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Full-Text Articles in Social and Behavioral Sciences
The Existence Of Maximal Elements And Equilibria In The Absence Of Transitivity, Ted Bergstrom
The Existence Of Maximal Elements And Equilibria In The Absence Of Transitivity, Ted Bergstrom
Ted C Bergstrom
This paper generalizes results of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive binary relations. It proves a generalization of Nash's theorem on the existence of non-cooperative equilibrium. It also shows that existence of competitive equilibrium can be proved as a consequence of the existence of a maximal element for an appropriately chosen binary relation.
The Core When Strategies Are Restricted By Law, Ted Bergstrom
The Core When Strategies Are Restricted By Law, Ted Bergstrom
Ted C Bergstrom
The alpha-core is defined to be the set of feasible allocations such that no coalition can do better for its members by selecting alternative strategies given “worst-case” assumptions about the behavior of other players. This paper explores the way that the alpha-core of a game is affected by restrictions on the legally admissible strategies of the players. It also explores the relation between Lindahl equilibrium and alpha-cores with suitable restrictions on strategies.