Value Of The Game In Game Theory


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Normal,,,,form,,,,game[edit].,,,,Game,,,theory,,,is,,,the,,,branch,,,of,,,mathematics,,,in,,,which,,,games,,,are,,,studied:,,,that,,,is,,,,models,,,describing,,,human,,,behaviour.,,,Their,,payoff,,table,,was:,,.,,The,,set,,of,,players,,N,,{displaystyle,,mathrm,,{N},,},,.,,Both,,,criminals,,,confessed,,,,and,,,both,,,went,,,to,,,jail,,,for,,,ten,,,years.1,,,The,,,police,,,,of,,,course,,,,were,,,triumphant,,,,since,,,the,,,criminals,,,would,,,have,,,been,,,free,,,in,,,a,,,year,,,had,,,both,,,remained,,,silent.,,,Mixed,,,,strategy,,,,for,,,,player,,,,i,,,,is,,,,a,,,,probability,,,,distribution,,,,P,,,,on,,,,Σ,,,,,,,,i,,,,{displaystyle,,,,Sigma,,,,,,,,^{i}},,,,.,,,,That,,,is,,,also,,,dominant,,,strategy,,,equilibrium.,,,See,,,Effectiveness.,,,Maskin,,,,(1986).,,,,

Coalition,,,,is,,,,any,,,,subset,,,,of,,,,the,,,,set,,,,of,,,,players:,,,,S,,,,⊆,,,,N,,,,{displaystyle,,,,mathrm,,,,{S},,,,subseteq,,,,mathrm,,,,{N},,,,},,,,.,,,,A,,,fair,,,game,,,has,,,value,,,of,,,zero,,,,otherwise,,,it,,,is,,,unfair,,,or,,,biased.,,,Dummy,,,,A,,,,player,,,,i,,,,is,,,,a,,,,dummy,,,,if,,,,he,,,,has,,,,no,,,,effect,,,,on,,,,the,,,,outcome,,,,of,,,,the,,,,game.,,,,Finite,,game,,is,,a,,game,,with,,finitely,,many,,players,,,each,,of,,which,,has,,a,,finite,,set,,of,,strategies.,,Like,,,Augustin,,,Cournot,,,(writing,,,in,,,the,,,1840's),,,we,,,will,,,think,,,of,,,two,,,companies,,,that,,,sell,,,mineral,,,water.,,,JSTOR2297588.,,,,However,,,,it,,,is,,,not,,,a,,,solution,,,for,,,nonconstant,,,sum,,,games.,,,

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