RDP 2007-12: Dynamic Pricing and Imperfect Common Knowledge Equation (6)

π t = ( 1 θ ) ( 1 β θ ) k = 0 ( 1 θ ) k m c t | t ( k ) + β θ k = 0 ( 1 θ ) k π t + 1 | t ( k + 1 ) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWda3aaS baaSqaaiaadshaaeqaaOGaeyypa0ZaaeWaaeaacaaIXaaccaGae8Ne I0IaeqiUdehacaGLOaGaayzkaaWaaeWaaeaacaaIXaGae8NeI0Iaeq OSdiMaeqiUdehacaGLOaGaayzkaaWaaabCaeaadaqadaqaaiaaigda cqWFsislcqaH4oqCaiaawIcacaGLPaaadaahaaWcbeqaaiaadUgaaa aabaGaam4Aaiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoakiaa d2gacaWGJbWaa0baaSqaaiaadshadaabbaqaaiaadshaaiaawEa7aa qaamaabmaabaGaam4AaaGaayjkaiaawMcaaaaakiabgUcaRiabek7a IjabeI7aXnaaqahabaWaaeWaaeaacaaIXaGae8NeI0IaeqiUdehaca GLOaGaayzkaaWaaWbaaSqabeaacaWGRbaaaaqaaiaadUgacqGH9aqp caaIWaaabaGaeyOhIukaniabggHiLdGccqaHapaCdaqhaaWcbaGaam iDaiabgUcaRiaaigdadaabbaqaaiaadshaaiaawEa7aaqaamaabmaa baGaam4AaiabgUcaRiaaigdaaiaawIcacaGLPaaaaaGccaGGUaaaaa@7639@