The following payoff matrix represents a simultaneous-move game between two players: John and Trevor. Each player has to choices: Black or White. The first number in each cell is the payoff to John, and the second number is the payoff to Trevor. Trevor Black White Black 15, 15 10, 10 John White 12, 10 13, 15 Refer to the table above. Which statement is true? a. Neither John nor Trevor have a dominant strategy in this game. O b. Only Trevor has a dominant strategy in this game. c. Only John has a dominant strategy in this game.

In the "Prisoners' Dilemma" game: both players have a dominant strategy not to confess. O only one player has a dominant strategy to confess. O both players have a dominant strategy to confess. O neither player has a dominant strategy.

7. Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Andrew Left Right Left 8,4 5,4 Beth Right 4,5 6,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth chooses

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Consider the following game:                                 Player 2                                  In     Out  Player 1      In     -2,-2    2, 0                      Out    0, 2     0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?

Consider the two-player game depicted below w А 1,5 2,2 0,4 3,11 В 13,0 4,1 2,5 4,2 с 1,3 2,6 5,2 2,0] a. What is Player 2's best response if Player 1 plays B? b. What is Player l's best response if Player 2 plays z? c. What are the pure strategy Nash Equilibria? సా

7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses

6.

Q3. Explain the concept of mixed strategy and how to calculate the value of game. Also provide a suitable example for mixed strategy. Determine which of the following two-person zero-sum games are strictly determinable and fair. Give the optimum strategies for each player in the case of it being strictly determinable. I. I. a- Player A Player B B1 B2 B3 A1 8 4 A2 5 -1 b. I II II IV V I 4 -2 -2 3 1 A II 1 -1 III -6 -5 -2 -4 4 IV 3 1 -8

Normal Form Game: The table below provides a normal form, 2 x 2 game. The players are Column and Row. Column can choose either LEFT or RIGHT, and Row can choose either UP or DOWN. Their payoffs for each combination of moves are provided in the four boxes. Column Row UP DOWN The combination of moves (UP, LEFT) is a Nash-Equilibrium. A. False O B. True 2 LEFT -1 -7 3 6 RIGHT -5 -10