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We write Pi for player i’s mixed strategy set and pi for an element of this set. Player i’s strategy is completely mixed if it assigns a positive probability to each of his pure strategies. 5 is a mixed strategy for player i, i=1, 2. Mixed strategies: what for? We discussed above that it is not easy to advise somebody on the best way to play the first price sealed bid all pay auction. For example playing 0 seems best if the opponent plays 2 or more, but if he plays 0 as well, then it is better to bid 1 and so on.

23╇ ■ How to build a game What happens in such a game, for any values of M and V? Who stops first? Can you reasonably expect that the opponent stops before you, or should you be cautious and stop the game as fast as possible? e. e. if the probability that the opponent stops at the next round is higher than 2/3. Things are even more complicated in a modified war of attrition game. If V is higher than 4, say 5 for example, then you may be induced to go on even if your opponent does not stop at his next decision round, but stops at his second next decision round because M–x

Yet this may have an impact. ). 8a, in that many students explained me that they wanted the object regardless of their gains and losses. 8c (in this matrix we subtract the revenue M=5 in order to clearly see the net wins or losses). 8c. 8c at the beginning of the next lecture in game theory, a week later. So the students learned nothing on game theory between the two playing sessions and the week between the two sessions prevented them making a direct link between the two games. 8c. 8c. 8c. 8c (strongest contrast).

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Algorithmic Methods in Algebra and Number Theory by Michael Pohst


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