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A Stochastic Competitive Research and Development Race Where “Winner Takes All” with Lower and Upper Bounds

Author

Listed:
  • Pelin G. Canbolat

    (The Technion, Israel Institute of Technology)

  • Boaz Golany

    (The Technion, Israel Institute of Technology)

  • Uriel G. Rothblum

    (The Technion, Israel Institute of Technology)

Abstract

The paper analyzes an environment in which several firms compete over the development of a project. Each firm decides how much to invest in the project while adhering to firm-specific lower and upper investment bounds. The completion time of the project by a firm has exponential distribution with rate that depends linearly on the investment of the firm. The firm that completes the project first collects all its revenues whereas the remaining firms earn nothing. The paper establishes the existence and uniqueness of both the Nash equilibrium and the globally optimal solution, provides explicit representations parametrically in the interest rate, and constructs computationally efficient methods to solve these two problems. It also examines sensitivity of Nash equilibrium to marginal changes in lower and upper bounds.

Suggested Citation

  • Pelin G. Canbolat & Boaz Golany & Uriel G. Rothblum, 2012. "A Stochastic Competitive Research and Development Race Where “Winner Takes All” with Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 986-1014, September.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0066-x
    DOI: 10.1007/s10957-012-0066-x
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    References listed on IDEAS

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    1. 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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