Player One and Two are in a war. Player One can send a message to his team, and Player Two can intercept it. There is a price for sending the message, and a price for intercepting it.
A is “don’t send any message”. B is “send a useless (blank, or random) message”. (Uses up 1 utility. Also gives the other player 2 free utility points.) C is “send a useful message”. (Uses up 1 utility, but gains 4 if not intercepted, and loses extra 1 if intercepted.) X is “intercept”, which costs 2 utility. However, intercepting a useful message gains you 3 utility (after paying 2). Y is “don’t intercept”.
(I think I got the numbers right, if they don’t match up somewhere, tell me and I’ll adjust them.)
The analog to the problem is this: sending a useless message can never beat doing nothing. (We’re assuming you don’t gain from the opponent wasting energy. It’s possible if the energy is small enough to be outweighed by the cost of sending the message.) So if Player Two sees a message, he should always assume it is useful. Therefore Two will intercept all messages. Therefore Player One should never send any messages.
However, if One does, in fact, send a message, then Two can’t rely on his rationality, and can’t assume the message has value to intercept.
Semi-plausible interpretation of the game:
Player One and Two are in a war. Player One can send a message to his team, and Player Two can intercept it. There is a price for sending the message, and a price for intercepting it.
A is “don’t send any message”. B is “send a useless (blank, or random) message”. (Uses up 1 utility. Also gives the other player 2 free utility points.) C is “send a useful message”. (Uses up 1 utility, but gains 4 if not intercepted, and loses extra 1 if intercepted.) X is “intercept”, which costs 2 utility. However, intercepting a useful message gains you 3 utility (after paying 2). Y is “don’t intercept”.
(I think I got the numbers right, if they don’t match up somewhere, tell me and I’ll adjust them.)
The analog to the problem is this: sending a useless message can never beat doing nothing. (We’re assuming you don’t gain from the opponent wasting energy. It’s possible if the energy is small enough to be outweighed by the cost of sending the message.) So if Player Two sees a message, he should always assume it is useful. Therefore Two will intercept all messages. Therefore Player One should never send any messages.
However, if One does, in fact, send a message, then Two can’t rely on his rationality, and can’t assume the message has value to intercept.