dynamic stackelberg problems

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1、Chapter19DynamicStackelbergProblems19.1.HistorydependencePreviouschaptersdescribeddecisionproblemsthatarerecursiveinwhatwecancall“natural”statevariables,i.e.,statevariablesthatdescribestocksofcapital,wealth,andinformationthathelpsforecastfuturevaluesofpricesand

2、quantitiesthatimpingeonfutureutilitiesorprofits.Inproblemsthatarerecursiveinthenaturalstatevariables,optimaldecisionrulesarefunctionsofthenaturalstatevariables.Thischapterisourfirstencounterwithaclassofproblemsthatarenotrecursiveinthenaturalstatevariables.Kydland

3、andPrescott(1977),Prescott(1977),andCalvo(1978)gavemacroeconomicexamplesofdecisionproblemswhosesolutionsexhibitedtimeinconsistencybecausetheyarenotrecursiveinthenaturalstatevariables.Thoseauthorsstudiedthedecisionproblemofalargeagent(agovernment)thatconfrontsac

4、ompetitivemarketcomposedofmanysmallprivateagentswhosedecisionsareinfluencedbytheirforecastsofthegovernment’sfutureactions.Insuchsettings,thenaturalstatevariablesofprivateagentsattimetarepartlyshapedbypastdecisionsthatwerein-fluencedbytheirearlierforecastsofthegov

5、ernment’sactionattimet.Inarationalexpectationsequilibrium,thegovernmentonaverageconfirmsprivateagents’earlierforecastsofthegovernment’stimetactions.Thisrequirementtoconfirmpriorforecastsputsconstraintsonthegovernment’stimetdecisionsthatpreventitsproblemfrombeingr

6、ecursiveinnaturalstatevariables.Theseadditionalconstraintsmakethegovernment’sdecisionruleattdependontheentirehistoryofthestatefromtime0totimet.Ittooksometimeforeconomiststofigureouthowtoformulatepolicyproblemsofthistyperecursively.Prescott(1977)assertedthatrecur

7、siveopti-malcontroltheorydoesnotapplytoproblemswiththisstructure.Thischapterandchapters20and23showhowPrescott’spessimismabouttheinapplicability–775–776DynamicStackelbergProblemsofoptimalcontroltheoryhasbeenoverturnedbymorerecentwork.1Animpor-tantfindingisthatift

8、henaturalstatevariablesareaugmentedwithadditionalstatevariablesthatmeasurecostsintermsofthegovernment’scurrentcon-tinuationvalueofconfirmingpastprivatesectorexpectationsabout