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Widespread Externalities and the f-Core

  • (with Mamoru Kaneko and Myrna Holtz Wooders) “Continuum Economies with Finite Coalitions: Core, Equilibrium and Widespread Externalities,” Journal of Economic Theory 49 (1989), 113–134.


    We develop a new model of a continuum economy with coalitions consisting of only finite numbers of agents. The core, called the f-core, is the set of allocations that are stable against improvement by finite coalitions and feasible by trade within finite coalitions. Even with widespread externalities — preferences depend on own consumptions and also on the entire allocation up to the null set — we obtain the result that the f-core coincides with the Walrasian allocations. Without widespread externalities, the f-core, the Aumann core, and the Walrasian allocations all coincide; however, with widespread externalities there is no obvious natural definition of the Aumann core. ScienceDirect link

  • Four Characterizations of Constrained Pareto Efficiency in Continuum Economies with Widespread Externalities,” Japanese Economic Review 46 (1995), 103–124.


    In continuum economies, widespread externalities are those over which each individual has negligible control. Nash–Walrasian equilibria with lump-sum transfers are defined, and their existence proved. They are then characterized by the property of “f-constrained Pareto efficiency” for finite coalitions. More general “private good” Nash–Walrasian equilibria are characterized as private good constrained Pareto efficient. Introducing complete Pigou taxes or subsidies leads to equilibria that are characterized by constrained efficiency and f-constrained efficiency for given levels of the widespread externalities. But full efficiency requires resolving the public good problem of determining those aggregate externalities or, equivalently, of setting appropriate Pigou prices. PDF file of preprint

  • History as a Widespread Externality in Some Arrow-Debreu Market Games,” in G. Chichilnisky (ed.), Markets, Information and Uncertainty: Essays in Economic Theory in Honor of Kenneth J. Arrow (Cambridge: Cambridge University Press, 1999) ch. 16, pp. 328–361.


    Two Arrow–Debreu market games are formulated whose straightforward Nash equilibria are Walrasian. Both have an auctioneer setting prices to maximize net sales value. In the second an additional redistributive agency maximizes welfare through optimal lump-sum transfers. In intertemporal economies, however, subgame imperfections can arise because agents understand how current decisions such as those determining investment influence either future prices (with finitely many agents), or future redistribution (even in continuum economies). The latter observation undermines the second efficiency theorem of welfare economics. Indeed, when the state of the economy affects future policy, it functions like a “widespread externality.” PDF file of preprint

  • On f-Core Equivalence in a Continuum Economy with General Widespread Externalities,” Journal of Mathematical Economics 32 (1999), 177–184.


    This paper partially extends the f-core equivalence theorem of Hammond, Kaneko and Wooders (1989) for continuum economies with widespread externalities — i.e., those over which each individual has negligible control. Externalities need not result directly from trading activities. Neither free disposal of divisible goods nor monotone preferences are assumed. Instead, a slightly strengthened form of local non-satiation suffices. However, in general it is proved only that any f-core allocation is a compensated Nash–Walrasian equilibrium. Finally, the proof uses an elementary argument which does not rely on Lyapunov’s theorem or convexity of the integral of a correspondence w.r.t. a non-atomic measure. PDF file of preprint

  • History: Sunk Cost or Widespread Externality?” second Arcelli Lecture at the University of Piacenza, April 2007; Warwick Economic Research Paper, no. 808; to appear in Rivista Internazionale di Scienze Sociali (2007), n. 2, 161–185.


    In an intertemporal Arrow–Debreu economy with a continuum of agents, suppose that the auctioneer sets prices while the government institutes optimal lump-sum transfers period by period. An earlier paper showed how subgame imperfections arise because agents understand how their current decisions such as those determining investment will inuence future lump-sum transfers. This observation undermines the second effciency theorem of welfare economics and makes "history" a widespread externality. A two-period model is used to investigate the constrained efficiency properties of different kinds of equilibrium. Possibilities for remedial policy are also discussed. PDF file of preprint

  • The Power of Small Coalitions in Large Economies,” Stanford University, Institute of Mathematical Studies in the Social Sciences, Economics Technical Report No. 501; to appear in M.O.L. Bacharach, M.A.H. Dempster and J.L. Enos (eds.) Mathematical Models in Economics: Oxford University Mathematical Economic Seminar 25th Anniversary Volume (Oxford: Oxford University Press — in press).


    As long as coalitions eventually become large, the Debreu–Scarf limit theorem for the core holds even if coalitions are restricted in size so that their proportion of agents shrinks to zero as the economy becomes infinitely large. Corresponding results hold for non-replica economies. In a limiting continuum economy, the core equivalence theorem holds even if there must be a “measure-consistent” partition of a coalition into self-sufficient subcoalitions each with a finite number of agents. These results help relate standard results to those presented in collaboration with Kaneko and Wooders concerning finite coalitions in continuum economies.