A Dynamic Model of Bertrand Competition for an Oligopolistic Market
We study an infinitely-repeated Bertrand competition game among a fixed number of firms in a market of both stochastic entry and stochastic demand. A firm’s entry into market in the next period is possible by making a positioning investment with stochastic success rate. The market demand in the next period is also stochastic and will not be realized until the firm enters the market. A successful investment allows a firm to participate in the Bertrand competition and an unsuccessful investment prevents a firm from entering the market, for the next period. We characterize the symmetric Markov perfect Nash Equilibrium (SMPNE) of such a dynamic game, where a firm’s strategy consists of two components: positioning strategy and pricing strategy. In examples with 1, 2, and 3 firms, we show the stage game market outcome, present the dynamic process of market structure, solve for the steady state of the dynamic system, and discuss about the speed of convergence to the steady state. Our work contributes to the dynamic oligopoly literature by allowing for two dimensions of stochastic uncertainty in firms’ decision-making.
KeywordsDynamic market Positional investment Demand uncertainty Bertrand competition
We thank Editors Leon A. Petrosyan, Vladimir Mazalov, Nikolay A. Zenkevich and an anonymous reviewer for helpful comments. We are grateful to B. Curtis Eaton, Jaimie W. Lien and Vladimir V. Mazalov for beneficial discussions and suggestions. This research is funded by National Natural Science Foundation of China (Projects No. 61661136002 and No. 71873074), the Fundamental Research Funds for the Central Universities, Tsinghua University Initiative Scientific Research Grant (Project No. 20151080397), and the Fundamental Research Funds for the Central Universities (Project No. 2016QD012). All errors are our own.
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