RDP 2007-12: Dynamic Pricing and Imperfect Common Knowledge Equation (A9)

π t = ( 1 β θ ) ( 1 θ ) k = 1 ( 1 θ ) k m c t ( k ) + β θ k = 1 ( 1 θ ) k π t + 1 | t ( k + 1 ) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHap aCdaWgaaWcbaGaamiDaaqabaGccqGH9aqpdaqadaqaaiaaigdaiiqa cqWFsislcqaHYoGycqaH4oqCaiaawIcacaGLPaaadaqadaqaaiaaig dacqWFsislcqaH4oqCaiaawIcacaGLPaaadaaeWbqaamaabmaabaGa aGymaiab=jHiTiabeI7aXbGaayjkaiaawMcaamaaCaaaleqabaGaam 4Aaaaakiaad2gacaWGJbWaa0baaSqaaiaadshaaeaadaqadaqaaiaa dUgaaiaawIcacaGLPaaaaaaabaGaam4Aaiabg2da9iaaigdaaeaacq GHEisPa0GaeyyeIuoaaOqaaiabgUcaRiabek7aIjabeI7aXnaaqaha baWaaeWaaeaacaaIXaGae8NeI0IaeqiUdehacaGLOaGaayzkaaWaaW baaSqabeaacaWGRbaaaOGaeqiWda3aa0baaSqaaiaadshacqGHRaWk caaIXaWaaqqaaeaacaWG0baacaGLhWoaaeaadaqadaqaaiaadUgacq GHRaWkcaaIXaaacaGLOaGaayzkaaaaaOGaaiOlaaWcbaGaam4Aaiab g2da9iaaigdaaeaacqGHEisPa0GaeyyeIuoaaaaa@73C1@