(First-pricesealed-bidauction)Aliceissellingher2000chevroletcavaliertoherfriends,BobandCharles.BobattachesavalueofS$8,000toAlice'soldcar,whileCharles'svalueofthecarisS$10,000.(ThesevaluationsarecommonknowledgebetweenBobandCharles.)Alicedesignsthefollowingauctiontosellhercar:First,sheaskseachofthemtowritehisbidonapieceofpaper.ThenBobandCharlesgivetheirbids(nonnegativeintegers)toAlice.NoticethatwhenBobandCharleswritedowntheirbids,theydon'tknoweachother'sbid(socalled'sealedbid').AfterAlicereceivesthesealedbids,thebidsareshowntoeveryone,andthecarwillbesoldtothepersonwhohasthehigherbidatthepriceequaltohisownbid.Whenthereisatie(BobandCharlesbidthesameamount),thenAlicewouldflipafaircointodecidewhowillgetthecar. InthisgameBobbids7999andCharlesbids8000isaNashequilibrium.

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2021-04-14 问题

(First-pricesealed-bidauction)Aliceissellingher2000chevroletcavaliertoherfriends,BobandCharles.BobattachesavalueofS$8,000toAlice'soldcar,whileCharles'svalueofthecarisS$10,000.(ThesevaluationsarecommonknowledgebetweenBobandCharles.)Alicedesignsthefollowingauctiontosellhercar:First,sheaskseachofthemtowritehisbidonapieceofpaper.ThenBobandCharlesgivetheirbids(nonnegativeintegers)toAlice.NoticethatwhenBobandCharleswritedowntheirbids,theydon'tknoweachother'sbid(socalled'sealedbid').AfterAlicereceivesthesealedbids,thebidsareshowntoeveryone,andthecarwillbesoldtothepersonwhohasthehigherbidatthepriceequaltohisownbid.Whenthereisatie(BobandCharlesbidthesameamount),thenAlicewouldflipafaircointodecidewhowillgetthecar. InthisgameBobbids7999andCharlesbids8000isaNashequilibrium.