On the Approximability of Budget Feasible Mechanisms

Abstract

Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint. We consider the problem of designing truthful budget feasible mechanisms for general submodular functions: we give a randomized mechanism with approximation ratio 7.91 (improving the previous best-known result 112), and a deterministic mechanism with approximation ratio 8.34. Further we study the knapsack problem, which is special submodular function, give a 2+ √ 2 approximation deterministic mechanism (improving the previous best-known result 6), and a 3 approximation randomized mechanism. We provide a similar result for an extended knapsack problem with heterogeneous items, where items are divided into groups and one can pick at most one item from each group.Finally we show a lower bound of approximation ratio of 1 + √ 2 for deterministic mechanisms and 2 for randomized mechanisms for knapsack, as well as the general submodular functions. Our lower bounds are unconditional, which do not rely on any computational or complexity assumptions.

Optimizing budget allocation among channels and influencers

“…This is consistent with common practices in organizations (e.g., working in multiplications of some fixed value) and related simulations [27]. Other work relating to the subject of budget constraints in markets and advertising appears in [6,14,8,2,5,29,7]. side model.…”

Mechanisms for complement-free procurement

“…The main result in [18] shows that for any increasing submodular function there is universally truthful constant factor approximation mechanism that is budget feasible. In [6] improved approximation ratios were achieved for the submodular case as well as various problems within the submodular class through use of sophisticated analysis. The framework has been adopted in the study of designing auctions for procuring private data [13] dynamic auctions [10] as well as other domains [6].…”

“…The frugality approach deals with buyer objectives with 0-1 values (e.g., the buyer wants the set of edges to be a spanning tree of a graph, and all spanning trees are equally desirable). 1 An alternative to frugality which encompasses much more general objectives, is the budget feasibility framework introduced in [18] and subsequently studied in [6,13,10]. In budget feasibility, our goal is to optimize the buyer's objective under a budget constraint.…”

Mechanisms for Fair Attribution

“…An alternative notion is that of budget feasible mechanism design initiated by Singer [2010] where the goal is to optimize a utility function under a hard budget constraint. This concept enables surprisingly positive results and has been studied in algorithmic mechanism design [Chen et al 2011;Dobzinski et al 2011;Badanidiyuru et al 2012;Bei et al 2012;Anari et al 2014] and used in various application domains that include social network analysis [Singer 2012], crowdsourcing [Yang et al 2012;Singer and Mittal 2013;Singla and Krause 2013b] and privacy auctions [Dandekar et al 2013;Singla and Krause 2013a]. The setting that we study most resembles that of budget feasible mechanism design.…”

“…In standard mechanism design settings, the costs are private information and agents are strategic. In such scenarios a reasonable approach is to design truthful mechanisms that have desirable guarantees [Singer 2010;Kempe et al 2010;Chen et al 2010Chen et al , 2011Dobzinski et al 2011;Badanidiyuru et al 2012;Bei et al 2012;Anari et al 2014]. In this paper we consider settings in which the agents' costs are known to the mechanism designer, and truthfulness is therefore not the design objective.…”