Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric
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V. A. Emelichev
Abstract
We consider a finite cooperative game of several players with parametric principle of optimality such that the relations between players in a coalition are based on the Pareto maximum. The introduction of this principle allows us to find a link between such classical concepts as the Pareto optimality and the Nash equilibrium. We carry out a quantitative analysis of the stability of the game situation which is optimal for the given partition method with respect to perturbations of parameters of the payoff functions in the space with the Hölder lp-metric, 1 ≤ p ≤ ∞. We obtain a formula for the radius of stability for such situation, so we are able to point out the limiting level for perturbations of the game parameters such that the optimality of the situation is preserved.
© de Gruyter 2009
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- New methods of investigation of perfectly balanced Boolean functions
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- Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
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Articles in the same Issue
- Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric
- New methods of investigation of perfectly balanced Boolean functions
- On completeness and A-completeness of S-sets of determinate functions containing all one-place determinate S-functions
- On repetition-free Boolean functions over pre-elementary monotone bases
- Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
- Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials
- On a class of statistics of polynomial samples
- Score lists in [h-k]-bipartite hypertournaments
- On one statistical model of steganography
