Amir Ronen

Computationally feasible VCG mechanisms

A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG (Vickrey, Clarke, Groves). When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are, therefore, computationally infeasible. However, if the optimal outcome is replaced by the results of a sub-optimal algorithm, the resulting mechanism (termed VCG-based) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield non-truthful VCG-based mechanisms. We generalize these results for affine maximizers. The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCG-based mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm’s output. We provide a strong rationale for truth-telling behavior. Our method satisfies individual rationality as well.

Algorithmic mechanism design (extended abstract)

We consider algorithmic problems in a distributed setting where the participants annot be assumed to follow the algorithm but rather their own self-interest. As such pxticipants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents’ interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. In this model the algorithmic solution is adorned with payments to the participants and is termed a mechanism. The payments should be carefully chosen a6 to motivate all participants to act as the algorithm designer wishes. We apply the standard tools of mechanism design to algorithmic problems and in particular to the shortest path problem. Our main technical contribution concerns the study of a representative problem, task scheduling, for which the standard tools do not suffice. We present several theorems regarding this problem including an approximation me&anism, lower bounds and a randomized mechanism. We also suggest and motivate extensions to the basic model and prove improved upper bounds in the extended model. Many open problems are suggested as well.

On approximating optimal auctions

We study the following problem: A seller wishes to sell an item to a group of self-interested agents. Each agent i has a privately known valuation vi for the object. Given a distribution on these valuations, our goal is to construct an auction that maximizes the sellers expected revenue (optimal auction). The auction must be incentive compatible and satisfy individual rationality. We present a simple generic auction that guarantees at least half of the optimal revenue. We generalize this result in several directions, in particular, for the case of multiple copies with unit demand. Our auction requires the ability to learn (or compute) in polynomial time the conditional distribution of the agent with the maximal valuation, given the valuations of the other agents. We show that this ability is in some sense essential. Finally we suggest a generalization of our auction and argue that it will generate a revenue which is close to optimal for reasonable distributions. In particular we show this under an independence assumption

Fault tolerant mechanism design

We introduce the notion of fault tolerant mechanism design, which extends the standard game theoretic framework of mechanism design to allow for uncertainty about execution. Specifically, we define the problem of task allocation in which the private information of the agents is not only their costs of attempting the tasks but also their probabilities of failure. For several different instances of this setting we present both, positive results in the form of mechanisms that are incentive compatible, individually rational, and efficient, and negative results in the form of impossibility theorems.

On the expected payment of mechanisms for task allocation

We study a generic task allocation problem called shortest paths: Let G be a directed graph in which the edges are owned by self interested agents. Each edge has an associated cost that is privately known to its owner. Let s and t be two distinguished nodes in G. Given a distribution on the edge costs, the goal is to design a mechanism (protocol) which acquires a cheap s-t path.We first prove that the class of generalized VCG mechanisms has certain monotonicity properties. We exploit this observation to obtain, under an independence assumption, expected payments which are significantly better than the worst case bounds of [4, 8]. We then investigate whether these payments can be improved when there is competition among paths. Surprisingly, we give evidence to the fact that in many cases such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated VCG mechanism. We then construct a novel general protocol combining the advantages of incentive compatible and non-incentive compatible mechanisms. Under reasonable assumptions on the agents we show that the overpayment of our mechanism is very small. Finally, we demonstrate that many task allocation problems can be reduced to shortest paths.

Nearly optimal multi attribute auctions

In almost every procurement situation, non-price attributes of the items to be purchased play a crucial role. Procurement protocols which take these attributes into account are called multi-attribute auctions.We study the following problem called optimal multi-attribute auction design: A buyer wants to procure an item which can be supplied in many possible configurations. The buyer has a value v(x) for each possible configuration x. Every seller i has a privately known cost ci(x) of supplying each possible configuration. Given a probability distribution on the cost functions, our goal is to design an auction which maximizes the expected utility of the buyer.This paper offers a generic method for the construction of nearly optimal multi-attribute auctions. The computational time of our mechanisms equals the time required for computing (or approximating) the optimal mechanism on a small number of agents. Our method can be successfully applied to many variants of multi-attribute auction design.

Mechanism design with incomplete languages

A major achievement of mechanism design theory is the family of truthful mechanisms often called VCG (named after Vickrey, Clarke and Groves). Although these mechanisms have many appealing properties, their essential intractability prevents them from being applied to complex problems like combinatorial auctions. In particular, VCG mechanisms require the agents to fully describe their valuation functions to the mechanism. Such a description may require exponential size and thus be infeasible for the agents.A natural approach for this problem is to introduce an intermediate language for the description of the valuations. Such a language must be succinct to both the agents and the mechanism. Unfortunately, the resulting mechanisms are neither truthful nor do they satisfy individual rationality.This paper suggests a general method for overcoming this difficulty. Given an intermediate language and an algorithm for computing the results, we propose three different mechanisms, each more powerful than its predecessor, but also more time consuming. Under reasonable assumptions, the results of our mechanisms are at least as good as the results of the algorithm on the actual valuations. All of our mechanisms have polynomial computational time and satisfy individual rationality.

Algorithms for Rational Agents

Many recent applications of interest involve self-interested participants. As such participants, termed agents, may manipulate the algorithm for their own benefit, a new challenge emerges: The design of algorithms and protocols that perform well when the agents behave according to their own self-interest. This led several researchers to consider computational models that are based on a sub-field of game-theory and micro-economics called mechanism design. This paper introduces this topic mainly through examples.It demonstrates that in many cases selfishness can be satisfactorily overcome, surveys some of the recent trends in this area and presents new challenging problems. The paper is mostly based on classic results from mechanism design as well as on recent work by the author and others.

The Local and Global Price of Anarchy of Graphical Games

This paper initiates a study of connections between local and global properties of graphical games. Specifically, we introduce a concept of local price of anarchy that quantifies how well subsets of agents respond to their environments. We then show several methods of bounding the global price of anarchy of a game in terms of the local price of anarchy. All our bounds are essentially tight.

On the expected payment of mechanisms for task allocation: [extended abstract]

We study a generic task allocation problem called shortest paths: Let G be a directed graph in which the edges are owned by self interested agents. Each edge has an associated cost that is privately known to its owner. Let s and t be two distinguished nodes in G. Given a distribution on the edge costs, the goal isto design a mechanism (protocol) which acquires a cheap s-t path. We first prove that the class of generalized VCG mechanisms has certain monotonicity properties. We exploit this observation to obtain, under an independence assumption, expected payments whichare significantly better than the worst case bounds of. We then investigate whether these payments canbe improved when there is a competition among paths. Surprisingly, we give evidence to the fact that typically such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated VCG mechanism. We then construct anovel general protocol combining the advantages of incentive compatible and non-incentive compatible mechanisms. Under reasonable assumptions on the agents we show that the overpayment of our mechanism is very small. Finally, we demonstrate that many task allocation problems can be reduced to shortest paths.