A Stochastic Competitive Research and Development Race Where ‘Winner Takes All’ with Lower and Upper Bounds

A Stochastic Competitive Research and Development Race Where ‘Winner Takes All’ with Lower and Upper Bounds

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Article ID: iaor20124817
Volume: 154
Issue: 3
Start Page Number: 986
End Page Number: 1014
Publication Date: Sep 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: game theory, simulation, research
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.

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