arXiv subjects

Michal Feldman

Publications and source records attributed to Michal Feldman.

104 records · Page 6Linked to original sources

arXiv2014

Approximate Strong Equilibrium in Job Scheduling Games

A Nash Equilibrium (NE) is a strategy profile resilient to unilateral deviations, and is predominantly used in the analysis of multiagent systems. A downside of NE is that it is not necessarily stable against deviations by coalitions. Yet, as we show in this paper, in some cases, NE does exhibit stability against coalitional deviations, in that the benefits from a joint deviation are bounded. In this sense, NE approximates strong equilibrium. Coalition formation is a key issue in multiagent systems. We provide a framework for quantifying the stability and the performance of various assignment policies and solution concepts in the face of coalitional deviations. Within this framework we evaluate a given configuration according to three measures: (i) IR_min: the maximal number alpha, such that there exists a coalition in which the minimal improvement ratio among the coalition members is alpha, (ii) IR_max: the maximal number alpha, such that there exists a coalition in which the maximal improvement ratio among the coalition members is alpha, and (iii) DR_max: the maximal possible damage ratio of an agent outside the coalition. We analyze these measures in job scheduling games on identical machines. In particular, we provide upper and lower bounds for the above three measures for both NE and the well-known assignment rule Longest Processing Time (LPT). Our results indicate that LPT performs better than a general NE. However, LPT is not the best possible approximation. In particular, we present a polynomial time approximation scheme (PTAS) for the makespan minimization problem which provides a schedule with IR_min of 1+epsilon for any given epsilon. With respect to computational complexity, we show that given an NE on m >= 3 identical machines or m >= 2 unrelated machines, it is NP-hard to determine whether a given coalition can deviate such that every member decreases its cost.

cs.GT↗

arXiv2013

Randomized Strategyproof Mechanisms for Facility Location and the Mini-Sum-of-Squares Objective

We consider the problem of locating a public facility on a line, where a set of $n$ strategic agents report their \emph{locations} and a mechanism determines, either deterministically or randomly, the location of the facility. Game theoretic perspectives of the facility location problem advanced in two main directions. The first direction is concerned with the characterization of \emph{strategyproof} (SP) mechanisms; i.e., mechanisms that induce truthful reporting as a dominant strategy; and the second direction quantifies how well various objective functions can be approximated when restricted to SP mechanisms. The current paper provides contributions in both directions. First, we construct a parameterized randomized SP mechanism, and show that all of the previously proposed deterministic and randomized SP mechanisms for the current settings can be formalized as special cases of this mechanism. Second, we give tight results for the approximation ratio of SP mechanisms with respect to the objective of minimizing the sum of squares of distances to the agents (\emph{miniSOS}). Holzman \cite{Holzman1990} provided an axiomatic foundation for this function, showing that it is the unique function that satisfies unanimity, continuity and invariance. We devise a randomized mechanism that gives a 1.5-approximation for the miniSOS function, and show that no other randomized SP mechanism can provide a better approximation. This mechanism chooses the average location with probability 1/2 and a \emph{random dictator} with probability 1/2. For deterministic mechanisms, we show that the median mechanism provides a 2-approximation, and this is tight. Together, our study provides fundamental understanding of the miniSOS objective function and makes a step toward the characterization of randomized SP facility location mechanisms.

cs.GT↗

arXiv2013

Limits of Efficiency in Sequential Auctions

We study the efficiency of sequential first-price item auctions at (subgame perfect) equilibrium. This auction format has recently attracted much attention, with previous work establishing positive results for unit-demand valuations and negative results for submodular valuations. This leaves a large gap in our understanding between these valuation classes. In this work we resolve this gap on the negative side. In particular, we show that even in the very restricted case in which each bidder has either an additive valuation or a unit-demand valuation, there exist instances in which the inefficiency at equilibrium grows linearly with the minimum of the number of items and the number of bidders. Moreover, these inefficient equilibria persist even under iterated elimination of weakly dominated strategies. Our main result implies linear inefficiency for many natural settings, including auctions with gross substitute valuations, capacitated valuations, budget-additive valuations, and additive valuations with hard budget constraints on the payments. Another implication is that the inefficiency in sequential auctions is driven by the maximum number of items contained in any player's optimal set, and this is tight. For capacitated valuations, our results imply a lower bound that equals the maximum capacity of any bidder, which is tight following the upper-bound technique established by Paes Leme et al. \cite{PaesLeme2012}.

