A Representation for Many Player Generalized Divide the Dollar Games

Garrison W. Greenwood () and Daniel Ashlock
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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

Games, 2023, vol. 14, issue 2, 1-15

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.

Keywords: player representation; bargaining games; divide the dollar; N-player mathematical games; evolution strategies (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
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