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We propose a class of stochastic orders, CAD, defined using conditional distributions, to compare interdependence of joint distributions. We show that for binary action, symmetric, separable games, and symmetric pure strategy Bayes-Nash equilibrium, increase in the similarity of information in the CAD order expands (shrinks) the equilibrium set when the game exhibits strategic complementarity (substitutability). We provide three different orders —- weak, intermediate, and strong, that establish the above relation for games where the net payoff is linear, convex, and increasing in aggregate action, respectively. Under additional assumptions, we show that the reverse direction of this relation also holds true.