cs.GT↗

arXiv2013

Pricing Public Goods for Private Sale

We consider the pricing problem faced by a seller who assigns a price to a good that confers its benefits not only to its buyers, but also to other individuals around them. For example, a snow-blower is potentially useful not only to the household that buys it, but also to others on the same street. Given that the seller is constrained to selling such a (locally) public good via individual private sales, how should he set his prices given the distribution of values held by the agents? We study this problem as a two-stage game. In the first stage, the seller chooses and announces a price for the product. In the second stage, the agents (each having a private value for the good) decide simultaneously whether or not they will buy the product. In the resulting game, which can exhibit a multiplicity of equilibria, agents must strategize about whether they will themselves purchase the good to receive its benefits. In the case of a fully public good (where all agents benefit whenever any agent purchases), we describe a pricing mechanism that is approximately revenue-optimal (up to a constant factor) when values are drawn from a regular distribution. We then study settings in which the good is only "locally" public: agents are arranged in a network and share benefits only with their neighbors. We describe a pricing method that approximately maximizes revenue, in the worst case over equilibria of agent behavior, for any $d$-regular network. Finally, we show that approximately optimal prices can be found for general networks in the special case that private values are drawn from a uniform distribution. We also discuss some barriers to extending these results to general networks and regular distributions.

cs.GT↗

arXiv2013

Combinatorial Walrasian Equilibrium

We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints.The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a Combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The difference between a CWE and a (non-combinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation profile admits a CWE that obtains at least half of the optimal (unconstrained) social welfare. Moreover, we devise a poly-time algorithm that, given an arbitrary allocation X, computes a CWE that achieves at least half of the welfare of X. Thus, the economic problem of finding a CWE with high social welfare reduces to the algorithmic problem of social-welfare approximation. In addition, we show that every valuation profile admits a CWE that extracts a logarithmic fraction of the optimal welfare as revenue. Finally, these results are complemented by strong lower bounds when the seller is restricted to using item prices only, which motivates the use of bundles. The strength of our results derives partly from their generality - our results hold for arbitrary valuations that may exhibit complex combinations of substitutes and complements.

cs.GT↗

arXiv2012

Simultaneous Auctions are (almost) Efficient

Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. Such procedures occur in practice (e.g. eBay) but are not truthful. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first- and second-price auctions when bidders have complement-free (a.k.a. subadditive) valuations. We show that the expected social welfare of any BNE is at least 1/2 of the optimal social welfare in the case of first-price auctions, and at least 1/4 in the case of second-price auctions. These results improve upon the previously-known logarithmic bounds, which were established by [Hassidim, Kaplan, Mansour and Nisan '11] for first-price auctions and by [Bhawalkar and Roughgarden '11] for second-price auctions.

cs.GT↗

arXiv2012

Signaling Schemes for Revenue Maximization

Signaling is an important topic in the study of asymmetric information in economic settings. In particular, the transparency of information available to a seller in an auction setting is a question of major interest. We introduce the study of signaling when conducting a second price auction of a probabilistic good whose actual instantiation is known to the auctioneer but not to the bidders. This framework can be used to model impressions selling in display advertising. We study the problem of computing a signaling scheme that maximizes the auctioneer's revenue in a Bayesian setting. While the general case is proved to be computationally hard, several cases of interest are shown to be polynomially solvable. In addition, we establish a tight bound on the minimum number of signals required to implement an optimal signaling scheme and show that at least half of the maximum social welfare can be preserved within such a scheme.

cs.GT↗

arXiv2012

Solving Cooperative Reliability Games

Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show that applying the reliability extension may stabilize the game, making the core non-empty even when the base game has an empty core.

