International Journal of Game Theory (1997) 26:379-401 Game Theory The Core of an Economy with Multilateral Environmental Externalities PARKASH CHANDER Indian Statistical Institute and California Institute of Technology, Sansanwal 7, New Delhi 110016, India HENRYTULKENS CORE, Universit~ Catholique de Louvain, 34 Voie du Roman Pays, B-1348 Louvain-la-Nenve, Belgium Abstract. When environmental externalities are international - i.e. transfrontier they most often are multilateral and embody public good characteristics. Improving upon inefficient laissez-faire equilibria requires voluntary cooperation for which the game-theoretic core concept provides optimal outcomes that have interesting properties against free riding. To define the core, however, the characteristic function of the game associated with the economy (which specifies the payoff achievable by each possible coalition of players-here, the countries) must also reflect in each case the behavior of the players which are not members of the coalition. This has been for a long time a disputed issue in the theory of the core of economies with externalities. Among the several assumptions that can be made as to this behaviour, a plausible one is defined in this paper, for which it is shown that the core of the game is nonempty. The proof is constructive in the sense that it exhibits a strategy (specifying an explicit coordinated abatement policy and including financial transfers) that has the desired property of nondomination by any proper coalition of countries, given the assumed behavior of the other countries. This strategy is also shown to have an equilibrium interpretation in the economic model. 1 Introduction We deal in this paper with an economy with several agents, whose productive activities generate "multilateral" externalities, i.e., externalities that each one of them can both generate and be a recipient of. We have in mind externalitites that are detrimental for the recipients. We also call these externalities "environ- mental" because we assume that they exhibit public goods (actually public "bads") characteristics in the sense that when they are generated, they affect all agents in the economy. We should also call them "additive" because we further assume that what is received by any recipicnt is simply the sum of what is emitted by the various generators. For such an economy we call upon the concept of the core of a cooperative game associated with it, in order to identify joint actions that would (a) improve upon inefficient laissez-faire equilibria, (b) achieve Pareto efficiency, and (c) induce this outcome in such a way that it deters both individual and coalitional free riding behaviours. 0020-7276/97/3/379-401 $2.50 9 1997 Physica-Verlag, Heidelberg