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background information background signal belief 7r beliefs where firms boundary conditions Brownian noise change in belief comparative statics competitive environment consumer surplus continuous-time converges convex function correlated equilibrium create price dispersion current revenue curve demand differentiated-goods duopoly discount rate Discussion Papers dynamic pricing game equation experimentation Figure firms create price firms randomize frequency given belief Harrington 1995 hence higher implies increases independent randomization inequality information content invariant belief joint randomization joint strategy Lebesgue measurable Markov perfect equilibrium measurable function mixed strategies pi myopic payoff function myopic price myopic strategy noise open interval open unit interval payoff-symmetric positive constants posterior beliefs price dispersion arises price matching price pairs price variance process of beliefs profits Proof of Proposition Proposition 4.1 pure strategy quantity signals range of beliefs shadow price signal-to-noise ratio solution solves the ODE standard deviation strictly convex sufficiently supersolution switches symmetric threshold value of information variable Wiener process zero