RDP 2007-12: Dynamic Pricing and Imperfect Common Knowledge Equation (A5)

p t = ( 1 θ ) ( 1 β θ ) k = 0 ( ( 1 β θ ) ( 1 θ ) ) k m c t ( k ) + + 1 1 + β θ β p t 1 + ( 1 θ ) θ β k = 0 ( ( 1 β θ ) ( 1 θ ) ) k p t + 1 | t ( k + 1 ) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGWb WaaSbaaSqaaiaadshaaeqaaOGaeyypa0ZaaeWaaeaacaaIXaaccaGa e8NeI0IaeqiUdehacaGLOaGaayzkaaWaaeWaaeaacaaIXaGae8NeI0 IaeqOSdiMaeqiUdehacaGLOaGaayzkaaWaaabCaeaadaqadaqaamaa bmaabaGaaGymaiab=jHiTiabek7aIjabeI7aXbGaayjkaiaawMcaam aabmaabaGaaGymaiab=jHiTiabeI7aXbGaayjkaiaawMcaaaGaayjk aiaawMcaamaaCaaaleqabaGaam4Aaaaakiaad2gacaWGJbWaa0baaS qaaiaadshaaeaadaqadaqaaiaadUgaaiaawIcacaGLPaaaaaGccqGH RaWkaSqaaiaadUgacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLd aakeaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaIXaGaey4kaSIaeqOS diMae8NeI0IaeqiUdeNaeqOSdigaaiaadchadaWgaaWcbaGaamiDai ab=jHiTiaaigdaaeqaaOGaey4kaSYaaeWaaeaacaaIXaGae8NeI0Ia eqiUdehacaGLOaGaayzkaaGaeqiUdeNaeqOSdi2aaabCaeaadaqada qaamaabmaabaGaaGymaiab=jHiTiabek7aIjabeI7aXbGaayjkaiaa wMcaamaabmaabaGaaGymaiabgkHiTiabeI7aXbGaayjkaiaawMcaaa GaayjkaiaawMcaamaaCaaaleqabaGaam4AaaaakiaadchadaqhaaWc baGaamiDaiabgUcaRiaaigdadaabbaqaaiaadshaaiaawEa7aaqaai abgEHiQiaacIcacaGGRbGaey4kaSIaaGymaiaacMcaaaGccaGGUaaa leaacaWGRbGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaaaaa@95CB@