3. Consider the two-player game given by the following payoff matrix. In each ce
ID: 1139247 • Letter: 3
Question
3. Consider the two-player game given by the following payoff matrix. In each cell, the first payoff is the payoff to Player 1, while the second is the payoff to Player 2. Plaver 2 0,02,24,13,01, -60,-12-3, -18 2, 2 5,24,12,0 1,-4-2, -8 4,45,34,23,-22,4 2,5 Player 1 D 4,45,25,04, 0, 3 -6,10 -12,0-4,1-2,30,57,'7 -18, -3-8,-2-4,2-2,40, 6 0,2 |2,4 |2,5|6,6 |7,7 8.8 6, 0 9,9 9,9 10, 10 (a) Find all strictly dominated strategies for each player, and explain why they are strictly dominated. (b) Once you have eliminated any strictly dominated strategies, are there any strictly dominated strategies in the reduced game? If so, identify and eliminate them, and explain your answer. If not, explain why not. (c) Find all Nash equilibria to this game in pure strategies. Explain why each one is a Nash equilibrium, and why there are n o others (d) Imagine that two people are selected to play this game, and that the payoffs are dollar values (a negative payoff means that the player must pay the game operator that amount) For simplification, suppose that the people are risk neutral, so that the dollar values they pay or receive represent their utilities. How do you think the game will be played? Upon what factors might your answer depend? NOTE: There is no "correct" answer here, and I am not looking for you to simply spout out one of the Nash Equilibria ifyou don't think that is what will happen. I really want to know whether you think one NE is likely to be played, or whether something else entirely might happen. You will be graded on your reasoning and explanation.Explanation / Answer
a) Player 2 will never play A because all the values of B are greater than A. So we can simply cut A column. Now, look at the reduced matrix. And Player 1 will also not play the A.
b) No, there is not any strictly dominated strategies in the reduced game because some elements are smaller and some are larger.
c) (B,B) and (G,G) are the only two Nash Equilibrium.
d) If the people are risk neutral then they will never play their weekly dominated strategies and we will be left with the same reduced table. From them, the Players choose only (G,G) because from her there is no possible deviation is possible.
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