Nonlinear Dynamics in a Cournot Duopoly with Different Attitudes towards Strategic Uncertainty

Luciano Fanti,Luca Gori,Mauro Sodini

doi:10.1155/2013/323290

Luciano Fanti, Luca Gori + Show 1 more

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https://doi.org/10.1155/2013/323290

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Abstract

This paper analyses the dynamics of a duopoly with quantity-setting firms and different attitudes towards strategic uncertainty. By following the recent literature on decision making under uncertainty, where the Choquet expected utility theory is adopted to allow firms to plan their strategies, we investigate the effects of the interaction between pessimistic and optimistic firms on economic dynamics described by a two-dimensional map. In particular, the study of the local and global behaviour of the map is performed under three assumptions: (1) both firms have complete information on the market demand and adjust production over time depending on past behaviours (static expectations—“best reply” dynamics); (2) both firms have incomplete information and production is adjusted over time by following a mechanism based on marginal profits; and (3) one firm has incomplete information on the market demand and production decisions are based on the behaviour of marginal profits, and the rival has complete information on the market demand and static expectations. In cases 2 and 3 it is shown that complex dynamics and coexistence of attractors may arise. The analysis is carried forward through numerical simulations and the critical lines technique.

Highlights

In this paper, we analyse the dynamics of a Cournot duopoly under strategic uncertainty with pessimistic and optimistic firms within the framework of a nonlinear dynamic oligopoly as those developed by a recent burgeoning literature.The issue of decision making under uncertainty as distinct from risk has recently been revisited, amongst others, by [2,3,4,5,6]
(1) both firms have complete information on the market demand and use the “best reply” adjustment mechanism to vary production period by period; (2) both firms have incomplete information on the market demand and adjust production by following a mechanism based on marginal profits; (3) one firm has incomplete information and production decisions are based on the behaviour of marginal profits, and the rival has complete information and static expectations
This paper developed a nonlinear Cournot duopoly to study the role of strategic uncertainty on the dynamics of the model economy

Summary

Introduction

We analyse the dynamics of a Cournot duopoly under strategic uncertainty with pessimistic and optimistic firms within the framework of a nonlinear dynamic oligopoly as those developed by a recent burgeoning literature (see [1] and the papers cited therein). In the literature on nonlinear oligopolies, two distinct assumptions with regard to available information are usually made: players have a complete knowledge of the market demand and use some form of expectations about the rival’s strategic variable decision (e.g., naive, rational, or adaptive expectations or, alternatively, some weighted sum of previous rules) to set the price or the quantity in the future period (e.g., [9, 10]); players have limited information about the market demand and use some forms of estimation of their own current marginal profits (e.g., [11,12,13,14]) or other adjustment mechanisms such as the local monopolistic approximation to determine the price or quantity in the future period [15].

The Model

Dynamics under Limited Information

Dynamics under Both Limited and Complete Information

Conclusions