Nash Two person cooperative game 20110119_13351130_0.pdf

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1、TWO-PERSONCOOPERATIVEGAMES'BYJOHNNASHInthispaper,theauthorextendshisprevioustreatmentof"TheBargainingProblem"toawiderclassofsituationsinwhichthreatscanplayarole.Anewapproachisintroducedinvolvingtheelaborationofthethreatconcept.INTRODUCTIONTHETHEORYpresentedherewasdevelopedtotreateconomic(orother)si

2、tuationsinvolvingtwoindividualswhoseinterestsareneithercom-pletelyopposednorcompletelycoincident.Thewordcooperativeisusedbecausethetwoindividualsaresupposedtobeabletodiscussthesituationandagreeonarationaljointplanofaction,anagreementthatshouldbeassumedtobeenforceable.Itisconventionaltocallthesesitu

3、ations"games"whentheyarebeingstudiedfromanabstractmathematicalviewpoint.Heretheoriginalsituationisreducedtoamathematicaldescription,ormodel.Intheabstract"game"formulationonlytheminimumquantityofinformationnecessaryforthesolutionisretained.Whattheactualalternativecoursesofactionareamongwhichtheindiv

4、idualsmustchooseisnotregardedasessentialinformation.Thesealternativesaretreatedasabstractobjectswithoutspecialqualitiesandarecalled"strategies."Onlytheattitudes(likeordislike)ofthetwoindividualstowardstheultimateresultsoftheuseofthevariouspossibleopposingpairsofstrategiesareconsidered;butthisinform

5、ationmustbewellutilizedandmustbeexpressedquantitatively.ThetheoryofvonNeumannandMorgensternappliestosomeofthegamesconsideredhere.Theirassumptionthatitispossiblefortheplayerstomake"side-payments"inacommodityforwhicheachindi-vidual(player)hasalinearutilitynarrowstherangeoftheirtheory'sapplicability.I

6、nthispaperthereisnoassumptionaboutside-payments.Ifthesituationpermitsside-paymentsthenthissimplyaffectsthesetofpossiblefinaloutcomesofthegame;side-paymentsaretreatedjustlikeanyotheractivitythatmaytakeplaceintheactualplayingofthegame-nospecialconsiderationisnecessary.ThevonNeumannandMorgensternappro

7、achalsodiffersbygivingamuchlessdeterminatesolution.Theirapproachleavesthefinalsituationonlydetermineduptoaside-payment.Theside-paymentisgenerallynotdeterminedbutisrestrictedtolieinacertainrange.Anearlierpap