Characterizing Incentive Compatibility for Convex Valuations

We study implementability in dominant strategies of social choice functions when sets of types are multi-dimensional and convex, sets of outcomes are arbitrary, valuations for outcomes are convex functions in the type, and utilities over outcomes and payments are quasilinear. Archer and Kleinberg [1] have proven that in case of valuation functions that are linear in the type monotonicity in combination with a local integrability condition are equivalent with implementability. We show that in the case of convex valuation functions one has to require in addition a property called decomposition monotonicity in order to conclude implementability from monotonicity and the integrability condition. Decomposition monotonicity is automatically satisfied in the linear case. Saks and Yu [9] have shown that for the same setting as in Archer and Kleinberg [1], but finite set of outcomes, monotonicity alone is sufficient for implementability. Later Archer and Kleinberg [1], Monderer [6] and Vohra ...

• Type: Conference
• Year: 2009
• Where: SAGT
• Authors: André Berger, Rudolf Müller, Seyed Hossein Naeemi
• Keywords: Decomposition Monotonicity, Game Theory, Monotonicity, SAGT 2009, Valuation Functions