Nash equilibria in a model of multiproduct price competition: an assignment problem |
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Affiliation: | 1. School of Finance, Renmin University of China, China;2. Department of Economics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong;1. Center Leo Apostel for Interdisciplinary Studies (CLEA), Free University of Brussels (VUB), Krijgskundestraat 33, 1160 Brussels, Belgium;2. Block 28 Lot 29 Phase III F1, Kaunlaran Village, Caloocan City, Philippines;3. School of Business and Research Centre IQSCS, University of Leicester, University Road, LE1 7RH Leicester, United Kingdom;1. Department of Economics and Management, University of Pisa, Italy;2. CNRS, CMAP - Ecole Polytechnique, France |
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Abstract: | We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers’ value function determines their willingness to pay for subsets of goods. We show that Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exist. The Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem’s projection on the firms’ price vectors. We identify the Nash-equilibrium prices for monotonic buyers’ value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game. |
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