John and Paul play the following gameThe computer draws rand

John and Paul play the following game:The computer draws randomly two positive, consecutive integers andassigns them (randomly) to the players. They get to know the other guy’snumber, but not their own. The player with smaller number has to pay theopponent the amount indicated by his number. Before the payment anyone of them can say pass, and new set of numbers is drawn.
Boys are smart so they will never pass because of the following reasoning:I know his number (say k). If mine is k 1, I loose and I have to pay
k 1. If mine is k + 1, I win and he gives me k. Therefore I win 1/2 on

average.What is wrong here? Is it possible that they can both keep winning?

Solution

yes it is possible that they can both keep winning because the average of winning of one player is 1/2 that means that the average og winning of the other will be the same 1/2

if they continue thinking like this they would pass the round and see if the number that the opponent is very lower for thinking that his number is greater but the opponent will see the number of the opponent and he can say that pass the round, so is very difficult to say if somebody wins all