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?

Hold ’em Poker is a multi-stage stochastic game with more than one player

Multi-player – the game can have from 2 to many players, with a common maximum size being in the 10 – 15 range.

Stochastic – the random dealing of cards to the players is the reason the game is stochastic.

Multi-stage – Hold ‘em has stages of the initial deal along with common cards, with betting.  Then, in several stages, more common cards are added, which can change how the players view their own chances and those of their opponents, and thus requiring a possible change of strategy.

Imperfect information vs Incomplete information

An imperfect information game refers to when an agent does not have some or all information about the actions of others, or which node of the game the agent is at, or what choices the agent made earlier (history) to get to this node.

An incomplete information game (also known as a Bayesian game), is when the game always has the same actions, but the outcomes can vary according to a probability distribution.