2 Examples of Bayesian Games 2 . 1 A Two Player Bargaining

Note: This is a only a draft version, so there could be flaws. If you find any errors, please do send email to [email protected]. A more thorough version would be available soon in this space. We have so far studied strategic form games with complete information. We will now study games with incomplete information, which are crucial to the theory of mechanism design. In particular, we study Bayesian games and introduce different equilibrium notions in Bayesian games such as Bayesian Nash equilibrium. A game with incomplete information is one in which, at the first point in time when the players can begin to plan their moves in the game, some players have private information about the game that other players do not know. In contrast, in complete information games, there is no such private information, and all information is publicly known to everybody. Clearly, incomplete information games are more realistic, more practical. The initial private information that a player has, just before making a move in the game, is called the type of the player. For example, in an auction involving a single indivisible item, each player would have a valuation for the item, and typically the player himself would know this valuation deterministically while the other players may only have a guess about how much this player values the item. John Harsanyi (Joint Nobel Prize winner in Economic Sciences in 1994 with John Nash and Rein-hard Selten) proposed in 1968, Bayesian form games to represent games with incomplete information.