Dynamic Bertrand Oligopoly |
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Authors: | Andrew Ledvina Ronnie Sircar |
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Institution: | 1.ORFE Department,Princeton University,Princeton,USA |
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Abstract: | We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another
by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the
dynamic setting. Within the static game, we characterize the Nash equilibrium when there are N players with heterogeneous costs. In the dynamic game with uncertain market demand, firms of different sizes have different
lifetime capacities which deplete over time according to the market demand for their good. We setup the nonzero-sum stochastic
differential game and its associated system of HJB partial differential equations in the case of linear demand functions.
We characterize certain qualitative features of the game using an asymptotic approximation in the limit of small competition.
The equilibrium of the game is further studied using numerical solutions. We find that consumers benefit the most when a market
is structured with many firms of the same relative size producing highly substitutable goods. However, a large degree of substitutability
does not always lead to large drops in price, for example when two firms have a large difference in their size. |
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