48 research outputs found
Subsidies, Knapsack Auctions and Dantzig’s Greedy Heuristic
A budget-constrained buyer wants to purchase items from a shortlisted set. Items are differentiated by quality and sellers have private reserve prices for their items. Sellers quote prices strategically, inducing a knapsack game. The buyer’s problem is to select a subset of maximal quality. We propose a buying mechanism which can be viewed as a game theoretic extension of Dantzig’s greedy heuristic for the classic knapsack problem. We use Monte Carlo simulations to analyse the performance of our mechanism. Finally, we discuss how the mechanism can be applied to award R&D subsidies
Subsidies, Knapsack Auctions and Dantzig's Greedy Heuristic
A budget-constrained buyer wants to purchase items from a shortlisted set. Items are differentiated by quality and sellers have private reserve prices for their items. Sellers quote prices strategically, inducing a knapsack game. The buyer's problem is to select a subset of maximal quality. We propose a buying mechanism which can be viewed as a game theoretic extension of Dantzig's greedy heuristic for the classic knapsack problem. We use Monte Carlo simulations to analyse the performance of our mechanism. Finally, we discuss how the mechanism can be applied to award R&D subsidies.Auctions, Subsidies, Market Design, Knapsack Problem
The Power of Fair Pricing Mechanisms
We explore the revenue capabilities of truthful, monotone (“fair”) allocation and pricing functions for resource constrained auction mechanisms within a general framework that encompasses unlimited supply auctions, knapsack auctions, and auctions with general non-decreasing convex production cost functions. We study and compare the revenue obtainable in each fair pricing scheme to the profit obtained by the ideal omniscient multi-price auction. We show that for capacitated knapsack auctions, no constant pricing scheme can achieve any approximation to the optimal profit, but proportional pricing is as powerful as general monotone pricing. In addition, for auction settings with arbitrary bounded non-decreasing convex production cost functions, we present a proportional pricing mechanism which achieves a poly-logarithmic approximation. Unlike existing approaches, all of our mechanisms have fair (monotone) prices, and all of our competitive analysis is with respect to the optimal profit extraction
How to allocate Research (and other) Subsidies
A budget-constrained buyer wants to purchase items from a short-listed set. Items are differentiated by observable quality and sellers have private reserve prices for their items. The buyer’s problem is to select a subset of maximal quality. Money does not enter the buyer’s objective function, but only his constraints. Sellers quote prices strategically, inducing a knapsack game. We derive the Bayesian optimal mechanism for the buyer’s problem. We ?nd that simultaneous take-it-or-leave-it offers are optimal. Hence, somewhat surprisingly, ex-postcompetition is not required to implement optimality. Finally, we discuss the problem in a detail free setting
A dynamic auction for multi-object procurement under a hard budget constraint
We present a new dynamic auction for procurement problems where payments are bounded by a hard budget constraint and money does not enter the procurer's objective function
How to allocate Research (and other) Subsidies
A budget-constrained buyer wants to purchase items from a short-listed set. Items are differentiated by observable quality and sellers have private reserve prices for their items. The buyer’s problem is to select a subset of maximal quality. Money does not enter the buyer’s objective function, but only his constraints. Sellers quote prices strategically, inducing a knapsack game. We derive the Bayesian optimal mechanism for the buyer’s problem. We ?nd that simultaneous take-it-or-leave-it offers are optimal. Hence, somewhat surprisingly, ex-postcompetition is not required to implement optimality. Finally, we discuss the problem in a detail free setting.Mechanism Design; Subsidies; Budget; Procurement; Knapsack Problem
Two-way Greedy: Algorithms for Imperfect Rationality
The realization that selfish interests need to be accounted for in the design
of algorithms has produced many contributions in computer science under the
umbrella of algorithmic mechanism design. Novel algorithmic properties and
paradigms have been identified and studied. Our work stems from the observation
that selfishness is different from rationality; agents will attempt to
strategize whenever they perceive it to be convenient according to their
imperfect rationality. Recent work has focused on a particular notion of
imperfect rationality, namely absence of contingent reasoning skills, and
defined obvious strategyproofness (OSP) as a way to deal with the selfishness
of these agents. Essentially, this definition states that to care for the
incentives of these agents, we need not only pay attention about the
relationship between input and output, but also about the way the algorithm is
run. However, it is not clear what algorithmic approaches must be used for OSP.
In this paper, we show that, for binary allocation problems, OSP is fully
captured by a combination of two well-known algorithmic techniques: forward and
reverse greedy. We call two-way greedy this algorithmic design paradigm. Our
main technical contribution establishes the connection between OSP and two-way
greedy. We build upon the recently introduced cycle monotonicity technique for
OSP. By means of novel structural properties of cycles and queries of OSP
mechanisms, we fully characterize these mechanisms in terms of extremal
implementations. These are protocols that ask each agent to consistently
separate one extreme of their domain at the current history from the rest.
Through the connection with the greedy paradigm, we are able to import a host
of approximation bounds to OSP and strengthen the strategic properties of this
family of algorithms. Finally, we begin exploring the power of two-way greedy
for set systems
Ex-Post Optimal Knapsack Procurement
We consider a budget-constrained mechanism designer who selects an optimal set of projects to maximize her utility. Projects may differ in their value for the designer, and their cost is private information. In this allocation problem, the quantity of procured projects is endogenously determined by the mechanism. The designer faces ex-post constraints: The participation and budget constraints must hold for each possible outcome, while the mechanism must be strategyproof. We identify settings in which the class of optimal mechanisms has a deferred acceptance auction representation which allows an implementation with a descending-clock auction. Only in the case of symmetric projects do price clocks descend synchronously such that the cheapest projects are implemented. The case in which values or costs are asymmetrically distributed features a novel tradeoff between quantity and quality. The reason is that guaranteeing allocation to the most favorable projects under strategyproofness comes at the cost of a diminished expected number of conducted projects
Truthful Multi-unit Procurements with Budgets
We study procurement games where each seller supplies multiple units of his
item, with a cost per unit known only to him. The buyer can purchase any number
of units from each seller, values different combinations of the items
differently, and has a budget for his total payment.
For a special class of procurement games, the {\em bounded knapsack} problem,
we show that no universally truthful budget-feasible mechanism can approximate
the optimal value of the buyer within , where is the total number of
units of all items available. We then construct a polynomial-time mechanism
that gives a -approximation for procurement games with {\em concave
additive valuations}, which include bounded knapsack as a special case. Our
mechanism is thus optimal up to a constant factor. Moreover, for the bounded
knapsack problem, given the well-known FPTAS, our results imply there is a
provable gap between the optimization domain and the mechanism design domain.
Finally, for procurement games with {\em sub-additive valuations}, we
construct a universally truthful budget-feasible mechanism that gives an
-approximation in polynomial time with a
demand oracle.Comment: To appear at WINE 201