Theory Lecture Note Set 2 Wayne
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چکیده
Definition 2.1. A game (in extensive form) is said to be zero-sum if and only if, at each terminal vertex, the payoff vector (p 1 ,. .. , p n) satisfies n i=1 p i = 0. Two-person zero sum games in normal form. Here's an example.. . −1 −3 −3 −2 0 1 −2 −1 2 −2 0 1 The rows represent the strategies of Player 1. The columns represent the strategies of Player 2. The entries a ij represent the payoff vector (a ij , −a ij). That is, if Player 1 chooses row i and Player 2 chooses column j, then Player 1 wins a ij and Player 2 loses a ij. If a ij < 0, then Player 1 pays Player 2 |a ij |. Note 2.1. We are using the term strategy rather than action to describe the player's options. The reasons for this will become evident in the next chapter when we use this formulation to analyze games in extensive form. Note 2.2. Some authors (in particular, those in the field of control theory) prefer to represent the outcome of a game in terms of losses rather than profits. During the semester, we will use both conventions.
منابع مشابه
Lecture Note Set 3
a1n∗1 ,n ∗ 2 ,...,n ∗ N ≥ a1n1,n∗2 ,...,nN ∀ ni ∈ M1 Department of Industrial Engineering, University at Buffalo, 301 Bell Hall, Buffalo, NY 142602050 USA; E-mail: [email protected]; Web: http://www.acsu.buffalo.edu/ ̃bialas. Copyright c © MMIII Wayne F. Bialas. All Rights Reserved. Duplication of this work is prohibited without written permission. This document produced March 10, 2003 at 12:19...
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تاریخ انتشار 2005