{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/85618"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/85618","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topics in the Design of Political and Economic Mechanisms","abstract":"Finally, the third essay analyzes conditions for the convexifiability of an agent's utility $u(a)$ viewed a function of his type. The study shows that if the set of types A is an m-dimensional rectangle, $m\\ge1,$ then u can be assumed convex in a without loss of generality. In particular, in any unidimensional model where A is convex and compact, u is essentially convex. Furthermore, if A is a compact, strictly convex set and its boundary $\\partial A$ is a level set of a nonsingular function, the study derives conditions on A and u ensuring that there exists a change of variables H such that $B=H\\sp{-1}(A)$ is a convex set and the function $U=u\\circ H:B\\to\\IR$ is strictly convex.","abstract_html":"Finally, the third essay analyzes conditions for the convexifiability of an agent's utility $u(a)$ viewed a function of his type. The study shows that if the set of types A is an m-dimensional rectangle, $m\\ge1,$ then u can be assumed convex in a without loss of generality. In particular, in any unidimensional model where A is convex and compact, u is essentially convex. 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The study shows that if the set of types A is an m-dimensional rectangle, $m\\ge1,$ then u can be assumed convex in a without loss of generality. In particular, in any unidimensional model where A is convex and compact, u is essentially convex. Furthermore, if A is a compact, strictly convex set and its boundary $\\partial A$ is a level set of a nonsingular function, the study derives conditions on A and u ensuring that there exists a change of variables H such that $B=H\\sp{-1}(A)$ is a convex set and the function $U=u\\circ H:B\\to\\IR$ is strictly convex.","Made available in DSpace on 2015-09-25T22:47:37Z (GMT). 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