Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the H\"older metric

V. A. Emelichev ; O. V. Karelkina

Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 43-50.

Résumé

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 $l_p$-metric, $1\le p\le\infty$. 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.

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