In a modified story of the prodigal son, a man had two sons, the prodigal and the one who stayed home. The man gave the prodigal son his share of the estate, which he squandered, and told the son who stayed home that all that he (the father) has is his (the son’s). When the man died, the prodigal son again wanted his share of the estate. They each tell the judge (it ends up in court) a share amount they would be willing to take,
the money goes to the game theory society. If Ii + IIj ≤ 1, then each gets the share they asked for and the rest goes to an antismoking group. (a) Find the game matrix and find all pure Nash equilibria.
(b) Find at least two distinct mixed Nash equilibria using the equality of payoffs Theorem 3.2.4?