Consider the following two-player game. X Y A 1, 2 3, 2 B 2, 0 1,...

Consider the following two-player game.

	X	Y
A	1, 2	3, 2
B	2, 0	1, 1

a) Find the best response function for player 1.

b) Find the best response function for player 2.

c) Graph the best response function for both players, putting either p1(A) or p1(B) on the x-axis and putting either p2(X) or p2(Y) on the y-axis.

d) Label all Nash equilibria on the graph from part c.

e) Clearly state all Nash equilibria.

Expert Solution

Answer for C and D)

Rahul Sunny answered 2 years ago

Consider the following game. Player 1’s payoffs are listed first: Player 2 X Y Player...

Consider the following game. Player 1’s payoffs are listed first: Player 2 X Y Player 1 A 90 , 1 10 , 0 B 10 , 0 50 , 1 C 100 , 0 80 , 1 Imagine that player 1 makes a decision first and Player 2 makes a decision after observing player 1’s choice. What is the subgame-perfect equilibrium of this game? Imagine that player 2 makes a decision first and Player 1 makes a decision after...

Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is...

Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is a debtor country. Reform Waste Aid 3, 2 -2, 3 No Aid -2, 1 0, 0 a) Compute all (pure and mixed) Nash equilibria. b) Do you think that the above game is the case of a resource curse? Interpret the game with a story of a resource curse.

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)

Consider the following equation: (3 − x^2 )y'' − 3xy' − y = 0 Derive the...

Consider the following equation: (3 − x^2 )y'' − 3xy' − y = 0 Derive the general solution of the given differential equation about x = 0. Your answer should include a general formula for the coefficents.

Consider a game in which, simultaneously, player 1 selects a number x ∈ [0, 8] and...

Consider a game in which, simultaneously, player 1 selects a number x ∈ [0, 8] and player 2 selects a number y ∈ [0, 8]. The payoffs are given by: u1(x, y) = 2xy − 8x − x 2 u2(x, y) = 4xy − y 2 (a) Calculate and graph the best responses for each player. (b) What strategies are never played? (c) Find all Nash equilibriums? (d) What is the preferred equilibrium in society? (e) How would we classify...

Consider the following game that has two players. Player A has three actions, and player B...

Consider the following game that has two players. Player A has three actions, and player B has three actions. Player A can either play Top, Middle or Bottom, whereas player B can play Left, Middle or Right. The payoffs are shown in the following matrix. Notice that a payoff to player A has been omitted (denoted by x). Player B Left Middle Right Top (-1,1) (0,3) (1,10) Middle (2,0) (-2,-2) (-1,-1) Bottom (x,-1) (1,2) (3,2) (player A) Both players...

1. Consider the following normal form game: 1\2 X Y Z A 3,3 0,5 0,4 B...

1. Consider the following normal form game: 1\2 X Y Z A 3,3 0,5 0,4 B 0,0 3,1 1,2 C -1,5 2,2 0,1 a. Does the game have a dominant strategy solution? If yes, which one? (no proof needed) (10 pts) b. Does the game have a solution to IEDS? What is it? Show your procedure. (10 pts)

Consider a game in which, simultaneously, player 1 selects any real number x and player 2...

Consider a game in which, simultaneously, player 1 selects any real number x and player 2 selects any real number y. The payoffs are given by: u1 (x, y) = 2x − x2 + 2xy u2 (x, y) = 10y − 2xy − y2. (a) Calculate and graph each player’s best-response function as a function of the opposing player’s pure strategy. (b) Find and report the Nash equilibria of the game. (c) Determine the rationalizable strategy profiles for this game.

Suppose f(x,y)=(1/8)(6-x-y) for 0<x<2 and 2<y<4. a. Find p(Y<3|X=1) b. Find p(Y<3|0.5<X<1)

f(x,y)=3(x+y) 0<x+y<1, 0<x<1, 0<y<1 (a) E(xy|x)=? (b) Cov(x,y)=? (c) x and y is independent? thank you!

Question