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On The Complexity Of Coalitional Reasoning

Author

Listed:
  • MARC PAULY

    (Department of Computer Science, University of Liverpool, Liverpool L69 7ZF, United Kingdom)

Abstract

Coalitional power in multistage processes is modeled using effectivity frames, which link an effectivity function to every possible state of the world. Effectivity frames are general enough to capture, e.g., what groups of agents can bring about in extensive games of perfect and almost perfect information. Coalition Logic is used to describe effectivity frames, and the question of generating an extensive game satisfying a given specification is formulated as a satisfiability problem in Coalition Logic. Using this logical reformulation, we show that the complexity of this implementation problem depends on two parameters: For coalitional specifications, the problem is shown to be PSPACE-complete. For individual specifications on the other hand, i.e., for specifications which only refer to the powers of individual agents, generating an implementation with perfect information is PSPACE-complete, whereas generating an implementation with almost perfect information is NP-complete.

Suggested Citation

  • Marc Pauly, 2002. "On The Complexity Of Coalitional Reasoning," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 237-254.
    • Handle: RePEc:wsi:igtrxx:v:04:y:2002:i:03:n:s0219198902000677
    DOI: 10.1142/S0219198902000677
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    Keywords

    Effectivity functions; modal logic; complexity theory; mechanism design;
    All these keywords.

    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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