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ChromeFle Edlt Vitw Hlstory Bookmarks Poople Window Help 43% ?https://inventwitr × H Could you teach X-G i Need To Solve x e i cheggeem % Quiz 5 C Secure https://www.webassign.net/web/Student/Assignment-Responses/last7dep-18382343 xC In A Study Of The x Jake Apps JT360 | Free Listen... .Compass I Moodle M Gmail M U of I Mail In Linkedin Handshake D unUC Enterprise NetflixThesaurus It is not strictly determined. (DNE) 8. -12.77 points TanFin12 9.5.009.CMI Notes Ask Your The payoff matrix for a game is -4 5 41 -4 1 1 3 -1 1 (a) Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column player C uses the minimax pure strategy. (b) Find the expected payoff to the row player if R uses the maximin strategy 50% of the time and chooses each of the other two rows 25% of the time while C uses the minimax strategy 60% of the time and chooses each of the other two columns 20% of the time. (Round your answer to two decimal places) nd (c) Which of these pairs of strategies is most advantageous to the row player O (a) 0 (b) Notes O Ask Your 9.

Explanation / Answer

We have been provided the payoff matrix as follows:

a.

We are required to find the expected payoff for the row player, when the row player uses maximin pure strategy, and the column player uses a minimax strategy (or a minimax regret strategy).

The maximin strategy requires players to maximize the minimum payoff they can get from each outcome. Thus, for the row player, let us calcuate the minimum payoffs he can get from each strategy he adopts.

The fourth column in the above table is the minimum payoff that the row player would receive. The player chooses that strategy which maximizes the payoff. Thus, he chooses the third row, which provides him with a minimum payoff of -1.

(We will remember this information so it can be used as is in the next question.)

The minimax strategy requires players to minimize the maximum regret of each strategy.

Regret is the difference between the maximum payoff and the other payoffs. Thus, the maximum payoff in each column is 3, 5 and 4 (column 1, column 2 and column 3).

Below is the regret table (first three rows) and the maximum regret of each column as the fourth row.

The fourth row is the maximum regret of each column. The player chooses that strategy which minimizes the value of the fourth row. Thus, he chooses the 3rd strategy (3rd column).

Thus, the row player chose the third row, and the column player chose the third column. Thus, the expected payoff for the row player is (3,3) in the payoff matrix which is 1.

b.

The row player chooses maximin stratergy 50% of the time, and the other two strategies 25% of the time.

The column player chooses minimax strategy 60% of the time and the other two columns 20% of the time.

Thus, 50% of the time, the row player chooses row 3 (maximin strategy from previous answer.) Thus, his payoff would be:

0.5 ( 0.6*1 + 0.2*-1 + 0.2*3)= 0.5(0.6-0.2+0.6)= 0.5(1.0)= 0.5

25% of the time, the row player chooses row 2. Thus, his payoff would be:

0.25( 0.6* 1 + 0.2*1 + 0.2*-4)= 0.25(0.6+0.2-0.8)= 0.25(0)= 0

25% of the time, the row player chooses row 1. Thus, his payoff would be:

0.25( 0.6*4 + 0.2*5 + 0.2*-4)= 0.25(2.4+1.0-0.8)= 0.25(2.6)= 0.65

Thus, the total expected payoff for the row player would be 0.5+0+0.65= 1.15

c.

The expected payoff for the row player in the bit 'a' is 1 and the expected payoff for the row player in the bit 'b' is 1.15.

Thus, the b strategy is more beneficial.

-4 5 4 -4 1 1 3 -1 1

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