You know the famous game-theory subject, the battle of the sexes. In a nutshell, it’s a game between A, who likes football and B, who prefers dance. But they also value each other’s company more than they dislike each other’s interests. Here is the overall payoff matrix written on the tastes.
| B | |||
| Football | Dance | ||
| A | Football | A:10, B:5 | A:0, B:0 |
| Dance | A:0, B:0 | A:5, B:10 |
In the classical case, A and B have 100% certainty about what the other person likes. Imagine, A becomes moody a few days a month and wants to be alone on those days. So from B’s standpoint, she knows A could be in a bad mood but doesn’t know when. So she attaches a probability, p, for A’s state.
From the side of B, there is a chance p that A wants her company.
| B | |||
| Football | Dance | ||
| A | Football | A:10, B:5 | A:0, B:0 |
| Dance | A:0, B:0 | A:5, B:10 |
And a chance (1-p) A doesn’t. And here is the corresponding payoff matrix.
| B | |||
| Football | Dance | ||
| A | Football | A:0, B:5 | A:10, B:0 |
| Dance | A:5, B:0 | A:0, B:10 |
Such cases come under the category of Bayesian Nash Equilibrium. In the original Nash equilibrium case, a player does things based on what the other player will do. In the case of Bayesian, the player acts, given what she knows the other person could do.
