On quasistability radius of a vector trajectorial problem with a principle of optimality generalizing Pareto and lexicographic principles

A multicriterion linear combinatorial problem with a parametric principle of optimality is considered. This principle is defined by a partitioning of partial criteria onto Pareto preference relation groups within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semi-continuity of the multiple-valued mapping that defines the choice function. A formula of quasistability radius is derived for the case of the metric l∞. Some known results are stated as corollaries. Mathematics Subject Classification 2000: 90C05, 90C10, 90C29, 90C31

On stability of Nash equilibrium situations and Pareto optimal situations in finite games

A non-cooperative finite game of several persons is considered in the case, where payoff functions are linear. Extreme levels of independent perturbations of payoff functions parameters, which remain Nash and Pareto optimality of a situation, are specified. Necessary and sufficient conditions of such stability are stated. AMS Mathematics Subject Classification : 90C27, 90C29

On stability of an optimal situation in a finite cooperative game with a parametric concept of equilibrium (from lexicographic optimality to Nash equilibrium)

A parametric concept of equilibrium (principle of optimality) in a finite cooperative game in normal form of several players is introduced. This concept is defined by means of the partition of players into coalitions. Lexicographically optimal situation and Nash equilibrium situation correspond to two special cases of this partition. The quantitative analysis of stability of an optimal situation for the independent perturbations of players' payoff functions is performed. The maximum level of such perturbations which save the optimality of a situation is found. Mathematics Subject Classification 2000: 90C05, 90C10, 90C29, 90C3

On stability in game problems of finding Nash set

A finite game of several players in the case of linear payoff functions is considered. Stability of the problem of finding the set of Nash equilibrium situations is investigated. The formula of the stability radius of this problem is derived