Mechanism Design: A Mathematical ProgrammingFramework for Principal-Agent Systems*
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Abstract
Mechanism design is often introduced as a reverseform of game-theoretic analysis because the designer startsfrom a desired objective and then constructs rules under whichstrategic agents choose outcomes consistent with that objective.This paper develops a mathematical programming frameworkfor principal-agent mechanism design under asymmetric infor-mation. The framework treats allocation and transfer rules asdecision variables and imposes incentive compatibility, individ-ual rationality, and feasibility as explicit constraints, consistentwith the optimization-based view of mechanism design. Theproposed mathematical formulation is intended to be directlyimplementable as a finite-dimensional optimization model whentypes and actions are discretized. The paper makes three con-tributions. First, it clarifies the relationship between the reversegame-theoretic interpretation and classical mechanism design,and inverse game-theoretic learning. Second, it formulates adirect-mechanism optimization model and derives its finite-typeLP and MILP specialization. Third, it discusses continuoustype spaces through finite-grid approximation and provides ageneral sensitivity interpretation for finite networks. A two-agentbinary-type example is used not as a new auction result, butas a benchmark recovery test showing that the optimizationtemplate recovers a second-price auction with a reserve pricefrom incentive and participation constraints. The framework isrelevant for systems in which incentives and outcomes must bedesigned jointly
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References
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