Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design

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. Keywords Algorithmic game theory · Mechanism design · Approximation algorithmsA preliminary version of these results was presented at SAGT 2015 [8].

New Bounds for Truthful Scheduling on Two Unrelated Selfish Machines

“…Our approach is to formulate a mathematical optimization problem for R n . This approach was not common until recently when several successful truthful or truthful in expectation mechanisms have been constructed using linear or nonlinear programs [2,3,7,15]. This paper continues the trend to combine optimization with mechanism design and has the following contributions: (13) in Corollary 3.…”

“…The generalization considers a broader class of algorithms and provides stronger upper bounds for n ≤ 4. Our approach is fundamentally different from the methods in [2,7,15]. To begin with, our method is suitable for the minimum makespan problem on unrelated machines, while the methods in [2,7,15] are not guaranteed to work for this problem.…”

“…Our approach is fundamentally different from the methods in [2,7,15]. To begin with, our method is suitable for the minimum makespan problem on unrelated machines, while the methods in [2,7,15] are not guaranteed to work for this problem. Next, [2,7,15] use LP relaxations of the corresponding integer programs while we use the tools from continuous optimization to obtain possibly non-linear, but tractable approximations.…”

“…Next, we compare our approach to the existing methods for upper bounds in [2,3,7,15] that use optimization. Our method for upper bounds generalizes the approach by Chen et al [3].…”

“…Monotone in expectation task allocation algorithms can be used in truthful in expectation mechanisms. For certain classes of problems (e.g., for combinatorial auctions), one can convert LP relaxations with rounding into truthful in expectation mechanisms, see Azar et al [2], Elbassioni et al [7] or Lavi and Swamy [15]. Truthful in expectation mechanisms could perform better in expectation than the universally truthful ones.…”