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Fixed-point theorems for multi-valued mappings and economic equilibrium existence theorems are generalized from the viewpoint that the continuity and/or convexity assumptions on a mapping may be replaced by weaker local conditions on the vector ®eld de®ned by the mapping. The generalization gives us natural conditions on individual (possibly non-ordered) preferences or aggregated demand behaviours so that we may obtain several extensions of recent results in social and game-theoretic equilibrium theories. JEL Classi®cation Numbers: C60, C62, C72, D50, D51.

In this paper, we introduce production into the standard general equilibrium model with asymmetric information, which was proposed by Dubey et al. (Cowles Foundation Discussion Paper 2000; Econometrica 2005). In such an economy, there is no rational explanation for producers’ delivery upper bounds while the endowments naturally limit consumers’ deliveries. However, we show that the typical equilibrium allocation of the asymmetric information economy necessarily and substantially depends on such exogenous upper bounds (Example 1 and Theorem 1). In other words, an equilibrium existence theorem without such upper bounds, even if such exists, will typically fail to treat the asymmetric information problem, e.g., the adverse selection problem. Hence, to treat the equilibrium existence problem under the informational asymmetry appropriately, we have to extend the standard model so that the delivery upper bounds need not to be specified explicitly. For this purpose, we propose a quite natural and realistic assumption with respect to the technological condition related to the market delivery, i.e., the existence of some small standardization, commoditization, and/or transaction costs of market deliveries is shown to be sufficient (Theorem 3).

An overlapping generations model with the double infinity of commodities and agents is the most fundamental framework to introduce outside money into a static economic model. In this model, competitive equilibria may not necessarily be Pareto-optimal. Although Samuelson (1958) emphasized the role of fiat money as a certain kind of social contract, we cannot characterize it as a cooperative game-theoretic solution like a core. In this paper, we obtained a finite replica core characterization of Walrasian equilibrium allocations under non-negative wealth transfer and a core-limit characterization of Samuelson's social contrivance of money. Preferences are not necessarily assumed to be ordered.

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