Approximate equilibrium in pure strategies for non-atomic games

Article Abstract:

Existence of a symmetric approximate equilibrium in pure strategies is established for an anonymous non-atomic game with a continuum of strategies. A corollary on assignment games with additively separable payoffs is also presented. Analysis deals with games with an uncountable number of players of each type. Symmetric equilibrium is demonstrated if payoffs are equicontinuous functions of the player's own strategy and the joint distribution. The auxialiary game with measure-valued payoffs is studied and density of degenerate best-response profiles established.

Game theory, Equilibrium (Economics)

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On the differentiability of the consumer demand function

Article Abstract:

Existing demand and utility function models are extended to prove the differentiability, separatability and concave quasilinearity of utility functions. The extensions, which include the assumption of positive Lipschitzian marginal utilities, proves the demand functions' complete differentiability. The result is applicable to infinite number of prices and income sets but does not encompass the concave quasilinearity utility which does not depend on the differentiability factor.

Research, Economic aspects, Consumer preferences, Utility theory, Utility functions, Demand functions (Economics), Demand functions

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Overlapping generations models with incomplete markets

Article Abstract:

A situation is modeled wherein overlapping generations have equilibria and an exchange economy has incomplete markets, bounded short sales, and one-period real assets. The model is defined for a continuum of tree branches.

Markets (Economics), Mathematical models, Continuity, Continuity (Mathematics)

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