cs.GT↗

arXiv2012

Stability Scores: Measuring Coalitional Stability

We introduce a measure for the level of stability against coalitional deviations, called \emph{stability scores}, which generalizes widely used notions of stability in non-cooperative games. We use the proposed measure to compare various Nash equilibria in congestion games, and to quantify the effect of game parameters on coalitional stability. For our main results, we apply stability scores to analyze and compare the Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG) ad auctions. We show that while a central result of the ad auctions literature is that the GSP and VCG auctions implement the same outcome in one of the equilibria of GSP, the GSP outcome is far more stable. Finally, a modified version of VCG is introduced, which is group strategy-proof, and thereby achieves the highest possible stability score.

cs.GT↗

arXiv2011

Truth and Envy in Capacitated Allocation Games

We study auctions with additive valuations where agents have a limit on the number of goods they may receive. We refer to such valuations as {\em capacitated} and seek mechanisms that maximize social welfare and are simultaneously incentive compatible, envy-free, individually rational, and have no positive transfers. If capacities are infinite, then sequentially repeating the 2nd price Vickrey auction meets these requirements. In 1983, Leonard showed that for unit capacities, VCG with Clarke Pivot payments is also envy free. For capacities that are all unit or all infinite, the mechanism produces a Walrasian pricing (subject to capacity constraints). Here, we consider general capacities. For homogeneous capacities (all capacities equal) we show that VCG with Clarke Pivot payments is envy free (VCG with Clarke Pivot payments is always incentive compatible, individually rational, and has no positive transfers). Contrariwise, there is no incentive compatible Walrasian pricing. For heterogeneous capacities, we show that there is no mechanism with all 4 properties, but at least in some cases, one can achieve both incentive compatibility and envy freeness.

cs.GT↗

arXiv2010

On the Interplay between Incentive Compatibility and Envy Freeness

We study mechanisms for an allocation of goods among agents, where agents have no incentive to lie about their true values (incentive compatible) and for which no agent will seek to exchange outcomes with another (envy-free). Mechanisms satisfying each requirement separately have been studied extensively, but there are few results on mechanisms achieving both. We are interested in those allocations for which there exist payments such that the resulting mechanism is simultaneously incentive compatible and envy-free. Cyclic monotonicity is a characterization of incentive compatible allocations, local efficiency is a characterization for envy-free allocations. We combine the above to give a characterization for allocations which are both incentive compatible and envy free. We show that even for allocations that allow payments leading to incentive compatible mechanisms, and other payments leading to envy free mechanisms, there may not exist any payments for which the mechanism is simultaneously incentive compatible and envy-free. The characterization that we give lets us compute the set of Pareto-optimal mechanisms that trade off envy freeness for incentive compatibility.

cs.GT↗

arXiv2009

Envy-Free Makespan Approximation

We study envy-free mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envy-free poly-time mechanism that approximates the minimal makespan to within a factor of $O(\log m)$, where $m$ is the number of machines. We also show a lower bound of $Ω(\log m / \log\log m)$. This improves the recent result of Hartline {\sl et al.} \cite{Ahuva:2008} who give an upper bound of $(m+1)/2$, and a lower bound of $2-1/m$. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan.

cs.GT↗

arXiv2009

Strategyproof Approximation Mechanisms for Location on Networks

We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a (2-2/n)-approximation for the social cost, where n is the number of agents, when the network is a circle (known as a ring in the case of computer networks); we design a novel "hybrid" strategyproof randomized mechanism that provides a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and we show that no randomized SP mechanism can provide an approximation ratio better than 2-o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two.

cs.GT↗

arXiv2005

A Price-Anticipating Resource Allocation Mechanism for Distributed Shared Clusters

In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed market-based resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their individual utility. We look at both the efficiency and the fairness of the allocation at the equilibrium, where fairness is evaluated through the measures of utility uniformity and envy-freeness. We show analytically and through simulations that despite being highly decentralized, such a system converges quickly to an equilibrium and unlike the social optimum that achieves high efficiency but poor fairness, the proposed allocation scheme achieves a nice balance of high degrees of efficiency and fairness at the equilibrium.

cs.DC↗