Incentive Compatible Cost Sharing of a Coalition Initiative with Probabilistic Inspection and Penalties for Misrepresent
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Incentive Compatible Cost Sharing of a Coalition Initiative with Probabilistic Inspection and Penalties for Misrepresentation William N. Caballero1 · Brian J. Lunday1 · Darryl K. Ahner1
© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2020
Abstract This research proposes cost sharing mechanisms such that payments for a coalition initiative are allocated among players based on their honest valuations of the initiative, probabilistic inspection efforts, and deception penalties. Specifically, we develop a set of multiobjective, nonlinear optimization problem formulations that alternatively impose Bayesian incentive compatible, strategyproof, or group strategyproof mechanisms with generalized cost sharing and penalty functions that can be tailored to specific applications. Any feasible solution to these problems corresponds to a Bayesian game with stochastic payoffs wherein a collectively honest declaration is a Bayes–Nash equilibrium, a Nash equilibrium in dominant strategies, or a collusion resistant Nash equilibrium, respectively, and wherein an optimal solution considers the central authority’s relative priorities between inspection and penalization. In addition to this general framework, we introduce special cases having specific cost sharing and penalty functions such that the set of mechanisms are budget-balanced-in-equilibrium and proportional by design. The convexity of the resulting mathematical programs are examined, and formulation size reductions due to constraint redundancy analyses are presented. The Pareto fronts associated with each multiobjective optimization problem are assessed, as are computer memory limitations. Finally, an experiment considers the clustering of available valuations and the player probability distributions over them to examine their effects. Keywords Cost sharing · Multiobjective optimization · Mechanism design
* William N. Caballero [email protected] Brian J. Lunday [email protected] Darryl K. Ahner [email protected] 1
Air Force Institute of Technology, 2950 Hobson Way, Wright‑Patterson AFB, OH, USA
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1 Introduction Cost sharing mechanisms generally focus on the utilization of monetary or utility transfers to invoke desirable behavior from agents. However, Ben-Porath et al. (2014) demonstrated how the same effects can be accomplished with a central authority probabilistically validating information received from a set of agents. Treating a coalition initiative as a public good, this research creates incentivecompatible mechanisms to share its costs by combining the concepts of utility transfer and probabilistic inspection. Probabilistic inspection enables a coalition’s central authority to identify deceptive action by agents and impose penalties, which can be distributed in turn to other agents as subsidies. Although mechanisms of this form are not well-studied in the cost sharing literature, the combination of probabilistic inspection
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