Nitpick: I am pretty sure non-zero-sum does not imply a convex Pareto front.
Instead of the lens of negotiation position, one could argue that mistake theorists believe that the Pareto Boundary is convex (which implies that usually maximizing surplus is more important than deciding allocation), while conflict theorists see it as concave (which implies that allocation is the more important factor).
If you have two strategy pairs (x0,y0),(x1,y1), you can form a convex combination of them like this: Flip a weighted coin; play strategy 0 on heads and strategy 1 on tails. This scheme requires both players to see the same coin flip.
If we use correlated equilibria as our solution concept rather than Nash, convexity is always guaranteed. Also, this is usually the more realistic assumption for modeling purposes. Nash equilibria oddly assume certainty about which equilibrium a game will be in even as players are trying to reason about how to approach a game. So it’s really only applicable to cases where players know what equilibrium they are in, EG because there’s a long history and the situation has equilibriated.
But even in such situations, there is greater reason to expect things to equilibriate to a correlated equilibrium than there is to expect a nash equilibrium. This is partly because there are usually a lot of signals from the environment that can potentially be used as correlated randomness—for example, the weather. Also, convergence theorems for learning correlated equilibria are just better than those for Nash.
Still, your comment about mistake theorists believing in a convex boundary is interesting. It might also be that conflict theorists tend to believe that most feasible solutions are in fact close to Pareto-efficient (for example, they believe that any apparent “mistake” is actually benefiting someone). Mistake theorists won’t believe this, obviously, because they believe there is room for improvement (mistakes to be avoided). However, mistake theorists may additionally believe in large downsides to conflict (ie, some very very not-pareto-efficient solutions, which it is important to avoid). This would further motivate the importance of agreeing to stick to the Pareto frontier, rather than worrying about allocation.
This. I think Mistake theorists would frequently question whether the game is actually zero-sum. This divergence in opinions about the nature of the game feels important to me.
Nitpick: I am pretty sure non-zero-sum does not imply a convex Pareto front.
Instead of the lens of negotiation position, one could argue that mistake theorists believe that the Pareto Boundary is convex (which implies that usually maximizing surplus is more important than deciding allocation), while conflict theorists see it as concave (which implies that allocation is the more important factor).
Oh I see, the Pareto frontier doesn’t have to be convex because there isn’t a shared random signal that the players can use to coordinate. Thanks!
Why would that make it convex? To me those appear unrelated.
If you have two strategy pairs (x0,y0),(x1,y1), you can form a convex combination of them like this: Flip a weighted coin; play strategy 0 on heads and strategy 1 on tails. This scheme requires both players to see the same coin flip.
If we use correlated equilibria as our solution concept rather than Nash, convexity is always guaranteed. Also, this is usually the more realistic assumption for modeling purposes. Nash equilibria oddly assume certainty about which equilibrium a game will be in even as players are trying to reason about how to approach a game. So it’s really only applicable to cases where players know what equilibrium they are in, EG because there’s a long history and the situation has equilibriated.
But even in such situations, there is greater reason to expect things to equilibriate to a correlated equilibrium than there is to expect a nash equilibrium. This is partly because there are usually a lot of signals from the environment that can potentially be used as correlated randomness—for example, the weather. Also, convergence theorems for learning correlated equilibria are just better than those for Nash.
Still, your comment about mistake theorists believing in a convex boundary is interesting. It might also be that conflict theorists tend to believe that most feasible solutions are in fact close to Pareto-efficient (for example, they believe that any apparent “mistake” is actually benefiting someone). Mistake theorists won’t believe this, obviously, because they believe there is room for improvement (mistakes to be avoided). However, mistake theorists may additionally believe in large downsides to conflict (ie, some very very not-pareto-efficient solutions, which it is important to avoid). This would further motivate the importance of agreeing to stick to the Pareto frontier, rather than worrying about allocation.
This. I think Mistake theorists would frequently question whether the game is actually zero-sum. This divergence in opinions about the nature of the game feels important to me.