Consider the following (stupid) 2-person, total conflict, zero sum game: There a

Question

Consider the following (stupid) 2-person, total conflict, zero sum game: There are three numbers {1, 2, 3}. Player A goes first and selects one of the numbers. Player B goes next and selects one of the remaining two numbers. Player A then receives the final number. The winner is the person with the largest sum.

1. Show that player A has 3 total strategies.
2. Show that Player B has 6 total strategies.
3. Using the value 1 if A wins, 0 for a tie, and -1 if B wins, please construct the payoff table for this game.
4. Are there any dominated strategies for either player?
5. What are the MiniMax and MaxiMin strategies? What are their payoffs?
6. Is there an optimal pure strategy choice for each player? if so, what is the value of the game?

Explanation / Answer

b) player B has the strategy of picking 2,when player A picks 1, and picking 2 when player A picks 3, same goes for player B picking 1 and 3. This gives us 6. What if player A does not pick what player B had assumed he would? Then you get the 8 your professor was talking about, in response to A's (1,2,3), B could pick (2,1,1),(2,1,2),(2,3,1),(2,3,2),(3,3,1),(3,3,2),(3,1,1),(3,1,2) strategies. c)sticking with the original 6: A 1 , 2 , 3 B 2, 1, 1 1 , 1, 1 2, 1, 2 1 , 1, 1 2, 3, 1 1 , 0, 1 2, 3, 2 1, 0, 1 3, 3, 1 0, 0, 1 3, 3, 2 0, 0, 1 3, 1, 1 0, 1, 1 3, 1, 2 0, 1, 1 d) dominated strategies for B are 2, 1, 1, and 2, 1, 2, there are not dominated strategies for A e) I forget how to solve this. f)for B, dominant strategies are 3, 3, 1 and 3, 3, 2, and for A a dominant strategy is 3

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