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If we include the larger research community -- economics, computer science, social sciences, business schools, operations research, etc -- I think there really is a partition between combinatorial gam …

Edit: The below does rely on the assumption that knives move continuously, see the comments. I think the procedure is "safe": Each player can guarantee not to envy either of the others by following t …

First, an exact equilibrium may not be computable in general, so usually the idea is to specify an error parameter $\epsilon$ and look for an $\epsilon$-equilibrium. Finding an $\epsilon$-Nash equili …

This could be a comment but it might clear things up. In short, a mixed strategy is a probability measure over a set of pure strategies (also called actions). If the set of actions is finite, we can r …

This is an interesting question. An expert in social choice would have an interesting reply. As a semi-expert I can say semi-interesting things. As you may know, a common voting setting in social choi …

Edit: I make the mistake below of proving a lower bound on the maximum number of boxes Alice must open, not the expected number. So this does not answer the question. . I think this sort of thing is …

This isn't a full answer but some setup and initial attempt. Maybe we can formalize a class of "board games" that we're happy with first. I'd propose that: A board is a set of locations. A piece oc …

Is it possible to find an equilibrium for this particular problem, and does it generalize to further players and prizes? Does it fit into some standard theory? Apologies for the late answer, but …

This is what it looks like to me: to get $H(y)$, we change strategy profile $z$ into $y$ one player at a time, summing the changes in utility. For any exact potential $P$ (which is actually equation 2 …