Abstract
Abstract The paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.
Highlights
A wide class of economic, social and political processes are well described by the methods of game theory
We introduce the concept of weak equilibrium according to Berge
Nash equilibrium; WBE — number of starting points when searching for a weak Berge equilibrium; tNE — the total amount of time to search a Nash equilibrium for the series of 10 games; tWBE — the total amount of time to search a weak Berge equilibrium for the series of 10 games
Summary
A wide class of economic, social and political processes are well described by the methods of game theory. In N-person games (N ≥ 3) with a finite set of strategies, the Berge equilibrium may not exist in the class of mixed strategies. Such example was constructed, in particular, in [11]. If the goals of two players are opposite, the third player will not be able to apply the Golden Rule to them simultaneously.
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