Abstract
In this chapter we announce a result on computing a set of stationary equilibrium strategies of the players in a n-person nonzero sum discounted stochastic game in which the transition probabilities depend on the actions of a single player by formulating the problem as a linear complementarity problem that can be solved by Lemke’s algorithm. This result has been published elsewhere. See Mohan, Neogy, and Parthasarathy in Complementarity and Variational Problems—State of Art, edited by M.C. Ferris and J-S. Pang (SIAM Philadelphia, 1997) 284-294.
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References
C. E. Lemke. “Bimatrix equilibrium points and mathematical programming,” Management Sci., 11, pp. 681–689, 1965.
A. S. Nowak and T. E. S. Raghavan. “A finite step algorithm via a bimatrix game to a single controller nonzero-sum stochastic game,” Mathematical Programming, 59, pp. 249–259, 1993.
T. Parthasarathy and T. E. S. Raghavan. “An orderfield property for stochastic games when one player controls transition probabilities,” J. Optimization Theory and Appl., 33, pp. 375–392, 1981.
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© 1999 Springer Science+Business Media New York
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Mohan, S.R., Neogy, S.K., Parthasarathy, T. (1999). On Linear Complementarity and A Discounted Polystochastic Game. In: Bardi, M., Raghavan, T.E.S., Parthasarathy, T. (eds) Stochastic and Differential Games. Annals of the International Society of Dynamic Games, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1592-9_10
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DOI: https://doi.org/10.1007/978-1-4612-1592-9_10
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