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

Abstract

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.

Keywords

• non-cooperative finite game
• Nash equilibrium situation
• Pareto and Smale optimal situations
• efficient situations
• situation stability
• situation stability radius