In Chapter 8, we will study strategic form games with incomplete information. These games involve at least one player who has uncertainty about the payoffs of other players. In real life, many strategic situations involve incomplete information. For example, the production cost, hence the operating profit, of a firm in an oligopolistic industry, or the valuation of a buyer about an object sold in an auction, is generally unknown to its competitors. We will call a strategic situation with incomplete information a (static noncooperative) Bayesian game. In Sect. 8.1, we will describe a Bayesian game and, in Sects. 8.2 and 8.3, we will, respectively, present the ex ante and interim Bayesian Nash equilibrium concepts with several propositions and examples.