Bayesian game

A game in which players have private information about their own types, such as preferences or costs, that affects their payoffs or available actions.

Harsanyi transformation: A representation of a game with private information as a game of incomplete information in which a chance move selects player types. It formalizes private types as nature’s initial move and gives the game its standard strategic form.
Game theory: The mathematical study of strategic interaction among decision-makers. Bayesian games extend strategic game models to situations with private information.
First-price sealed-bid auction: An auction in which each bidder submits a hidden bid and the highest bidder pays their own bid. Each bidder’s valuation is private, making bids depend on beliefs about rivals.
Perfect information: A game has perfect information when every player observes the full history of prior actions at each decision point. A Bayesian game can involve uncertainty about types even when actions are observable.
Bayesian Nash equilibrium: A strategy profile in which each player’s strategy maximizes expected payoff given beliefs about other players’ types and strategies. It is the central solution concept for strategic choices under private information.
Type (game theory): A player's private description of relevant characteristics, such as preferences, costs, or available actions. Types encode the private attributes that distinguish players within the model.
Winner's curse: The tendency for the winner of a common-value auction to have overestimated the item’s value. Winning conveys information about rivals’ estimates that bidders must account for.
Complete information: A game has complete information when every player knows the players’ payoff functions and available actions. Bayesian games relax this assumption by allowing payoff-relevant characteristics to be private.
Common prior: A probability distribution over possible states of the world that all players share as their prior belief. It supplies the shared starting beliefs used to evaluate uncertain types.
Information set: A set of decision nodes that a player cannot distinguish when choosing an action. It represents which parts of the game’s history a player can observe.

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