BEA104 Game Theory for Business and Social Sciences: Nash Equilibria

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BEA104 Game Theory for Business and Social Sciences

Question

Answered

Question:

Answer all the following questions.

1.

Find all the pure strategy Nash equilibria in the following Provide details of the solution concept used explaining all the steps

		P2
		North	South	East
P1	Earth	10, 20	20, 10	10, 0
	Water	0, 50	10, 20	70, 40
	Wind	-10, 10	30, 0	50, 20

P2: north dominates south (20>10, 50>20, 10> 0), making south a dominated strategy, which yields the below:

		P2
		North	East
P1	Earth	10, 20	10, 0
	Water	0, 50	70, 40
	Wind	-10, 10	50, 20

The highlighted is the only NE that I can identify; is there anymore?

2.

The trust game is a two-player sequential-move game. Player 1, the Trustor, has an endowment (E), which he can invest in a project by the Player 2, the Trustee. If the Endowment is invested, the Trustee generates a profit of 3E, which he is free to share (give back 1.5E to the Trustor) or not share (give back 0 to the Trustor) with the Trustor.

Represent this sequential game in its extensive form (game tree). Using rollback (backward induction), state what is the equilibrium which will be achieved in this game.

Slightly confused by the endowment not being numerically specified, hence the 0 (-x?).

Performbrief review of the academic literature of Trust Describe behavior of individuals in this game with respect to the predictions you outlined in part (a). In your own words, why do you think behavior deviates from the rollback equilibrium in these games? [Spend no more than a page on answering this question]

3.

Two players John and Dany come from Denmark, which imposes a strong cultural value on equality. They are to participate in a game where they are put in separate rooms and are each to pick one of the five letters: G, K, L, Q or W. If they choose the same letters, only then they both get prizes as follows. Otherwise they get 0.

Letter	G	K	L	Q	W
John’s Prize	1	2	3	4	5
Dany’s Prize	5	4	3	3	1

Draw the table for this game and identify the Nash equilibria.

		Dany
		G	K	L	Q	W
John	G	1, 5	1, 4	1, 3	1, 2	1, 1
	K	2, 5	2, 4	2, 3	2, 2	2, 1
	L	3, 5	3, 4	3, 3	3, 2	3, 1
	Q	4, 5	4, 4	4, 3	4, 2	4, 1
	W	5, 5	5, 4	5, 3	5, 2	5, 1

Absolutely clueless on how to construct this…

Can one of the equilibria be a focal point? Which one? Why?

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BEA104 Game Theory for Business and Social Sciences