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Pivoting Algorithms For Some Classes Of Stochastic Games: A Survey

Author

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  • S. R. MOHAN

    (Indian Statistical Institute, Delhi Centre, New Delhi-110016, India)

  • S. K. NEOGY

    (Indian Statistical Institute, Delhi Centre, New Delhi-110016, India)

  • T. PARTHASARATHY

    (Indian Statistical Institute, Delhi Centre, New Delhi-110016, India)

Abstract

In this paper, we survey the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies of the players for special cases of nonzero-sum stochastic games, using finite-step algorithms based on pivoting. Examples of finite-step pivoting algorithms are the various simplex-type algorithms, such as the primal simplex or dual simplex method for solving the linear programming problem or Lemke's or Lemke-Howson's algorithm for solving the linear complementarity problem. Also included are Lemke-type algorithms for solving various generalisations of the linear complementarity problem. The survey also includes a few new results and observations.

Suggested Citation

  • S. R. Mohan & S. K. Neogy & T. Parthasarathy, 2001. "Pivoting Algorithms For Some Classes Of Stochastic Games: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 253-281.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000385
    DOI: 10.1142/S0219198901000385
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    Cited by:

    1. Prasenjit Mondal, 2018. "Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs," Operational Research, Springer, vol. 18(2), pages 451-468, July.
    2. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, December.
    3. K. C. Sivakumar & M. S. Gowda & G. Ravindran & Usha Mohan, 2020. "Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India," Annals of Operations Research, Springer, vol. 287(2), pages 565-572, April.
    4. N. Krishnamurthy & S. K. Neogy, 2020. "On Lemke processibility of LCP formulations for solving discounted switching control stochastic games," Annals of Operations Research, Springer, vol. 295(2), pages 633-644, December.
    5. Dipti Dubey & S. K. Neogy & Debasish Ghorui, 2017. "Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 535-554, December.
    6. S. K. Neogy & Prasenjit Mondal & Abhijit Gupta & Debasish Ghorui, 2018. "On Solving Mean Payoff Games Using Pivoting Algorithms," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-26, October.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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