Cooperative Game-Theoretic Models of the Cournot Oligopoly

Abstract

In this paper, we build and investigate cooperative games with different characteristic functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot oligopoly game-theoretic models in normal form. Also, we build and investigate cooperative three-player games with the same characteristic functions on the base of these models, including the calculation of Shapley value. We compare payoffs received by the players according to different optimality principles of cooperative games and games in normal form.

Game-Theoretic Models of Coopetition in Cournot Oligopoly

“…For example, it holds when α i = 1 for any i and in the same time c i + b i = c j + b j for some i and j. Then the solution coincides with the solution received in [34,35] with substitution of c i by c i + b i . In this section we will assume that 0 < α i < 1 for any i.…”

“…Korolev and Ougolnitsky analyzed cooperative game theoretic models of Cournot oligopoly [34]. Korolev et al investigated dynamic models of Cournot oligopoly [35].…”

“…In our previous paper [34] in the latter situation we have introduced an indicator of the average sensibility of demand in relation to the marginal costs λ = a c , where a is a demand parameter, c-marginal costs. In our consideration c < a n 2 , and because in the examples n = 3 then λ < 9.…”