Question
In: Advanced Math
3. Dictator and Ultimatum Games with Fehr-Schmidt Preferences. Now let the two utility functions be given...
3. Dictator and Ultimatum Games with Fehr-Schmidt Preferences. Now let the two utility functions be given by,
UA = xA − .6 max(xB − xA, 0) − βA max(xA − xB, 0),
UB = xB − αB max(xA − xB, 0).
(a) Suppose that the two agents play a dictator game in which player A is given an endowment of 100 and may transfer any amount s ∈ [0, 100] to player B. The material payoffs are then given by (xA, xB) = (100 − s, s). Compute player A's strategy for all possible values of βA.
(b) Now suppose that the two agents are playing an ultimatum game with an endowment of 100. Write down the set of players, the pure strategy space of each player and the payoff functions.
(c) Calculate B's best response to every offer s ∈ [0, 100].
(d) How does the subgame perfect equilibrium of the game depend on αB and βA?
Solutions
Colby Messinger answered 6 months agoRelated Solutions
Assuming that a responder in the ultimatum game has Fehr-Schmidt inequity aversion utility, and the responder...
Assuming that a responder in the ultimatum game has
Fehr-Schmidt inequity aversion utility, and the responder Is
indifferent between accepting and rejecting a proposal to get $1
while the proposer keeps $9, find the responder's value of Alpha.
Remember if the proposal is rejected, both people get zero dollars.
Enter your answer as a decimal.
For each of the following utility functions, explain whether the preferences that they represent are strictly...
For each of the following utility functions, explain whether the
preferences that they represent are strictly convex. Use
indifference curve diagrams to help explain your answers.
1. Preferences represented by u (x1, x2) = x1 + x2.
2. Preferences, represented by u (x1, x2) = min {x1, x2}.
Suppose there are two consumers, A and B. The utility functions of each consumer are given...
Suppose there are two consumers, A and B. The utility functions
of each consumer are given by:
UA(X,Y) = X2Y UB(X,Y) = X*Y
Therefore: For consumer A: MUX = 2XY; MUY = X2
For consumer B: MUX = Y; MUY = X
The initial endowments are: A: X = 75; Y = 15 B: X = 75; Y =
5
a) (20 points) Suppose the price of Y, PY = 1. Calculate the
price of X, PX that will lead...
Suppose there are two consumers, A and B. The utility functions of each consumer are given...
Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA(X,Y) = X2Y
UB(X,Y) = X*Y
Therefore:
For consumer A: MUX = 2XY; MUY =
X2
For consumer B: MUX = Y; MUY = X
The initial endowments are:
A: X = 120; Y = 6
B: X = 30; Y = 14
a) (20 points) Suppose the price of Y, PY = 1. Calculate
the price of X, PX that will lead...
Suppose there are two consumers, A and B. The utility functions of each consumer are given...
Suppose there are two consumers, A and B. The utility functions
of each consumer are given by: UA(X,Y) = X2Y UB(X,Y) = X*Y
Therefore: For consumer A: MUX = 2XY; MUY = X2 For consumer B:
MUX = Y; MUY = X
The initial endowments are: A: X = 75; Y = 15 B: X = 75; Y =
5
a) (20 points) Suppose the price of Y, PY = 1. Calculate the
price of X, PX that will lead...
Describe short(!) th most important point of the following a Preferences, utility functions, and measures of...
Describe short(!) th most important point of the following
a Preferences, utility functions, and measures of risk
aversion.
b Portfolio choice theory.
c CAPM and APT.
d The state-contingent claim model.
For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)=...
For two goods x and y, the individual’s preferences are measured
by the utility function ?(?,?)= ?0.5?0.5, the
price of good y is $10, income equals $100, and the price of good x
increase from $5 to $10. Draw the price consumption curve for x and
y and compute the slop of the price consumption curve. Show your
calculation step by step.
Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...
Let the utility function be given by
u(x1, x2) = √x1 + x2.
Let m be the income of the consumer, P1 and P2 the prices of good 1
and good 2, respectively.
To simplify, normalize the price of good 1, that is P1 = £1.
(a) Write down the budget constraint and illustrate the set of
feasible bundles using a figure.
(b) Suppose that m = £100 and that P2 = £10. Find the optimal
bundle for the consumer....
Suppose there are 2 consumers, A and B. The utility functions ofeach consumer are given...
Suppose there are 2 consumers, A and B. The utility functions of
each consumer are given by: UA(X, Y ) = X^1/2 Y^1/2 UB(X, Y ) = 3X
+ 2Y The initial endowments are: WXA = 10, WYA = 10, WXB = 6, WYB =
6a) (20 points) Using an Edgeworth Box, graph the initial
allocation (label it W) and draw the indifference curve for each
consumer that runs through the initial allocation. Be sure to label
your graph carefully...
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from
X to X. For any relation R on X, define a relation S on F by: for
all f, g ∈ F, f S g if and only if there exists x ∈ X so that
f(x)Rg(x).
For each of the following statements, prove or disprove the
statement.
(a) For all relations R on X, if R is reflexive then S is
reflexive....
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