Incentive Compatible Cost Sharing of a Coalition Initiative with Probabilistic Inspection and Penalties for Misrepresentation

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.