In mobile commerce, companies provide location based services to mobile users, who report their locations with a certain level of granularity to maintain a degree of anonymity. This level of granularity depends on their perceived risk as well as the incentives they receive in the form of monetary benefits or improved mobile services. This paper formulates a quantitative model in which information theoretic metrics such as entropy, quantify the anonymity level of mobile users. The individual perceived risks of users and the benefits they obtain are defined as functions of their chosen location information granularity. The interaction between the mobile commerce company and its users is investigated using mechanism design techniques as a privacy game. The user best responses and optimal strategies for the company are derived under budgetary constraints on incentives, which are provided to users in order to convince them to share their private information at the desired level of granularity. Information limitations in the system are analyzed to capture more realistic scenarios where the companies do not have access to user utility functions. Iterative distributed algorithm and regression learning methods are investigated to design mechanisms that overcome these limitations. The results obtained are demonstrated with a numerical example and simulations based on real GPS data.
Abstract-We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for "near-feasibility" of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed.Note to Practitioners-Our results will be useful in all resource allocation problems that involve gathering of information privately held by strategic users, where the utilities are any concave function of the allocations, and where the resource planner is not interested in maximizing revenue, but in efficient sharing of the resource. Such situations arise quite often in fair sharing of internet resources, fair sharing of funds across departments within the same parent organization, auctioning of public goods, etc. We study methods to achieve near budget balance by first collecting payments according to the celebrated VCG mechanism, and then returning as much of the collected money as rebates. Our focus on linear rebate functions allows for easy implementation. The resulting convex optimization problem is solved via relaxation to a randomized linear programming problem, for which several efficient solvers exist. This relaxation is enabled by constraint sampling. Keeping practitioners in mind, we identify the number of samples that assures a desired level of "near-feasibility" with the desired confidence level. Our methodology will occasionally require subsidy from outside the system. We however demonstrate via simulation that, if the mechanism is repeated several times over independent instances, then past surplus can support the sub...
This paper studies the effects of and countermeasures against adversarial behavior in network resource allocation mechanisms such as auctions and pricing schemes. It models the heterogeneous behavior of users, which ranges from altruistic to selfish and to malicious, within the analytical framework of game theory. A mechanism design approach is adopted to quantify the effect of adversarial behavior, which ranges from extreme selfishness to destructive maliciousness. First, the well-known result on the Vicrey-Clarke-Groves (VCG) mechanism losing its efficiency property in the presence of malicious users is extended to the case of divisible resource allocation to motivate the need to quantify the effect of malicious behavior. Then, the Price of Malice of the VCG mechanism and of some other network mechanisms are derived. In this context, the dynamics and convergence properties of an iterative distributed pricing algorithm are analyzed. The resistance of a mechanism to collusions is investigated next, and the effect of collusion of some malicious users is quantified. Subsequently, the assumption that the malicious user has information about the utility function of selfish users is relaxed, and a regression-based iterative learning scheme is presented and applied to both pricing and auction mechanisms. Differentiated pricing as a method to counter adversarial behaviors is proposed and briefly discussed. The results obtained are illustrated with numerical examples and simulations.
In designing a mechanism for allocation of a divisible resource, the designer needs to know the player utility functions, which are often infinitely dimensional, in order to choose the appropriate pricing and allocation rules. This paper utilizes Gaussian process regression learning techniques to infer general player preferences by a designer in a mechanism design setting. In pricing mechanisms, the price taking players are charged with the appropriate value of Lagrange multiplier, in order to achieve efficiency. This value is obtained iteratively through learning. Likewise, the reserve price in auction mechanisms with price anticipating players, a parameter in allocation and pricing rules, is modified iteratively using online learning to move the system solution to near efficiency. A numerical example illustrates the approach and demonstrates the online learning algorithm.
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