By A. van der Neut

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However, this may not be feasible for a coalition S without calling on the resources of the adverse coalition. This is a serious issue since S is not, in general, the grand coalition. The core allocation found in Example 4 is a recursive core allocation for that game. Indeed, it is not surprising that the payoff functions motivated by a "theory of justice" are consistent with both core allocation ideas. The existence of recursive core allocations in Examples 4 and 5 imply the recursive core is non-empty for at least some games.

3 I have added some new results stimulated by the work of Geistdoerfer-Florenzano (1982), Moore (1975), McKenzie (1981) and Mehta (1987) as wen as several examples, motivating discussions and references to more recent literature. This paper shows that Nash equilibrium and competitive equilibrium exist as maximal elements of judiciously chosen non-transitive binary relations that are continuous enough and convex enough to have maximal elements. That this should be possible is strongly suggested by the structure of Gale and Mas Colen's proof.

Moore proves the existence of quasi-equilibrium without assuming Wi E Xi for a model with transitive, locally nonsatiated preferences. Moore uses an assumption that each consumer is "productive in the economy", which is very similar to our "conflict of interest" assumption. McKenzie {1981} extended Moore's results to the case of preferences which need not be transitive or locally nonsatiated. 15 While it is probably true that in a modern economies, many consumers would not live long without trade, it is not obvious that the "consumption sets" of equilibrium theory should be identified with sets of commodity bundles that allow a person to "survive".