-poor policies could bring considerable sustainability benefits and also ensure enhanced equity in access to the resource.     

The asymptotic shapley value for a simple market game

We consider the game in which b buyers each seek to purchase 1 unit of an indivisible good from s sellers, each of whom has k units to sell. The good is worth 0 to each seller and 1 to each buyer. Using the central limit theorem, and implicitly convergence to tied down Brownian motion, we find a closed form solution for the limiting Shapley value as s and b increase without bound. This asymptotic value depends upon the seller size k, the limiting ratio b/ks of buyers to items for sale, and the limiting ratio of the excess supply relative to the square root of the number of market participants. This work was sponsered in part by NSF Grant DMS-03-01795.     

Heterogeneity vs. externalities in technological competition: A tale of possible technological landscapes

The article presents a stochastic interaction model based on Gibbs random fields to analyze technological competition in a population of heterogeneous adopters with local or global externalities. The relationships between both heterogeneity and externalities and imperfect and asymmetric information are first emphasized. When local externalities and heterogeneity coexist, the technological landscapes of the industry are then shown to depend on the relative influence of these two parameters, with a phase transition: technologies coexist either in approximately equal market shares when heterogeneity is high enough or with one of the technologies only surviving in technological niches when local externalities dominate. Niches do also spontaneously appear: technological options survive in economic space due to the existence of some amount of heterogeneity among agents. On the contrary, when global externalities are added, pure standardization almost always occurs. We finally argue that different public policies should be designed so as to fit with different technological landscapes.     

Collective contests with externalities

This paper examines collective contests associated with externalities. The collective contest is modelled as a two-stage game in which intra-group sharing rules and individual outlays are determined sequentially. Depending upon the restrictions on the intra-group sharing rules and the extent of externalities, we identify three kinds of Nash equilibria, and compare them with the outcome of the contest between individuals. This paper also proposes a real rent-dissipation rate as a measure of social waste when externalities are present. The externalities are shown to have significant effects on the relationship between the number of players and the real rent-dissipation rate.     

Potentializability and consistency for multi-choice solutions

The paper introduces and discusses several characterizations of the multi-choice Shapley value (introduced by Nouweland et al. in ZOR-Math Methods Oper Res 41:289–311, 1995), on the domain of multi-choice games. These characterizations generalize the potential approach and results of Calvo and Santos (Math Soc Sci 34:175–190, 1997) into this domain, and the relations are treated with the axiomatic approach in Calvo and Santos (Math Soc Sci 40:341–354, 2000). Also, based on the axioms of two-person standardness and consistency, we offer an axiomatization of the multi-choice Shapley value. The authors are grateful to Professor Sjaak Hurkens and the anonymous referees for very helpful suggestions and comments.     

Efficient egalitarian equivalent allocations over a single good

This paper studies efficient and egalitarian allocations over a single heterogeneous and infinitely divisible good. We prove the existence of such allocations using only measure-theoretic arguments. Under the additional assumption of complete information, we identify a sufficient condition on agents’ preferences that makes it possible to apply the Pazner–Schmeidler rule for uniquely selecting an efficient egalitarian equivalent allocation. Finally, we exhibit a simple procedure that implements the Pazner–Schmeidler selection in a subgame-perfect equilibrium. We thank Gabrielle Demange, William Thomson, two referees and seminar audiences at Boston, Palermo and Rochester University for their comments. Financial support from MIUR is acknowledged.