Parameterization of Strategy-Proof Mechanisms in the Obnoxious Facility Game

In the obnoxious facility game, a location for an undesirable facility is to be determined based on the voting of selfish agents. Design of group strategy proof mechanisms has been extensively studied, but it is known that there is a gap between the social benefit (i.e., the sum of individual benefits) by a facility location determined by any group strategy proof mechanism and the maximum social benefit over all choices of facility locations; their ratio, called the benefit ratio can be 3 in the line metric space. In this paper, we investigate a trade-off between the benefit ratio and a possible relaxation of group strategy proofness, taking 2-candidate mechanisms for the obnoxious facility game in the line metric as an example. Given a real λ ≥ 1 as a parameter, we introduce a new strategy proofness, called “λ-group strategy-proofness,” so that each coalition of agents has no incentive to lie unless every agent in the group can increase her benefit by strictly more th...

• Type: Journal
• Year: 2016
• Where: WALCOM
• Authors: Morito Oomine, Aleksandar Shurbevski, Hiroshi Nagamochi
• Keywords: Algorithms, WALCOM 2016