Applying metaheuristic techniques to search the space of bidding strategies in combinatorial auctions

Many non-cooperative settings that could potentially be studied using game theory are characterized by having very large strategy spaces and payoffs that are costly to compute. Best response dynamics is a method of searching for pure-strategy equilibria in games that is attractive for its simplicity and scalability (relative to more analytical approaches). However, when the cost of determining the outcome of a particular set of joint strategies is high, it is impractical to compute the payoffs of all possible responses to the other players actions. Thus, we study metaheuristic approaches--genetic algorithms and tabu search in particular--to explore the strategy space. We configure the parameters of metaheuristics to adapt to the problem of finding the best response strategy and present how it can be helpful in finding Nash equilibria of combinatorial auctions which is an important solution concept in game theory.

[1]  P. Cramton.  The FCC Spectrum Auctions: An Early Assessment , 1997 .

[2]  Ronald M. Harstad,et al.  Computationally Manageable Combinational Auctions , 1998 .

[3]  J. Nash.  Two-Person Cooperative Games , 1953 .

[4]  R. Gibbons.  Game theory for applied economists , 1992 .

[5]  F. Kelly,et al.  A Combinatorial Auction with Multiple Winners for Universal Service , 2000 .

[6]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[7]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[8]  Sven de Vries,et al.  Combinatorial Auctions: A Survey , 2003, INFORMS J. Comput..

[9]  S. Griffis.  EDITOR , 1997, Journal of Navigation.

[10]  R. Cassady.  Auctions and Auctioneering , 2023 .

[11]  Andrew McLennan,et al.  Gambit: Software Tools for Game Theory , 2006 .

[12]  Robert Wilson,et al.  A global Newton method to compute Nash equilibria , 2003, J. Econ. Theory.

[13]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[14]  M. R. Rao,et al.  Combinatorial Optimization , 1992, NATO ASI Series.

[15]  Ashish Sureka,et al.  Using tabu best-response search to find pure strategy nash equilibria in normal form games , 2005, AAMAS '05.

[16]  A. Talman,et al.  Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general labelling , 1987 .

[17]  S. Rassenti,et al.  A Combinatorial Auction Mechanism for Airport Time Slot Allocation , 1982 .

[18]  R. McKelvey,et al.  Computation of equilibria in finite games , 1996 .