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Compact Representations Of Search In Complex Domains

Author

Listed:
  • YOSI BEN-ASHER

    (CS department haifa university, Haifa, Israel)

  • EITAN FARCHI

    (I.B.M Research Center, Haifa, Israel)

Abstract

We introduce a new zero-sum matrix game for modeling search in structured domains. In this game, one player tries to find a "bug" while the other tries to hide it. Both players exploit the structure of the "search" domain. Intuitively, this search game is a mathematical generalization of the well known binary search. The generalization is from searching over totally ordered sets to searching over more complex search domains such as trees, partial orders and general set systems. As there must be one row for every search strategy, and there are exponentially many ways to search even in very simple search domains, the game's matrix has exponential size ("space"). In this work we present two ways to reduce the space required to compute the Nash value (in pure strategies) of this game:• First we show that a Nash equilibrium in pure strategies can be computed by using a backward induction on the matrices of each "part" or sub structure of the search domain. This can significantly reduce the space required to represent the game.• Next, we show when general search domains can be represented as DAGs (Directed Acycliqe Graphs). As a result, the Nash equilibrium can be directly computed using the DAG. Consequently the space needed to compute the desired search strategy is reduced toO(n2)wherenis the size of the search domain.

Suggested Citation

  • Yosi Ben-Asher & Eitan Farchi, 2005. "Compact Representations Of Search In Complex Domains," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 73-90.
  • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:01:n:s0219198905000399
    DOI: 10.1142/S0219198905000399
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    Keywords

    Nash equilibrium; search games; pure strategies; mixed strategies;
    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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