• 2021-04-14
    (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.