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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 endpositions. A real nvector 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 2player zerosum 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...
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 Fall '09
 QIN
 Game Theory, information set, player, King Solomon, perfect recall, potential entrant suppose

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