Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization

Article Abstract:

Conditions for generalizing the Weierstrass theorem and the maximum theorem proposed by Berge (1959) are derived. To obtain these, a new class of transfer continuities is introduced. Subsequently, Walker's maximum theorem (1979) is also generalized by 'relaxing the openness of the graph of preference correspondences and the lower semi-continuity of the feasible action correspondence. Using these generalizations, existence theorems on the Nash equilibrium of games and equilibrium of generalized games are also generalized.

Research, Equilibrium (Economics)

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Non-cooperative games on hyperfinite Loeb spaces

Article Abstract:

A study was conducted to characterize a category of measure spaces called hyperfinite Loeb spaces as a model of situations in which individual players are strategically negligible. The influence of the Nash equilibrium on the game-theoretic situations was examined. Results indicated that a sequence of finite games supporting an increasing number of players or sample points cannot always be represented by a limit game on a Lebesgue space.

Econometrics & Model Building, Analysis, Business models

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