TheMontyHallproblemcanbemodeledasaBayesiangametoanalyzethestrategicinteractionsbetweentheplayerandthehost.Inthissetup,theplayer'sinitialchoiceandthehost'sactionofrevealingagoataretreatedasmovesinagameofincompleteinformation.Theplayer'suncertaintyabouttheprize'slocationiscapturedbyapriorprobabilitydistribution,whilethehost'sstrategydependsonthegame'srules(e.g.,alwaysrevealingagoatandofferingaswitch).BayesianNashequilibriumcanthenbeusedtodeterminetheoptimalstrategies,showingthatswitchingdoorsmaximizestheplayer'swinningprobability(2/3)understandardassumptions.Thisframeworkformalizestheproblem'sprobabilisticreasoningusinggame-theoreticconcepts.
