pr2.sequen

# pr2.sequen - Sequential Games Sequential Move Games ECON...

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ECON 461 Spring 2010 , H. Ofek Sequential Games Sequential Move Games A. Game Trees 2 ECON 461 Spring 2010 , H. Ofek Sequential Games Sequential-Move Games: Example 2 players (I and II) take alternate moves. Player I makes the opening move by occupying any cell. Then each player in turn occupies a new cell under the following rules: 1. The cell was not previously occupied 2. The cell number is not to exceed by more than by 1 the number in the previous move. (For instance, if cell “2” was occupied in the first move, the cells open for occupation in the second move are “1” and “3” but not “5”) The player occupying cell “1” loses. 2 5 1 3

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1 2 3 5 1 3 1 2 1 2 3 1 1 1 3 1 2 1 1 (L,W) (W,L) (L,W) (W,L) (L,W) (L,W) (W,L) (W,L) (L,W) (W,L) Root 2 5 1 3 Associated Game Tree Player I Player II Terminal node Decision nodes (W,L) = (Win, Lose) 4 ECON 461 Spring 2010 , H. Ofek Sequential Games Terminology 1 2 3 5 1 3 1 2 1 2 3 1 1 1 3 1 2 1 1 (L,W) (W,L) (L,W) (W,L) (L,W) (L,W) (W,L) (W,L) (L,W) (W,L) Root (W,L) = (Win, Lose) Player I Player II Terminal node Decision nodes Decision nodes Branches Terminal nodes Payoffs