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Cost And Complexity Of Harnessing Games With Payments

Author

Listed:
  • RAPHAEL EIDENBENZ

    (Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland)

  • YVONNE ANNE PIGNOLET

    (IBM Research, Zurich Laboratory, Switzerland)

  • STEFAN SCHMID

    (Deutsche Telekom Laboratories/TU Berlin, Berlin, Germany)

  • ROGER WATTENHOFER

    (Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland)

Abstract

This article studies how a mechanism designer can influence games by promising payments to the players depending on their mutual choice of strategies. First, we investigate the cost of implementing a desirable behavior and present algorithms to compute this cost. Whereas a mechanism designer can decide efficiently whether strategy profiles can be implemented at no cost at all our complexity analysis indicates that computing an optimal implementation is generallyNP-hard. Second, we introduce and analyze the concept ofleveragein a game. The leverage captures the benefits that a benevolent or a malicious mechanism designer can achieve by implementing a certain strategy profile region within economic reason, i.e., by taking the implementation cost into account. Mechanism designers can often manipulate games and change the social welfare by a larger extent than the amount of money invested. Unfortunately, computing the leverage turns out to be intractable as well in the general case.

Suggested Citation

  • Raphael Eidenbenz & Yvonne Anne Pignolet & Stefan Schmid & Roger Wattenhofer, 2011. "Cost And Complexity Of Harnessing Games With Payments," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 13-44.
    • Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:01:n:s0219198911002824
    DOI: 10.1142/S0219198911002824
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    References listed on IDEAS

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    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
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    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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