Question

1. Explain the concept of Nash equilibrium in a couple of sentences.

2. Consider the two-player game described by the payoff matrix below.

                        Player B
                         L      R
                U    1, 1    0, 0
Player A
                D    0, 0   4, 4

(a) Find all pure-strategy Nash equilibrium for this game.
(b) This game also has a mixed-strategy Nash equilibrium; find the probabilities the players use in this equilibrium, together with an explanation for your answer.
(c) Keeping in mind Schelling’s focal point idea, what equilibrium do you think is the best prediction of how the game will be played? Explain.

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2.

(a) If player A plays U then player B will choose to play L because payoff from playing L given player A is playing U is higher in contrast to playing R, if player B will play L given A has played U then player A has no incentive to divert, because both the player are doing their best given what other player is doing and no player has an incentive to divert, (U,L) is a pure strategy Nash equilibrium of the game.
If player A plays D then player B will choose to play R because payoff from playing R given player A is playing D is higher in contrast to playing L, if player B will play R given A has played D then player A has no incentive to divert, because both the player are doing their best given what other player is doing and no player has an incentive to divert, (D,R) is a pure strategy Nash equilibrium of the game....

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