Empirical Mechanism Design: Designing Mechanisms from Data

We introduce a methodology for the design of parametric mechanisms, which are multiagent systems inhabited by strategic agents, with knobs that can be adjusted to achieve specific goals. We assume agents play approximate equilibria, which we estimate using the probably approximately correct learning framework. Under this assumption, we further learn approximately optimal mechanism parameters. We do this both theoretically, assuming a finite design space, and heuristically, using Bayesian optimization (BO). Our BO algorithm incorporates the noise associated with modern concentration inequalities, such as Hoeffding’s, into the underlying Gaussian process. We show experimentally that our search techniques outperform standard baselines in a stylized but rich model of advertisement exchanges.

[1]  Vahab S. Mirrokni,et al.  Sink equilibria and convergence , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[2]  Maria-Florina Balcan,et al.  A General Theory of Sample Complexity for Multi-Item Profit Maximization , 2017, EC.

[3]  Vahab S. Mirrokni,et al.  Bid optimization for broad match ad auctions , 2009, WWW '09.

[4]  Subramanian Ramamoorthy,et al.  Learning Best Response Strategies for Agents in Ad Exchanges , 2018, EUMAS.

[5]  Michael P. Wellman,et al.  Stochastic Search Methods for Nash Equilibrium Approximation in Simulation-based Games , 2022 .

[6]  Eli Upfal,et al.  Learning Simulation-Based Games from Data , 2019, AAMAS.

[7]  Paul W. Goldberg,et al.  The complexity of computing a Nash equilibrium , 2006, STOC '06.

[8]  Michel Gendreau,et al.  Combinatorial auctions , 2007, Ann. Oper. Res..

[9]  E. Maasland,et al.  Auction Theory , 2021, Springer Texts in Business and Economics.

[10]  Yoshua Bengio,et al.  Random Search for Hyper-Parameter Optimization , 2012, J. Mach. Learn. Res..

[11]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[12]  Victor Naroditskiy,et al.  On Approximate Welfare- and Revenue-Maximizing Equilibria for Size-Interchangeable Bidders , 2017, AAMAS.

[13]  Vincent Conitzer,et al.  Computationally Feasible Automated Mechanism Design: General Approach and Case Studies , 2010, AAAI.

[14]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[15]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[16]  Tuomas Sandholm,et al.  Automated Mechanism Design: A New Application Area for Search Algorithms , 2003, CP.

[17]  Claire Mathieu,et al.  Greedy bidding strategies for keyword auctions , 2007, EC '07.

[18]  Michael P. Wellman,et al.  Learning payoff functions in infinite games , 2005, Machine Learning.

[19]  Michal Feldman,et al.  Combinatorial Walrasian Equilibrium , 2016, SIAM J. Comput..

[20]  Yishay Mansour,et al.  Ad Exchange - Proposal for a New Trading Agent Competition Game , 2012, AMEC/TADA.

[21]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[22]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[23]  Michael P. Wellman,et al.  Price Prediction Strategies for Market-Based Scheduling , 2004, ICAPS.

[24]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[25]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[26]  Vijay V. Vazirani,et al.  An Auction-Based Market Equilibrium Algorithm for the Separable Gross Substitutability Case , 2004, APPROX-RANDOM.

[27]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.