ECO 355 Game Theory I need a right answer of this problem. QUESTION 3 4.0 1,1 3,

Question

ECO 355 Game Theory I need a right answer of this problem.

QUESTION 3 4.0 1,1 3, 2 Consider the extensive form game between Player 1 and Player 2, At each decision node one player has to decide whether to stay in ( 1 ) or to leave (O). First Player 1 moves. If Player 1 leaves, the game ends. If Player one stays then Player 2 moves, and so on and so forth until someone leaves or Player 1 choses a second time when the game ends. Player 1 has pure strategies in this game, and the game has pure strategy Nash equilibria (Please, type a numerical answer, for example: 0, 1,2, 3...)

Explanation / Answer

3.

Strategies player 1

S1 = {I, O} *{I, O} = {(I, I) (I, O) (O, I) , (O, O) }

S2 { I, O}

Player 2

I

O

Player 1

I, I

4,0

-1, -1

I, O

3, 2

-1, -1

O, I

1, 1

1, 1

O, O

1, 1

1, 1

We will find the best response for each player

BR1 (I) = (I, I)

BR1 (O) = { (O, I), (O, O) }

BR2 (I, I) = I

BR1 (I, O) = I

BR1 (O, I) = I, O

BR1 (O, O) = I, O

SINCE NASH EQUILIBRIUM IS THE MUTUAL BEST RESPONSE

So the NASH equilibrium is { ((I, I), I), ((O, I), O), ((O, O), O)}

Player 1 has 4 pure strategies in this game.

The game has three pure strategy nash equilibrium.

Player 2

I

O

Player 1

I, I

4,0

-1, -1

I, O

3, 2

-1, -1

O, I

1, 1

1, 1

O, O

1, 1

1, 1

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