Lecture Note Set1. Game Theory by Wayne F.Bialas

By Wayne F.Bialas

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Xk } ∀k∈K ηki = {y1i , . . 1. Princess and the Monster. This game is played in complete darkness. A princess and a monster know their starting positions in a cave. The game ends when they bump into each other. Princess is trying to maximize the time to the final encounter. The monster is trying to minimize the time. 2. Lady in the Lake. This game is played using a circular lake. The lady is swimming with maximum speed v . A man (who can’t swim) runs along the shore of the lake at a maximum speed of vm .

These include attributes such as quality of life and aesthetics. Much of this discussion has been borrowed from Keeney and Raiffa [1]. Other important references include Luce and Raiffa [2], Savage [4], and von Neumann and Morgenstern [5]. The basic problem of assessing value can be posed as follows: A decision maker must choose among several alternatives, say W1 , W2 , . . , Wn , where each will result in a consequence discernible in terms of a single attribute, say X . The decision maker does not know with certainty which consequence will result from each of the variety of alternatives.

A man (who can’t swim) runs along the shore of the lake at a maximum speed of vm . The lady wins if she reaches shore and the man is not there. 3. The solution of an arbitrary extensive form game may require enumeration. But under some conditions, the structure of some games will permit a recursive solution procedure. Many of these results can be found in Ba¸sar and Olsder [1]. 5. Player i is said to be a predecessor of Player j if Player i is closer to the initial vertex of the game’s tree than Player j .

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