Abstract
R. Lavi and C. Swamy (FOCS 2005, J. ACM 58(6), 25, 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and usually faster multiplicative weights update method instead. The simplification comes at the cost of slightly weaker approximation and truthfulness guarantees.
Highlights
Algorithmic mechanism design is the art of designing and implementing the rules of a game to achieve a desired outcome from a set of possible outcomes
Lavi and Swamy [18, 19] showed that certain linear programming based approximation algorithms for the social welfare problem can be turned into randomized mechanisms that are truthful-in-expectation, i.e., reporting the truth maximizes the expected utility of a player
We first consider the case where the LP-relaxation of SWM in Step 1 of the LS-scheme can be solved exactly and efficiently and our problem reduces to the design of a practical algorithm for Step 2
Summary
Algorithmic mechanism design is the art of designing and implementing the rules of a game to achieve a desired outcome from a set of possible outcomes. The underlying optimization problem is the computation of an outcome maximizing social welfare given the valutions of the players. If the underlying optimization problem can be efficiently solved to optimality, the celebrated VCG mechanism (see, e.g., [20]) achieves truthfulness, social welfare optimization, and polynomial running time. Lavi and Swamy [18, 19] showed that certain linear programming based approximation algorithms for the social welfare problem can be turned into randomized mechanisms. It applies to integer linear programming problems of the packing type for which the linear programming relaxation can be solved exactly and for which an α-integrality gap verifier is available. Step 1 requires solving n + 1 linear programs, one for the fractional solution and one for each price; an exact solution requires the use of the Ellipsoid method
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