RDP 2007-12: Dynamic Pricing and Imperfect Common Knowledge Equation (43)

c x t | t ( 0 : ) = ( 1 θ ) ( 1 β θ ) k = 0 ( 1 θ ) k ( d x t | t ( k : ) + 1 1 × 2 x t | t ( k ) ) + β θ k = 0 ( 1 θ ) k c M x t | t ( k + 1 : ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbeGaa83yai aa=HhadaqhaaWcbaGaamiDamaaeeaabaGaamiDaaGaay5bSdaabaWa aeWaaeaacaaIWaaccaGae4NoaOJaeyOhIukacaGLOaGaayzkaaaaaO Gaeyypa0ZaaeWaaeaacaaIXaGae4NeI0IaeqiUdehacaGLOaGaayzk aaWaaeWaaeaacaaIXaGae4NeI0IaeqOSdiMaeqiUdehacaGLOaGaay zkaaWaaabCaeaadaqadaqaaiaaigdacqGFsislcqaH4oqCaiaawIca caGLPaaadaahaaWcbeqaaiaadUgaaaaabaGaam4Aaiabg2da9iaaic daaeaacqGHEisPa0GaeyyeIuoakmaabmaabaGaa8hzaiaa=Hhadaqh aaWcbaGaamiDamaaeeaabaGaamiDaaGaay5bSdaabaWaaeWaaeaaca WGRbGae4NoaOJaeyOhIukacaGLOaGaayzkaaaaaOGaey4kaSIaa8xm amaaBaaaleaadaWgaaadbaGaaGymaiab+Dna0kaaikdaaeqaaaWcbe aakiaahIhadaqhaaWcbaGaamiDaiaacYhacaWG0baabaWaaeWaaeaa caWGRbaacaGLOaGaayzkaaaaaaGccaGLOaGaayzkaaGaey4kaSIaeq OSdiMaeqiUde3aaabCaeaadaqadaqaaiaaigdacqGFsislcqaH4oqC aiaawIcacaGLPaaadaahaaWcbeqaaiaadUgaaaGccaWFJbGaamytai aa=HhadaqhaaWcbaGaamiDamaaeeaabaGaamiDaaGaay5bSdaabaWa aeWaaeaacaWGRbGaey4kaSIaaGymaiab+Pda6iabg6HiLcGaayjkai aawMcaaaaaaeaacaWGRbGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGH ris5aaaa@8EBC@