Discuss the following question in the discussion forum: What are the limitations of the normal and extensive forms for modelling large or realistic game-theoretic settings?

The normal form representation of a game works in the following conditions:

- there is a finite number of players

- the players know each others’ possible actions

- players are considered to act simultaneously rather than in sequence (e.g. taking turns)

- as a practical question, the actions are finite and limited in number

- if the game is repeated, the players simply play the same strategy each round, and don’t remember what happened in earlier rounds.

- the strategy is the same in each round (stationary strategy)

The normal form representation of a game is limited in the following conditions and does not work well:

- there is an infinite number of players

- the players may not know some each other’s actions

- if the game is repeated, the players may consider previous rounds as part of deciding the strategy for the current round.

The extensive form representation of a game works when:

- there is a finite number of players and actions

- the players may not know each other’s actions

- the game may be repeated a finite number of times.

- if the game is repeated, the players may consider previous rounds as part of forming the strategy for the current round.

The extensive form representation of a game is limited in the following conditions and does not work as well:

- there is an infinite number of players.  Note that the extensive form can be the basis of infinite series solution.

- the game is repeated an infinite number of times

- the action is represented by points on the real number line.

- the number of players are infinite or even uncountably infinite.

 Information is from the textbook, sections 3, 4, 5, 6