A necessary and sufficient condition for rationalizability in a quasilinear context
The aim of this note is to give a simple characterization of the rationalizability of decision rules (or action profiles). The necessary and sufficient condition we obtain suggests interesting analogies between the Implementation Problem and Revealed Preference Theory. Two particular cases are examined: (a) The one-dimensional context, which shows that our condition is a generalization of the monotonicity condition of Spence- Mirrlees. (b) The linear step-up, which shows that rationalizability in multiple dimension requires more than monotonicity: it implies also symmetry conditions which are translated by partial differential equations (analogue in this context of Slutsky equations for revealed preference theory).
scientific article; zbMATH DE number 4022969