Extensive_form

Extensive_form - Games in Extensive Form Econ 210C UCSB...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Games in Extensive Form Econ 210C UCSB Spring 2011 1. Game Tree (a) A finite set N = { 1 , 2 , ,n }- representing the set of players i = 1 , 2 , ,n < in the game. (b) A rooted T = ( D,E,d )- where the nodes d D represent positions and the edges e E represent the choices . The root node d D repre- sents the start position and the directed paths leading out of d represent possible courses of play. (c) A partition of D into n + 2 subsets: D- set of chance positions. At such positions the move is made by chance. Probability distributions must be exogenously specified at such positions. D i ( i N )- set of personal nodes (decision nodes). When the course of play reaches a node in D i , it is i s turn to choose. Z- set of terminal nodes or end-positions. A real n-vector must be attached to each node in Z , representing the payoff that each player is to receive for the game just concluded. (d) A further partition of each set D i into information sets I i- representing sets of positions which player i cannot tell apart. No path of play may pass through the same information set twice. Moreover, nodes in the same information set must have the same available choices. 1 Example: Consider a 2-player zero-sum game, in extensive form in which player 1 consists of two people (with a joint bank account), Alice and Bill, and player 2 is just a single person, Jack. Two cards, one marked High and one marked Low, are dealt at random to Alice and Jack. The person with the High card receives $1 from the person with the Low card, and then has...
View Full Document

Page1 / 7

Extensive_form - Games in Extensive Form Econ 210C UCSB...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online