The direct answer is “yes”, as you might have discovered by googling.
But different pure solutions can always be linearly combined—at least if the combination is supposed to be an expected utility rather than a guaranteed utility.
In an American football game, a coin is flipped at the start to produce a fair linear combination of “kicking off” and “receiving”.
But if dclayh had used google instead of asking the question in a comment, you never would have had the opportunity to respond with your point about expected utility.
Asking in a comment could also attract the interest of others who might not have thought to ask that question, and gives others the opportunity to give their own answer or link to a resource they think is particularly good, that they might be able to answer follow up questions about.
Has anyone dealt with bargaining games where different pure solutions cannot be linearly combined (i.e. a non-convex solution space)?
The direct answer is “yes”, as you might have discovered by googling.
But different pure solutions can always be linearly combined—at least if the combination is supposed to be an expected utility rather than a guaranteed utility.
In an American football game, a coin is flipped at the start to produce a fair linear combination of “kicking off” and “receiving”.
But if dclayh had used google instead of asking the question in a comment, you never would have had the opportunity to respond with your point about expected utility.
Asking in a comment could also attract the interest of others who might not have thought to ask that question, and gives others the opportunity to give their own answer or link to a resource they think is particularly good, that they might be able to answer follow up questions about.