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On the Stackelberg strategy in nonzero-sum games

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Abstract

The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated, and necessary and sufficient conditions for its existence are derived. Several game problems, such as games where one of the two players does not know the other's performance criterion or games with different speeds in computing the strategies, are best modeled and solved within this solution concept. In the case of dynamic games, linear-quadratic problems are formulated and solved in a Hilbert space setting. As a special case, nonzero-sum linear-quadratic differential games are treated in detail, and the open-loop Stackelberg solution is obtained in terms of Riccati-like matrix differential equations. The results are applied to a simple nonzero-sum pursuit-evasion problem.

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Authors and Affiliations

  1. Coordinated Science Laboratory and Department of Electrical Engineering, University of Illinois, Urbana, Illinois

    M. Simaan (Research Associate) & J. B. Cruz Jr. (Professor)

Authors
  1. M. Simaan
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  2. J. B. Cruz Jr.
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Communicated by Y. C. Ho

This work was supported in part by the US Air Force under Grant No. AFOSR-68-1579D, in part by NSF under Grant No. GK-36276, and in part by the Joint Services Electronics Program under Contract No. DAAB-07-72-C-0259 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.

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Simaan, M., Cruz, J.B. On the Stackelberg strategy in nonzero-sum games. J Optim Theory Appl 11, 533–555 (1973). https://doi.org/10.1007/BF00935665

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