We present a functional framework for automated Bayesian and worst-case mechanism design, based on a two-stage game model of strategic interaction between the designer and the mechanism participants. At the core of our framework is a black-box optimization algorithm which guides the process of evaluating candidate mechanisms. We apply the approach to several classes of two-player infinite games of incomplete information, producing optimal or nearly optimal mechanisms using various objective functions. By comparing our results with known optimal mechanisms, and in some cases improving on the best known mechanisms, we provide evidence that ours is a promising approach to parametrized mechanism design for infinite Bayesian games.
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Ben-Tal A., Nemirovski A. (2002) Robust optimization: Methodology and applications. Mathematical Programming 92: 453–480
Brandt, F., Sandholm, T., & Shoham, Y. (2007). Spiteful bidding in sealed-bid auctions. In Twentieth International Joint Conference in Artificial Intelligence, Hyderabad, India, pp. 1207–1214.
Brandt, F., & Wei G. (2001). Antisocial agents and Vickrey auctions. In Eighth International Workshop on Agent Theories, Architectures, and Languages. Lecture Notes in Computer Science (Vol. 2333, pp. 335–347). Seattle, WA: Springer.
Byde A. (2006) Applying evolutionary search to a parametric family of auction mechanisms. Australian Journal of Management 31(1): 1–16
Conitzer, V., & Sandholm, T. (2002). Complexity of mechanism design. In Eighteenth Conference on Uncertainty in Artificial Intelligence, Edmonton, AB, Canada, pp. 103–110.
Conitzer, V., & Sandholm, T. (2003a). Applications of automated mechanism design. In UAI-03 Bayesian Modeling Applications Workshop, Acapulco, Mexico.
Conitzer, V., & Sandholm, T. (2003b). Computational criticisms of the revelation principle. In Workshop on Agent Mediated Electronic Commerce-V, Melbourne, Australia.
Corana A., Marchesi M., Martini C., Ridella S. (1987) Minimizing multimodal functions of continuous variables with simulated annealing algorithm. ACM Transactions on Mathematical Software 13(3): 262–280
Cramton P., Gibbons R., Klemperer P. (1987) Dissolving a partnership efficiently. Econometrica 55(3): 615–632
Fleischer, M. (1995). Simulated annealing: Past, present, and future. In Winter Simulation Conference, Arlington, VA, pp. 155–161.
Gallien J. (2006) Dynamic mechanism design for online commerce. Operations Research 54: 291–310
Ganzfried, S., & Sandholm, T. (2010). Computing equilibria by incorporating qualitative models. In Ninth International Conference on Autonomous Agents and Multi-Agent Systems, Toronto, ON, Canada, pp. 183–190.
Guo M., Conitzer V. (2009) Worst-case optimal redistribution of VCG payments in multi-unit auctions. Games and Economic Behavior 67(1): 69–98
Guo M., Conitzer V. (2010) Optimal-in-expectation redistribution mechanisms. Artificial Intelligence 174(5–6): 363–381
McAfee R. P. (1992) Amicable divorce: Dissolving a partnership with simple mechanisms. Journal of Economic Theory 56(2): 266–293
McKelvey, R. D., McLennan, A. M., & Turocy, T. L. (2010). Gambit: Software tools for game theory, version 0.2010.09.01. http://www.gambit-project.org.
McMillan J. (1994) Selling spectrum rights. The Journal of Economic Perspectives 8(3): 145–162
Morgan J., Steiglitz K., Reis G. (2003) The spite motive and equilibrium behavior in auctions. Contributions to Economic Analysis and Policy 2(1): 1102–1107
Myerson R. B. (1981) Optimal auction design. Mathematics of Operations Research 6(1): 58–73
Nisan N. (2007) Introduction to mechanism design (for computer scientists). In: Nisan N., Roughgarden T., Tardos E., Vazirani V. V. (eds) Algorithmic game theory. Cambridge University Press, Cambridge, pp 209–241
Nocedal J., Wright S. (2006) Numerical optimization. Springer, New York
Phelps, S., Parsons, S., McBurney, P., & Sklar, E. (2002) Co-evolutionary mechanism design: A preliminary report. In Workshop on Agent-Mediated Electronic Commerce, Bologna, Italy, pp. 123–142.
Phelps, S., Parsons, S., Sklar, E., & McBurney, P. (2003). Using genetic programming to optimise pricing rules for a double-auction market. In Workshop on Agents for Electronic Commerce, Melbourne, Australia.
Reeves, D. M. (2005). Generating trading agent strategies: Analytic and empirical methods for infinite and large games. PhD thesis, University of Michigan.
Reeves, D. M., & Wellman, M. P. (2004). Computing best-response strategies in infinite games of incomplete information. In Twentieth Conference on Uncertainty in Artificial Intelligence, Banff, Canada, pp. 470–478.
Roth A. E., Peranson E. (1999) The redesign of the matching market for American physicians: Some engineering aspects of economic design. American Economic Review 89: 748–780
Siarry P., Berthiau G., Durbin F., Haussy J. (1997) Enhanced simulated annealing for globally minimizing functions of many continuous variables. ACM Transactions on Mathematical Software 23(2): 209–228
Spall J. C. (2003) Introduction to stochastic search and optimization. Wiley, New York
Vorobeychik, Y. (2009). Simulation-based game theoretic analysis of keyword auctions with low-dimensional bidding strategies. In Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, Montreal, QC, Canada, pp. 583–590.
Vorobeychik, Y., Kiekintveld, C., & Wellman, M. P. (2006). Empirical mechanism design: Methods, with application to a supply-chain scenario. In Seventh ACM Conference on Electronic Commerce, Ann Arbor, MI, pp. 306–315.
Vorobeychik, Y., & Wellman, M. P. (2008). Stochastic search methods for Nash equilibrium approximation in simulation-based games. In Seventh International Conference on Autonomous Agents and Multiagent Systems, Estoril, Portugal, pp. 1055–1062.
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Vorobeychik, Y., Reeves, D.M. & Wellman, M.P. Constrained automated mechanism design for infinite games of incomplete information. Auton Agent Multi-Agent Syst 25, 313–351 (2012). https://doi.org/10.1007/s10458-011-9177-2
- Computational game theory
- Computational mechanism design