Discuss your perspective on the use of game theory. How do "Nash Equilibrium" and the idea of one "player" impacting another "player" within an organization affect the economic decisions and growth of an organization?

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Patrina SchowalterLv2

31 Aug 2018

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Problem 1

In each of the three games shown below, let p be the probability that player 1 plays cooperates (and 1- p the probability that player 1 defects), and let q be the probability that Player 2 plays cooperates (and 1- q the probability that player 2 defects).

PrisonerÃ¢â¬â¢s Dilemma

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	10,80
	defect	80,10	40,40

Stag Hunt

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	5,40
	defect	40,5	40,40

Chicken

	Player 2
Player 1		cooperate	defect
	cooperate	70,70	50,80
	defect	80,50	40,40

1. For each game, draw a graph with player 1Ã¢â¬â¢s best response function (choice of p as a function of q), and player 2Ã¢â¬â¢s best response function (choice of q as a function of p), with p on the horizontal axis and q on the vertical axis.

2. Using this graphs, find all the Nash equilibriums for the game, both pure and mixed strategy Nash equilibriums (if any). Label these equilibriums on the corresponding graph.

3. In those games that have multiple pure strategy Nash equilibriums, how do the expected payoffs from playing the mixed strategy Nash equilibrium compare with the payoffs from playing the pure strategy Nash equilibriums? Which type of strategy (mixed or pure) would players prefer to play in these games?

Problem 2

Two people are involved in a dispute. Player 1 does not know whether player 2 is strong or weak; she assigns probability ÃÂ± to player 2 being strong. Player 2 is fully informed. Each player can either fight or yield. Each player obtains a payoff of 0 is she yields (regardless of the other personÃ¢â¬â¢s action) and a payoff of 1 if she fights and her opponent yields. If both players fight, then their payoffs are (-1; 1) if player 2 is strong and (1;-1) if player 2 is weak. The Bayesian game is the following, depending on the type of player 2:

	Y	F		Y	F
Y	0, 0	0, 1	Y	0, 0	0, 1
F	1, 0	-1, 1	F	1, 0	1, -1
Player 2 is strong (ÃÂ±)			Player 2 is weak (1-ÃÂ±)			Player 2 is strong (ÃÂ±)

After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of ÃÂ± (ÃÂ± Ã¢â°Â¤ 1/2 or ÃÂ± Ã¢â°Â¥1/2).

jadebuffalo465

Economists argue that consumers are utility maximizers who weigh the pleasure of consuming an extra unit versus the cost to consume an extra unit. Behavioural economists and psychologists both question this vision of human interaction. There is a game that behavioural economists use called the dictator game. In this game, two people have to decide how to divide up some money given to them. One person is the dictator who decides what percentage to give to the other player. The second player has only one decision to accept or decline the offer of the first player (who is called the dictator). If the second person accepts the offer both players walk away with the money. If the second player rejects the offer neither the dictator nor the second player gets anything.

So imagine you are playing this game as the second player and you are both given 10 dollars and the dictator decides to offer you 25 cents and that she/he will keep $9.25. Your only choice is to accept the 25 cents or reject the offer and get no money at all.

What would you do? What would be considered rational from the perspective of utility maximization? What would you do if this is a continued game and the same scenario will happen multiple times not just once? Do you think others will react the same way you would?

byzantiumjackal917

There is a beach that runs east-west. Ice cream vendors can choose any of nine locations along the beach. Location 1 is at the west end, location 2 is just to the east of 1, 3 is just to the east of 2, and so on. There are 10 consumers at each location. Consumers follow these rules:

If they buy ice cream, they will buy from the closest vendor. If there are two vendors the same distance away, half will buy from one and a half from the other.

Each consumer will buy one ice cream cone as long as they do not need to walk more than two locations. So, for example, customers at 4 will buy from a vendor at 2, 3, 4, 5, or 6 but they will not buy from a vendor at 1, 7, 8, or 9.

If there is no vendor within two locations, a customer will not buy ice cream.

Vendor A and vendor B will choose their locations simultaneously. Each wants to maximize the number of ice cream cones it sells. They could choose the same location.

Find the Nash equilibrium (or Nash equilibria if you believe there is more than one) of this game.

5. 1. Player 1 and Player 2 will play the following game. Player 1 will choose x₁ and Player 2 will choose x₂ simultaneously. Their payoffs Ï₁ and Ï₂ are

Ï₁ = 90x₁ x₁² x₁x₂

Ï₂ = 90x₂ x₂² x₁x₂

(a) Find each player's best reply.

(b) Show that x₁ = x₂ = 30 is the Nash equilibrium of this game.