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Nash equilibria in a model of multiproduct price competition: an assignment problem

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  • Arribas, Ivan
  • Urbano, Amparo

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 subgame perfect Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exits. The (subgame perfect) 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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  • Arribas, Ivan & Urbano, Amparo, 2005. "Nash equilibria in a model of multiproduct price competition: an assignment problem," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 351-385, April.
    • Handle: RePEc:eee:mateco:v:41:y:2005:i:3:p:351-385
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    1. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
    2. Perez-Castrillo, David & Sotomayor, Marilda, 2002. "A Simple Selling and Buying Procedure," Journal of Economic Theory, Elsevier, vol. 103(2), pages 461-474, April.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    5. Tauman, Yair & Urbano, Amparo & Watanabe, Junichi, 1997. "A Model of Multiproduct Price Competition," Journal of Economic Theory, Elsevier, vol. 77(2), pages 377-401, December.
    6. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    7. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    8. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    9. Shaked, Avner & Sutton, John, 1983. "Natural Oligopolies," Econometrica, Econometric Society, vol. 51(5), pages 1469-1483, September.
    10. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    11. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    12. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    13. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    14. Jaskold Gabszewicz, J. & Thisse, J. -F., 1980. "Entry (and exit) in a differentiated industry," Journal of Economic Theory, Elsevier, vol. 22(2), pages 327-338, April.
    15. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    1. Arribas, I. & Urbano, A., 2018. "Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 83-94.
    2. Arribas, I. & Urbano, A., 2017. "Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 167(C), pages 14-38.
    3. Ivan Arribas & Amparo Urbano, 2004. "Mixed Bundling Strategies And Multiproduct Price Competition," Working Papers. Serie AD 2004-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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    More about this item

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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