Extensive form representation game theory

The payoffs are represented at the end of each branch. In the first game tree we can see how player 1 is the first to decide, while player 2 will make a decision after observing what player 1 has decided. The payoffs represented at the end of each brand represent all possible outcomes. For instance, if player 1 chooses strategy A and player 2 chooses strategy B, the set of payoffs will be p 1A ,p 2B. A good example of a sequential game described with the extensive form is when considering collusion agreements , as depicted in the second game tree.

Two firms share the market, colluding and maintaining high prices. Each firm can decide to stop colluding and start a price war, in order to increase their market share, even force the other to quit the market.

Firm 1 can either keep colluding with firm 2, or start a price war. If firm 1 decides to keep colluding, firm 2 will need to make a decision. If they both agree to collude, they will get 5,5.

However, if one of them decides to start a price war, the set of payoffs will be either 4,3 or 3,4, depending on which one starts the war and therefore acquires a greater market share.

This result may change when considering repeated games. These information sets, usually represented by a dashed line uniting two nodes or by encircling them, mean that the player does not know in which node he is, which implies imperfect information, like when using the strategic form. Jan Lope Gallego. Summary In this first Learning Path on Game theory, we learn about the main tools and conditions required in order to make a thorough analysis of games.

We see how the quality of information shape the way we solve games, and learn about how to describe them. Game theory: a definition Information: Complete information Common knowledge Perfect information Description of games: Strategic form Extensive form.

Complete information and common knowledge are usually mandatory conditions for most games. However, whether a game consists of perfect or imperfect information determines the best way to analyse the game, and therefore the best way to describe it, by using the strategic form usually for imperfect information games or the extensive form mainly for perfect information games.

Game theory I: Strategic form. You currently have 4. Which one should you "combine"? Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Extensive Form Representation Ask Question. Asked 1 year, 10 months ago. Active 1 year, 10 months ago. Viewed 66 times. Then Player 1 chooses either Right or Left and does not observe nature's choice. My take: Is this correct? I am not really sure about the instructions in bold. Improve this question. What exactly is it that you are "not sure about" in that part? That is where I got stuck. Should there be any such nodes for Player 2 in your example?

Show 1 more comment. Active Oldest Votes. Improve this answer. I percieve these types of answers as giving the man a fish, rather than teaching them to fish or do game theory. Might be a knife-edge case though What exactly is the effort made here? That's considerably more than most of the pls-solve-my-homework questions here have to offer.

As for fishing, well, there are different philosophies out there