Question

Suppose that a decision-maker’s preferences over the set A={a, b, c} are represented by the payoff function u for which u(a) = 0, u(b) = 1, and u(c) = 4.

(a) Give another example of a function f:A→R that represents the decision-maker’s preferences.

(b) Is there a function that represents the decision-maker’s preferences and assigns negative numbers to all elements of A?

Answer 1

Solution-

(a) Set A = {a,b,c}

u(a)= 0

u(b)= 1

u(c)= 4

Example of function f:A->R is as follows-

R={(a,0), (b,1), (c,4)}

Where, R= f(x), X is the subset of A.

(b) Function that represents the decission's maker prefrences and assigns negative number to all elements of A-

f: A->R^-1 = {(0,a), (1,b), (4,c)}