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A Representation for Many Player Generalized Divide the Dollar Games

Author

Listed:
  • Garrison W. Greenwood

    (Department of Electrical & Computer Engineering, Portland State University, Portland, OR 97207-0751, USA)

  • Daniel Ashlock

    (Department of Mathematics and Statistics, University of Guelph, Guelph, ON N1G 2W1, Canada)

Abstract

Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has n > 2 players. Evolutionary algorithms can be used to evolve individual players for this generalized game but representation—i.e., a genome plus a move or search operator(s)—must be carefully chosen since it affects the search process. This paper proposes an entirely new representation called a demand matrix. Each individual in the evolving population now represents a collection of n players rather than just an individual player. Players use previous outcomes to decide their choices (bids) in the current round. The representation scales linearly with the number of players and the move operator is a variant of an evolution strategy. The results indicate that this proposed representation for the generalized divide the dollar game permits the efficient evolution of large player populations with high payoffs and fair demand sets.

Suggested Citation

  • Garrison W. Greenwood & Daniel Ashlock, 2023. "A Representation for Many Player Generalized Divide the Dollar Games," Games, MDPI, vol. 14(2), pages 1-15, February.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:2:p:19-:d:1077719
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    References listed on IDEAS

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    1. de Clippel, Geoffroy & Moulin, Herve & Tideman, Nicolaus, 2008. "Impartial division of a dollar," Journal of Economic Theory, Elsevier, vol. 139(1), pages 176-191, March.
    2. Murali Agastya, 1997. "Adaptive Play in Multiplayer Bargaining Situations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 411-426.
    3. Nejat Anbarci, 2001. "Divide-the-Dollar Game Revisited," Theory and Decision, Springer, vol. 50(4), pages 295-303, June.
    4. Ken Binmore, 1998. "Game Theory and the Social Contract - Vol. 2: Just Playing," MIT Press Books, The MIT Press, edition 1, volume 2, number 0262024446, December.
    5. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
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