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📗 (Fall 2017 Midterm Q12, Fall 2016 Midterm Q8, Fall 2014 Final Q13, Fall 2012 Final Q17) Which nodes are pruned by alpha-beta pruning? The max player moves first.
📗 Select the nodes:
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📗 (Fall 2017 Midterm Q12, Fall 2016 Midterm Q8, Fall 2014 Final Q13, Fall 2012 Final Q17) Which nodes are pruned by alpha-beta pruning? The min player moves first.
📗 Select the nodes:
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📗 (Fall 2017 Midterm Q3) Consider a game board consisting of bits initially at . Each player can simultaneously flip any number of bits in a move, but needs to pay the other player one dollar for each bit flipped. The player who achieves wins and collects dollars from the other player. What is the game theoretic value (in dollars) of this game for the first player?
📗 Note: "game theoretic value" is what we called "value of the game" in the lectures.
📗 Answer: .
📗 (Fall 2014 Final Q4) Given the following game matrix (zero-sum game), suppose A (row) knows that B (col) will use the mixed strategy on I, II, III. What is the expected payoff for A if A plays optimally?
📗 (Fall 2014 Final Q5) Identify the pure strategy Nash equilibria in the following zero-sum game. A (row) is the max player, B (col) is the min player.
📗 (Fall 2012 Final Q18) What is the game theoretical value of the following matrix form game? A (row) is the max player, B (col) is the min player. If there are multiple Nash equilibria, use the one with the largest value (to the max player).
A \ B
I
II
III
I
II
III
📗 Note: here, I am using "game theoretical value" and the "row (max) player's value in a Nash equilibrium" interchangeably, which is slightly different from Professor Zhu's definition in Fall 2012 Final Q18. In the case there is only one Nash equilibrium, the value should be the same.
📗 Answer: .
📗 (Fall 2016 Final Q7) Perform iterated elimination of strictly dominated strategies. Player A's strategies are the rows. The two numbers are (A, B)'s payoffs, respectively. Recall each player wants to maximize their own payoff. Enter the payoff pair that survives the process (i.e. payoffs from rationalizable actions). There should be only one such pair.
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📗 Answer: .
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