Question 9 A man (M) and his estranged wife (W) seeking sole custody of their child. The man "values" the child at Vm>0 and the wife "values" the child at Vw>0. The family court would like to assign custody to the parent that places the highest value. If the court knew these values, then the matter is trivially resolved. But the problem is that the Family Court only knows that one parent values custody at least 100 whereas the other values no more than 50 the court does not know which parent values the custody more. To ensure that its desired outcome is reached, the following scheme is set up. M is given two strategies "yes" or "no" which state whether he really wants custody. W is given two strategies "challenge" which denotes I want to challenge M's claim if he were to say play 'yes ' or "no challenge" - I do not really want custody. M is given the custody only if he plays "yes" and W plays "no challenge". In all other cases W is given custody. However, if M plays "yes" and W plays "challenge" , both of them will have to pay a fine of f dollars. Assuming that M is asked first and Vm = 50, Vw = 110 and f = 75.Use backward induction, O W gets the child O M gets the child and the equilibrium strategy is M plays "yes" and W plays "challenge". O M gets the child and the equilibrium strategy is M plays "yes" and W plays "no challenge". None of the above