为什么说性别博弈（Battle of the sexes）的相关均衡（Correlated equilibrium）有无数个？
The graph superimposes the map for the best reply of Player 1 and the map for the best reply of Player 2. Each map reports the probabilities with which Player ii should pick his first strategy as a function of the probability with which the opponent picks her first strategies. The three Nash equilibria for the game correspond to three intersection points: two are equilibria in pure strategies (corner points) and one is in completely mixed strategies (interior point). "the main hypothesis for this being that two is the least amount of sexes required to maintain genetic diversity and that evolution will prefer the simplest solution" I very much doubt that is main hypothesis .. it is far more likely simply the fact that the more of a species you require to get together for reproduction to happen the less likely it is to happen and the more likely they are to go extinct, over the long term the odds will simply kill them off, especially if there are any competitors that only need two or one. Under this definition, a curve shaped like the left-half of a U-shaped parabola, but never reaching a point at which its derivative is 0, is the type of nice convex to the origin indifference curve we dream about as economists. If we were to allow the slope of the indifference curve to become positive after some point then it will be possible to find draw a line from the origin that crosses two points of the curve, in which case the curve would not be convex to the origin. When a utility function is a function of two variables x and y, an indifference curve is convex to the origin if the derivative of the indifference curves are always negative and the second derivatives are positive. That is, the indifference curves slope downwards always but the slope of the slope increases (from a negative value to a less negative value) as we move to the right. That is, the marginal rate of substitution (the negative of the slope of the indifference curve or equivalently, the magnitude of the slope of the indifference curve) decreases as we move to the right along an indifference curve.