Cournot competition under uncertainty: conservative and optimistic equilibria

Abstract

In this paper we analyze competition between firms with uncertain demand functions. A duopoly model is considered in which two identical firms producing homogeneous commodities compete in quantities. They face uncertain market demand in a context in which two different future scenarios are possible, and no information about the probability distribution of occurrence of the scenarios is available.This decision-making situation is formalized as a normal-form game with vector-valued utility functions for which the notion of Pareto equilibrium is adopted as a natural extension of that of Cournot equilibrium. Under standard assumptions about the demand functions, we characterize the complete set of Pareto equilibria. In the second part of the paper, we analyse the equilibria to which the agents will arrive depending on their attitude to risk. We find that equilibria always exist if both agents are simultaneously pessimistic or optimistic. In the non-trivial cases, for pessimistic firms, infinitely many equilibria exist, whereas when firms act optimistically, only those pairs of strategies corresponding to the Cournot equilibria in each scenario can be equilibria.

Duopolistic competition with multiple scenarios and different attitudes toward uncertainty

“…This generalizes the result obtained by Caraballo et al. () for linear models. Moreover, in linear models, when both firms are optimistic, equilibria always exist, while this cannot be assured for the general model.…”

“…The consequence of the symmetry of the model is that the set of conservative equilibria is a symmetric set. This generalizes the result obtained by Caraballo et al (2015) for linear models. Moreover, in linear models, when both firms are optimistic, equilibria always exist, while this cannot be assured for the general model.…”

“…As a consequence of this result, when only a switch between scenarios occurs, the existence of equilibria is assured. This is the case of linear demand functions as shown in Caraballo et al (2015).…”

“…That is, we study the cases in which both firms have the same attitude to uncertainty, and the cases in which this attitude is different. In Caraballo et al (2015), we analyzed duopolistic competitions under uncertainty in which demand functions are linear and the firms exhibit identical extreme attitudes toward uncertainty. Now, we extend and complete the investigation of strategic competition between firms in a multiple scenario framework.…”

Radar Waveform Strategy Based on Game Theory

“…Ref. [23] analyzed the game equilibria always exist if two agents have symmetric information. If a game is competitive and has a unique pure-strategy Nash equilibrium, all the players prefer to stay at Nash equilibrium under the assumptions of conservativeness and rationality.…”