Date of Award


Document Type


Degree Name

Master of Science in Operations Research


Department of Operational Sciences

First Advisor

Brian J. Lunday, PhD.


Burden sharing within an international alliance is a contentious topic, especially in the current geopolitical environment, that in practice is generally imposed by a central authority's perception of its members' abilities to contribute. Instead, we propose a cost sharing mechanism such that burden shares are allocated to nations based on their honest declarations of the alliance's worth. Specifically, we develop a set of multiobjective nonlinear optimization problem formulations that respectively impose Bayesian Incentive Compatible (BIC), Strategyproof (SP), and Group Strategyproof (GSP) mechanisms based on probabilistic inspection efforts and deception penalties that are budget balanced and in the core. Any feasible solution to these problems corresponds to a single stage Bayesian stochastic game wherein a collectively honest declaration is a Bayes-Nash equilibrium, a Nash Equilibrium in dominant strategies, or a collusion resistant Nash equilibrium, respectively, but the optimal solution considers the alliance's central authority preferences. Each formulation is shown to be a nonconvex optimization problem. The solution quality and computational effort required for three heuristic algorithms as well as the BARON global solver are analyzed to determine the superlative solution methodology for each problem. The Pareto fronts associated with each multiobjective optimization problem are examined to determine the tradeoff between inspection frequency and penalty severity required to obtain truthfulness under stronger assumptions. Memory limitations are examined to ascertain the size of alliances for which the proposed methodology can be utilized. Finally, a full block design experiment considering the clustering of available alliance valuations and the member nations' probability distributions therein is executed on an intermediate-sized alliance motivated by the South American alliance UNASUR.

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