Characterization of Group-Strategyproof Mechanisms for Facility Location in Strictly Convex Space

We characterize the class of group-strategyproof mechanisms for the single facility location game in any unconstrained strictly convex space. A mechanism is \emph{group-strategyproof}, if no group of agents can misreport so that all its members are \emph{strictly} better off. A strictly convex space is a normed vector space where $\|x+y\|<2$ holds for any pair of different unit vectors $x \neq y$, e.g., any $L_p$ space with $p\in (1,\infty)$. We show that any deterministic, unanimous, group-strategyproof mechanism must be dictatorial, and that any randomized, unanimous, translation-invariant, group-strategyproof mechanism must be \emph{2-dictatorial}. Here a randomized mechanism is 2-dictatorial if the lottery output of the mechanism must be distributed on the line segment between two dictators' inputs. A mechanism is translation-invariant if the output of the mechanism follows the same translation of the input. Our characterization directly implies that any (randomized) translation-invariant approximation algorithm satisfying the group-strategyproofness property has a lower bound of $2$-approximation for maximum cost (whenever $n \geq 3$), and $n/2 - 1$ for social cost. We also find an algorithm that $2$-approximates the maximum cost and $n/2$-approximates the social cost, proving the bounds to be (almost) tight.Comment: Accepted to ACM Conference on Economics and Computation (EC) 202

Euclidean Preferences, Option Sets and Strategy Proofness

In this note, we use the technique of option sets to sort out the implications of coalitional strategyproofness in the spatial setting. We also discuss related issues and open problems

Sharing the cost of multicast transmissions in wireless networks

AbstractA crucial issue in non-cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network. Each station acts as a selfish agent that may misreport its utility (i.e., the maximum cost it is willing to incur to receive the service, in terms of power consumption) in order to maximize its individual welfare, defined as the difference between its true utility and its charged cost. A provider can discourage such deceptions by using a strategyproof cost sharing mechanism, that is a particular public algorithm that, by forcing the agents to truthfully reveal their utility, starting from the reported utilities, decides who gets the service (the receivers) and at what price. A mechanism is said budget balanced (BB) if the receivers pay exactly the (possibly minimum) cost of the transmission, and β-approximate budget balanced (β-BB) if the total cost charged to the receivers covers the overall cost and is at most β times the optimal one, while it is efficient if it maximizes the sum of the receivers’ utilities minus the total cost over all receivers’ sets. In this paper, we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks, in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or BB when the power assignments are induced by a fixed universal spanning tree, or (3ln(k+1))-BB (k is the number of receivers), otherwise. Then we consider the case in which the stations lay in a d-dimensional Euclidean space and the powers fall as 1/dα, and provide strategyproof mechanisms that are either 1-BB or efficient for α=1 or d=1. Finally, we show the existence of 2(3d-1)-BB strategyproof mechanisms in any d-dimensional space for every α⩾d. For the special case of d=2 such a result can be improved to achieve 12-BB mechanisms