caa a22 4500 445842237 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00245-010-9110-0 doi (NATIONALLICENCE)springer-10.1007/s00245-010-9110-0 Dynamic Bertrand Oligopoly [Elektronische Daten] [Andrew Ledvina, Ronnie Sircar] 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. Springer Science+Business Media, LLC, 2010 Stochastic differential games nationallicence Nash equilibrium nationallicence Bertrand oligopoly nationallicence Substitutable goods nationallicence Systems of HJB equations nationallicence Asymptotic expansions nationallicence Ledvina Andrew ORFE Department, Princeton University, Sherrerd Hall, 08544, Princeton, NJ, USA aut Sircar Ronnie ORFE Department, Princeton University, Sherrerd Hall, 08544, Princeton, NJ, USA aut Applied Mathematics & Optimization Springer-Verlag 63/1(2011-02-01), 11-44 0095-4616 63:1<11 2011 63 245 https://doi.org/10.1007/s00245-010-9110-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-010-9110-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ledvina Andrew ORFE Department, Princeton University, Sherrerd Hall, 08544, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Sircar Ronnie ORFE Department, Princeton University, Sherrerd Hall, 08544, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 63/1(2011-02-01), 11-44 0095-4616 63:1<11 2011 63 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer