Extensive game theory

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It can even be used for aromatherapy and skin care treatments as well. In game theory , the extensive form is away of describing a game using a game tree. 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. If Player 1 chooses R, then Player 2 will choose r. Player 1 is left with the option of choosing L and getting 0, or choosing R and getting 1. Here's another quick extensive form game between an industry entrant and an industry incumbant.

The Entrant can either stay out of the industry and not get any profits, or can enter the industry. If he enters, the incumbant will either fight him with a price war or accommodate and both firms will share the profits:. It looks scary: the Entrant might enter and lose money; however, he also knows that the Incumbant will lose money if he fights and still earn profits if he accommodates.

The Incumbant has no credible threat. The Entrant will enter and the Incumbant will accommodate. Other sites in the eonor. Extensive Form Games In the introduction to game theory and Nash Equilibrium , only normal form matrix form games were discussed. For example, here is a game where Player 1 moves first, followed by Player 2: In this game, Player 1 can either choose L or R after which Player 2 can choose l or r. If we were to convert this game to normal form, it would look like this: Player 2 l,l l,r r,l r,r Player 1 L 4,1 4,1 0,2 0,2 R 3,1 1,2 3,1 1,2 We can solve this game by backward induction.

If he enters, the incumbant will either fight him with a price war or accommodate and both firms will share the profits: It looks scary: the Entrant might enter and lose money; however, he also knows that the Incumbant will lose money if he fights and still earn profits if he accommodates. Economics Articles. Economic Data. Economics Glossary. Economic Indicators.

Fiscal Policy. Comparative Advantage. The Supply Curve. Price Elasticity. Marginal Revenue. Output Decision.