In this paper we consider the pairwise kidney exchange game. This game naturally appears in situations that some service providers benefit from pairwise allocations on a network, such as the kidney exchanges between hospitals. present a @math -approximation randomized truthful mechanism for this problem. This is the best known result in this setting with multiple players. However, we note that the variance of the utility of an agent in this mechanism may be as large as @math , which is not desirable in a real application. In this paper we resolve this issue by providing a @math -approximation randomized truthful mechanism in which the variance of the utility of each agent is at most @math . Interestingly, we could apply our technique to design a deterministic mechanism such that, if an agent deviates from the mechanism, she does not gain more than @math . We call such a mechanism an almost truthful mechanism. Indeed, in a practical scenario, an almost truthful mechanism is likely to imply a truthful mechanism. We believe that our approach can be used to design low risk or almost truthful mechanisms for other problems.
This paper deals with the implementation of Social Choice Functions in fair multiagent decision problems. In such problems the determination of the best alternatives often relies on the maximization of a non-utilitarian Social Welfare Function so as to account for equity. However, in such decision processes, agents may have incentive to misreport their preferences to obtain more favorable choices. It is well known that, for Social Choice Functions based on the maximization of an affine aggregator of individual utilities, we can preclude any manipulation by introducing payments (VCG mechanisms). Unfortunately such truthful mechanisms do not exist for non-affine maximizers (Roberts' Theorem). For this reason, we introduce here a notion of "almost-truthfulness" and investigate the existence of payments enabling the elaboration of almost-truthful mechanisms for non-additive Social Welfare Functions such as Social Gini Evaluation Functions used in fair optimization. This manuscript presents an alternative implementation of the truthful-in-expectation mechanism of Dughmi, Roughgarden and Yan for combinatorial auctions with weighted-matroid-rank-sum valuations. The new implementation uses only value queries and is approximately truthful-in-expectation, in the sense that by reporting truthfully each agent maximizes his utility within a multiplicative 1-o(1) factor. It still provides an optimal (1-1 e-o(1))-approximation in social welfare. We achieve this by first presenting an approximately maximal-in-distributional-range allocation rule and then showing a black-box transformation to an approximately truthful-in-expectation mechanism. We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language in our auctions allows marginal-decreasing piecewise constant curves. First, we develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a (1+e)≈ in worst-case time T = O(n3 e), given n bids each with a constant number of pieces. Second, we embed this approximation scheme within a Vickrey-Clarke-Groves (VCG) mechanism and compute payments to n agents for an asymptotic cost of O(T log n). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by e (1+e) V, where V is the total surplus in the efficient outcome.