I want to solidify my understanding of the von-Neumann-Morgenstern axioms. How would you analyze these scenarios using the lens of these axioms?
Suppose that Person A owns a potentially expensive baseball card. All people within this universe abide by maximizing subjective utility, aligning with the von-Neumann-Morgenstern axioms.
a. In a universe in which both person A and person B have the same utility function and same wealth to start off with, why would person A want to sell the baseball card to person B instead of owning it, and In the same instance, why would person B want to purchase the card instead of returning it? (Note: Technically, person A owns the baseball card, so he does have slightly more money)
b. In this scenario, person B wants to purchase a different card from person C. Is there ever a scenario where person B would purchase a card from person C for a set amount, and then immediately flip the purchase to sell to person D for less money?
In the context of just the Von Neumann Theorem, I don't think there is anything sophisticated going on here. As the problem is stated, there doesn't seem to be any sort of transaction costs being occurred.
For part a. Person A will sell the card if and only if he receives the monetary amount that is of equal or greater value to that of the card. Additionally, person B will buy the card if and only if they receive the card for less than or equal value to that of the card. Since person A and B have the same utility function, this transaction occurs if and only if the card is sold for its exact value.
For part b. The answer is no following identical reasoning.