FixedPointTheoremswithApplicationstoEconomicsandGameTheory

Oneoftheproblemsineconomicsthateconomistshavedevotedaconsiderableamountofattentioninprevalentyearshasbeentoensureconsistencyinthemodelstheyemploy.Assumingmarketstobegenerallyinsomestateofequilibrium,itisaskedunderwhatcircumstancessuchequilibriumispossible.Thefundamentalmathematicaltoolsusedtoaddressthisconcernarefixedpointtheorems:theconditionsunderwhichsetsofassumptionshaveasolution.Thisbookgivesthereaderaccesstothemathematicaltechniquesinvolvedandgoesontoapplyfixedpointtheoremstoprovingtheexistenceofequilibriaforeconomicsandforco-operativeandnoncooperativegames.Specialemphasisisgiventoeconomicsandgamesincaseswherethepreferencesofagentsmaynotbetransitive.Theauthorpresentstopicalproofsofoldresultsinordertofurtherclarifytheresults.Healsoproposesfreshresults,notablyinthelastchapter,thatrefertothecoreofagamewithouttransitivity.Thisbookwillbeusefulasatextorreferenceworkformathematicaleconomistsandgraduateandadvancedundergraduatestudents.