Choosing Samples to Compute Heuristic-Strategy Nash Equilibrium

 Title: Choosing Samples to Compute Heuristic-Strategy Nash Equilibrium Author: Walsh, William E.; Parkes, David C.; Das, Rajarshi Note: Order does not necessarily reflect citation order of authors. Citation: Walsh, William E., David C. Parkes, and Rajarshi Das. 2004. Choosing samples to compute Heuristic-Strategy Nash Equilibrium. In Agent-mediated electronic commerce V: Designing mechanisms and systems, ed. P. Faratin, et al., 109-123. New York, NY: Springer. Previously published in Lecture Notes in Computer Science 3048: 109-123. Access Status: Full text of the requested work is not available in DASH at this time (“dark deposit”). For more information on dark deposits, see our FAQ. Full Text & Related Files: Walsh_Choosing.pdf (141.2Kb; PDF) Abstract: Auctions define games of incomplete information for which it is often too hard to compute the exact Bayesian-Nash equilibrium. Instead, the infinite strategy space is often populated with heuristic strategies, such as myopic best-response to prices. Given these heuristic strategies, it can be useful to evaluate the strategies and the auction design by computing a Nash equilibrium across the restricted strategy space. First, it is necessary to compute the expected payoff for each heuristic strategy profile. This step involves sampling the auction and averaging over multiple simulations, and its cost can dominate the cost of computing the equilibrium given a payoff matrix. In this paper, we propose two information theoretic approaches to determine the next sample through an interleaving of equilibrium calculations and payoff refinement. Initial experiments demonstrate that both methods reduce error in the computed Nash equilibrium as samples are performed at faster rates than naive uniform sampling. The second, faster method, has a lower metadeliberation cost and better scaling properties. We discuss how our sampling methodology could be used within experimental mechanism design. Published Version: doi:10.1007/b99040 Other Sources: http://www.eecs.harvard.edu/econcs/pubs/sampling_long.pdf Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4686810 Downloads of this work: