Find the Equilibria/Equilibrium using the following solution concepts: 1)IESDS 2

Question

Find the Equilibria/Equilibrium using the following solution concepts:

1)IESDS

2)Nash Equilibrium.

For subparts a,b,c, and d.

ame obe Acrobat Reader File EditView Window Help Sign In Home Tools HW 6 Game theo.. x - 115% Find the Equilibria/Equilibrium using the following solution concepts Export PDF ^ 1) IESDS 2) Nash Equilibrium Adobe Export PDF Convert PDF Files to Word or Excel Online Select PDF File Hw 6-Game theory.pdf × COLIN Left Right Convert to Up 4, 2 Microsoft Worddocx) v ROWENA Document Language English (U.S) Change Down 5, 2 COLIN Left Middle Right 5,5 9,2 2,7 Convert Up 2,9 6, 2 Create PDF ROWENA Straight 6,4 5, 3 Store and share files in the Document Cloud Down Learn More 12:22 PM 11/30/2017

Explanation / Answer

a)

In the above game the nash equilibrium is UP, RIGHT and the solution of the game is 4 , 2 . Now why this is a nash equilibrium because 4>2 i.e up is prefer to down and 2>1 i.e Right is prefer to Left . So up, right is nash equilibrium.

Now if we do the solution by iterative method by dominant strategy then we can say Right is dominant strategy of Colin . Because 2,3 > 1,2 . So we eliminate the left. Now after Right the dominant strategy of Rowena is UP. Because 4>2. Now in dominant strategy the solution is UP, RIGHT. Solution of the game is 4 , 2.

b) In this game the nash equilibrium is Stright , Left . Because 6 is greater than 4 and 2 . Similarly 4 is greater than 2 and 3. So straight , Left is the nash equilibrium and solution of the game is 6 , 4 . In no other strategy it does not happen.

Now if we do the solution by IESDS that is iterative method by dominant strategy . Here the dominant strategy is Left and Middle, so eliminate Right strategy for Colin. If we remove right then the dominant strategy for Rowena is Straight . It means Straight is dominating than Up and Down. So we take Straight . Now among left and middle Colin will always play Left. So solution of the game is Straight , Left ( 6, 4 ).

C) In this game the nash equilibrium is Straight , Right and solution of the game is 3, 5 . Because 3 is greater than 2 and 5 is greater both 4 and 2 . So straight right is nash equilibrium.

Now by dominant strategy we can say for Colin middle is dominated by left and right . So we eliminate middle. Now among up, straight and down , Rowena will play straight . Because straight is dominatiing . Then Colin will play Right. So ultimately solution of the game is Straight, Right i.e 3,5.

D) In this game UP, EAST is the nash equilibrium . Because 5 i.e Up is greater than 4,3,4 i.e high, low and down and Similarly East (5) is greater than north , south and west i.e 5 > 4,3,4. So nash equilibrium of this game is UP, EAST ( 5,5) .

Rowena/Colin LEFT RIGHT UP 3 , 1 4, 2 DOWN 5 , 2 2 , 3

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