2016/06/15 by Robert Alexander Crowell, Crowell, Robert Alexander, Ngoc Mai Tran +1 · 1 citation
Computer Science · Engineering · Mathematics · Medicine · #14T05 #91A80 #Combinatorics #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Computer science #Convex analysis #Convex geometry #Convex hull #Convex optimization #Dimension (graph theory) #Economics #Equivalence (formal languages) #FOS: Computer and information sciences #FOS: Mathematics #Finance #Geometry #Incentive #Incentive compatibility #Mathematical economics #Mathematical optimization #Mathematics #Mechanism design #Microeconomics #Optimization and Control (math.OC) #Payment #Platelet Disorders and Treatments #Polynomial and algebraic computation #Pure mathematics #Regular polygon #Revenue #Simplex #Tropical geometry #cs.GT #graph theory and CDMA systems #math.CO #math.OC #msc:14T05 #msc:91A80
paper · pdf · doi:10.48550/arxiv.1606.04880
Major revision of the previous version
openalex publication_date 2016/06/15 · arxiv created 2018/11/18 · arxiv updated 2018/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a novel framework to construct and analyze finite valued, multidimensional mechanisms using tropical convex geometry. We geometrically characterize incentive compatibility using cells in the tropical convex hull of the type set. These cells are the sets of incentive compatible payments and form tropical simplices, spanned by generating payments whose number equals the dimension of the simplex. The analysis of the collection of incentive compatible mechanisms via tropical simplices and their generating payments facilitates the use of geometric techniques. We use this view to derive a new geometric characterization of revenue equivalence but also show how to handle multidimensional mechanisms in the absence of revenue equivalence.