How to have same utility function for two persons? I have a question regarding utility functions:

Utility can be defined as follows:

$U=1+e^{\frac{x}{RT}}$

U:Utility

x: What we want to find the utility for (Certain equivalent)

RT: Risk tolerance

My question is what conditions must be upheld in order for two persons to create the same utility functions for a bet? 

Example:

Person A bet \$5 that horse number 1 wins. Person B bet \$20 that horse number 2 do not win. Is it then possible that their utility functions is the same given that their probabilities for horse 1 winning is the same and that they have the same risk tolerance?
Strictly speaking, infinitely different utility functions can give the same preferences over lotteries. If person A has utility function $f(x)$ then person B with utility function $g(x)=A+B\cdot f(x)$, $B&gt;0$ will make identical decisions over all lotteries. There would be no way to know which individual was actually using utility function $f(x)$ and which was using $g(x)$ because they would always make the same decisions.