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Препринт

Rational decision making under uncertainty of reaction: Nash-2 equilibrium concept

The paper examines an interaction of boundedly rational agents that are able to calculate their benefits after reaction of an opponent to their own deviations from the current strategy. Accounting for strategic aspects of interaction among players can be implemented as a generalization of the Nash equilibrium concept. This is a possible compromise behavior: not absolutely myopic as Nash concept and not as wise as supergame approach. This leads to a farsighted equilibrium concept that we call a Nash-2 equilibrium. We prove the existence of Nash-2 equilibrium for almost every 2-person game and discuss the problem of possible multiplicity of such equilibria. For a number of models (Bertrand duopoly with homogeneous and heterogeneous product, Cournot duopoly, Tullock contest) the Nash-2 equilibrium sets are obtained and treated as tacit collusion or strong competition depending additional security considerations. For n-person games the idea of selective farsightness is introduced by means of reflection network among players. Examples demonstrate that the reflection network topology fundamentally affects possible equilibria.