In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results...

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) su¢ cient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost su¢ cient for complete information implemen...

We analyze the problem of fully implementing a social choice function when the planner does not know the agents’ beliefs about other agents’ types. We identify an ex post monotonicity condition that is necessary and in economic environments sufficient for full implementation in ex post equilibrium; we also identify an ex post monotonicity no veto condition that is sufficient. These results are ...

In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.

where t1 < t2 are two constants, (fi(~u)) is given as above. Our new monotonicity formulae are focused on more attention to the monotonicity of non-linear terms. Our point of view is that we introduce an index called β to measure the monotonicity of the non-linear terms in the problems. The index in the study of monotonicity formulae is very useful in understanding the behavior of blow up seque...