We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibr...

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the supermodular stochastic ordering if it yields a higher expectation than the other for all supermodular objective functions. We pro...

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the supermodular stochastic ordering if it yields a higher expectation than the other for all supermodular objective functions. We pro...

We establish an identity for $$Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) $$ , when $$\varvec{X}$$ and $$\varvec{Y}$$ both have matrix variate skew-normal distributions the function f satisfies some weak conditions. The characteristic of skew normal distribution is then derived. make use it to derive necessary sufficient conditions comparison under six different orders, such as usu...

We take an order-centric approach to an incomplete-information version of the supermodular game (SG). In particular, we first introduce concepts related to ordered normal form games and the stochastic dominance order. Then, we work on a Bayesian SG, for which we show the existence of a monotone equilibrium and its monotonic trend as the player type distribution varies. Our results complement th...

This paper studies supermodular mechanism design in environments with finite type spaces and interdependent valuations. In such environments, it is difficult to implement social choice functions in ex-post equilibrium, hence Bayesian Nash equilibrium becomes the appropriate equilibrium concept. The requirements for agents to play a Bayesian equilibrium are strong, so we propose mechanisms that ...