Budget feasible mechanisms on matroids

Motivated by many practical applications, in this paper we study budget feasible mechanisms where the goal is to procure independent sets from matroids. More specifically, we are given a matroid =(,) where each ground (indivisible) element is a selfish agent. The cost of each element (i.e., for selling the item or performing a service) is only known to the element itself. There is a buyer with a budget having additive valuations over the set of elements E. The goal is to design an incentive compatible (truthful) budget feasible mechanism which procures an independent set of the matroid under the given budget that yields the largest value possible to the buyer. Our result is a deterministic, polynomial-time, individually rational, truthful and budget feasible mechanism with 4-approximation to the optimal independent set. Then, we extend our mechanism to the setting of matroid intersections in which the goal is to procure common independent sets from multiple matroids. We show that, given a polynomial time deterministic blackbox that returns -approximation solutions to the matroid intersection problem, there exists a deterministic, polynomial time, individually rational, truthful and budget feasible mechanism with (3+1) -approximation to the optimal common independent set

POEM: Pricing Longer for Edge Computing in the Device Cloud

Multiple access mobile edge computing has been proposed as a promising technology to bring computation services close to end users, by making good use of edge cloud servers. In mobile device clouds (MDC), idle end devices may act as edge servers to offer computation services for busy end devices. Most existing auction based incentive mechanisms in MDC focus on only one round auction without considering the time correlation. Moreover, although existing single round auctions can also be used for multiple times, users should trade with higher bids to get more resources in the cascading rounds of auctions, then their budgets will run out too early to participate in the next auction, leading to auction failures and the whole benefit may suffer. In this paper, we formulate the computation offloading problem as a social welfare optimization problem with given budgets of mobile devices, and consider pricing longer of mobile devices. This problem is a multiple-choice multi-dimensional 0-1 knapsack problem, which is a NP-hard problem. We propose an auction framework named MAFL for long-term benefits that runs a single round resource auction in each round. Extensive simulation results show that the proposed auction mechanism outperforms the single round by about 55.6% on the revenue on average and MAFL outperforms existing double auction by about 68.6% in terms of the revenue.Comment: 8 pages, 1 figure, Accepted by the 18th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP

Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

Idiosyncratic risk, aggregate risk, and the welfare effects of social security

We ask whether a pay-as-you-go financed social security system is welfare improving in an economy with idiosyncratic productivity and aggregate business cycle risk. We show analytically that the whole welfare benefit from joint insurance against both risks is greater than the sum of benefits from insurance against the isolated risk components. One reason is the convexity of the welfare gain in total risk. The other reason is a direct risk interaction which amplifies the utility losses from consumption risk. We proceed with a quantitative evaluation of social security’s welfare effects. We find that introducing an unconditional minimum pension leads to substantial welfare gains in expectation, even net of the welfare losses from crowding out. About 60% of the welfare gains would be missing when simply summing up the isolated benefits

On the Efficiency of All-Pay Mechanisms

We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi- unit auction. We show that, for bidders with submodular valuations, the mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency of this mechanism outperforms all the known bounds on the price of anarchy of mechanisms used for multi-unit auctions. Finally, we analyze single-item all-pay auctions motivated by their connection to contests and show tight bounds on the price of anarchy of social welfare, revenue and maximum bid.Comment: 26 pages, 2 figures, European Symposium on Algorithms(ESA) 201

Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality

A comparison of arbitration procedures for risk averse disputants

We propose an arbitration model framework that generalizes many previous quantitative models of final offer arbitration, conventional arbitration, and some proposed alternatives to them. Our model allows the two disputants to be risk averse and assumes that the issue(s) in dispute can be summarized by a single quantifiable value. We compare the performance of the different arbitration procedures by analyzing the gap between the disputants' equilibrium offers and the width of the contract zone that these offers imply. Our results suggest that final offer arbitration should give results superior to those of conventional arbitration.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran