Optimal Amount and Timing of Investment in a Stochastic Dynamic Cournot Competition

Yasunori Fujita

doi:10.4236/tel.2016.61001

Abstract

By making use of the optimal stopping theory, we construct a multi-stage stochastic Cournot model to examine the effect of increase in uncertainty and number of entrants on the amount and timing of strategic cost reduction investment. It is revealed that firms should enlarge and postpone the investment if 1) the market is more uncertain, or 2) there exist more firms in the market.

Highlights

Studies on oligopolistic markets under uncertainty, which progressed by paying attention to information sharing with rivals (Basar and Ho (1974) [1], Ponssard (1979) [2], Novshek and Sonnenschein (1982) [3], Gal-Or (1986) [4], etc.), have entered a new stage since Youn and Tremblay (2015) [5] introduced Brownian motion into the modelling of quantity competition
We construct a multi-stage stochastic Cournot model based on the optimal stopping theory to examine the effect of increase in uncertainty and number of entrants on the amount and timing of the strategic cost reduction investment
By constructing a theoretical model that combines Cournot competition with stochastic motion, the present paper attempts to examine the effect of an increase in uncertainty and number of entrants on the amount and timing of the strategic cost reduction investment

Summary

Introduction

Studies on oligopolistic markets under uncertainty, which progressed by paying attention to information sharing with rivals (Basar and Ho (1974) [1], Ponssard (1979) [2], Novshek and Sonnenschein (1982) [3], Gal-Or (1986) [4], etc.), have entered a new stage since Youn and Tremblay (2015) [5] introduced Brownian motion into the modelling of quantity competition. As earlier studies that utilized stochastic motions for formulation of quantity competition, Fujita (2007) [6] revealed the consequences of interaction of exporting firms and Fujita (2008) [7] demonstrated another economic channel for the excess entry theorem, by combining market equilibrium theory with optimal stopping theory, which had been used to develop strategies on timing in a stochastically fluctuating economy since McDonald and Siegel (1986) [8] demonstrated the “value of waiting”. (2016) Optimal Amount and Timing of Investment in a Stochastic Dynamic Cournot Competition. We construct a multi-stage stochastic Cournot model based on the optimal stopping theory to examine the effect of increase in uncertainty and number of entrants on the amount and timing of the strategic cost reduction investment. It is revealed that firms should enlarge and postpone the investment if 1) the market is more uncertain, or 2) there exist more firms in the market

Basic Model

Condition for the Optimal Timing of the Investment

Optimal Amount and Timing of the Investment

Concluding Remarks