Mathematical Methods of Operations Research

, Volume 52, Issue 2, pp 237–249

On a game in manufacturing

Authors

  • V. J. Baston
    • Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom (e-mail: vjdb@maths.soton.ac.uk)
  • A. Y. Garnaev
    • Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom (e-mail: vjdb@maths.soton.ac.uk)

DOI: 10.1007/s001860000075

Cite this article as:
Baston, V. & Garnaev, A. Mathematical Methods of OR (2000) 52: 237. doi:10.1007/s001860000075

Abstract.

We analyse a non-zero sum two-person game introduced by Teraoka and Yamada to model the strategic aspects of production development in manufacturing. In particular we investigate how sensitive their solution concept (Nash equilibrium) is to small variations in their assumptions. It is proved that a Nash equilibrium is unique if it exists and that a Nash equilibrium exists when the capital costs of the players are zero or when the players are equal in every respect. However, when the capital costs differ, in general a Nash equilibrium exists only when the players' capital costs are high compared to their profit rates.

Key words: Game theory, Nash equilibrium, game of timing, non-zero sum game.
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© Springer-Verlag Berlin Heidelberg 2000