How Many People Can Be Controlled in a Group Pursuit Game

Part of the Theory and Decision Library book series (TDLC, volume 36)

Abstract

In this paper we study a time-optimal model of pursuit. The game is supposed to be a nonzero-sum simple pursuit game between a pursuer and m evaders acting independently of each other. Here we assume that the evaders are discriminated and dictated the extremely disadvantageous behaviour by the pursuer who has an element of punishment at his disposal. The aim of this paper is to find an equilibrium situation and to define the maximum number of participants of the game that can be kept in submission. For every evader we construct a realizability area of punishment strategy and investigate the question of its existence depending on various initial positions of the players P and E i , i = 1,..., m.

Keywords

Nash Librium NASH 

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References

  1. Isaacs, R. (1965), Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit. Control and Optimization. New York: Wiley.Google Scholar
  2. Owen, G. (1995), Game Theory, 3rd edn. San Diego: Academic Press.Google Scholar
  3. Petrosjan, L. and Tomskii, G. (1983), Geometry of Simple Pursuit. Moscow: Science.Google Scholar
  4. Tarashnina, S. (1998), Nash Equilibria in a Differential Pursuit Game with one Pursuer and m Evaders. Game Theory and Applications, Vol. 3. New York: Nova Science, 115–123Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  1. 1.Faculty of Applied Mathematics and Control ProcessesSaint-Petersburg State UniversityPetrodvorets, Saint-PetersburgRussia

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