Section 6: Stochastic Games and Games with Uncertainty

Key Learning Points

• Introduce the concepts and representations of stochastic games and Bayesian games.
• Introduce the distinction between ex-ante, ex-interim, and ex-post utility.
• Define the Bayesian Nash equilibrium, which is the standard solution concept for Bayesian games.

Activities

1. Read Sections 6.2.1 and 6.3 of Chapter 6 of the textbook.
2. Watch the following videos on YouTube:
   1. Stochastic Games
   2. Bayesian Games: Taste
   3. Bayesian Games: First Definition
   4. Bayesian Games: Second Definition
   5. Analyzing Bayesian Games
   6. Bayesian Games: Another Example

   If you still have difficulty in understanding Bayesian Nash equilibrium, please see the following videos on YouTube:

   1. Incomplete information
   2. Bayesian Nash Equilibrium
3. Consider the following game with incomplete information according to Definition 6.3.2: N = {I, II}; A1 = {T1, B1, T2, B2}, A2 = {L, R}; Θ₁ = {I₁, I₂}, Θ₂ = {II}; p(I₁, II) = p(I₂, II) = ½; the utility function for Player I and Player II is shown below.

   

   Please calculate the Bayesian Nash equilibria of the game.

4. Discuss the following questions in the discussion forum:
   1. We know that an MDP is simply a stochastic game with only one player, while a repeated game is a stochastic game with one stage game. Can you give an example of a stochastic games with more than one stage and more than one player?
   2. What is the difference between imperfect information and incomplete information?