Mathematical methods of game and economic theory. (English) Zbl 0452.90093

Aubin, Jean-Pierre

Studies in Mathematics and its Applications, Vol. 7. Amsterdam, New York, Oxford: North-Holland Publishing Company. XXXII, 619 p. $ 109.75; Dfl. 225.00 (1979).

MSC:

91Axx	Game theory
91-02	Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
91B50	General equilibrium theory
46A03	General theory of locally convex spaces
46B99	Normed linear spaces and Banach spaces; Banach lattices
46C99	Inner product spaces and their generalizations, Hilbert spaces
49N15	Duality theory (optimization)
91A99	Game theory
49J27	Existence theories for problems in abstract spaces
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

mathematical economics; convex analysis; optimization theory; continuity; compactness; convexity; fixed point theorems; Kuhn-Tucker theory; infinite dimensional spaces; Banach spaces; Hilbert spaces; Hausdorff locally convex spaces; spaces with the Mackey topology; indicators; support functions; recession cones; barrier cones; variational inequalities; existence; uniqueness; characterization of solutions; Hahn- Banach separation theorem; duality in finite dimensional spaces; stability of solutions; subdifferentiability; perturbations of the objective function; game theory; general economic equilibrium; cooperative games; Nash bargaining solution; core; Shapley value; iterated games; constrained games; fuzzy coalitions; fuzzy core; nucleous; minisup theorem; Ky Fan’s inequality; Walrasian allocations; non-linear analysis; optimal control theory; duality in infinite dimensional spaces