Theorem of the Bayes-Nash Equilibrium

Theorem of the Bayes-Nash Equilibrium states that in games where players have private information and uncertain outcomes, each player chooses a strategy that maximizes their expected payoff, considering their beliefs about other players’ types and strategies. At equilibrium, no player can improve their expected result by unilaterally changing their own strategy. Essentially, it ensures that when everyone acts based on their best guesses about others, the overall strategies become stable, and no one has an incentive to deviate, leading to a predictable outcome in complex strategic situations involving uncertainty.