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07/29/2016 04:18 PM by Laurence Leff; game-tree recursive game saffidine what to do with non-pareto equilibria

How does one handle non-pareto Nash Equilibria in recursive games.

Using game-tree approaches, I am dealing with the situation when
at each move, the two players issue their moves simultaneously. Of course,
one can get several Nash Equilibria, both pure and mixed. I am using the
approach of [Saffidine, 2012]. That is, at each depth in the game tree,
one prunes elements.
However, unlike this work, we are NOT assuming a zero-sum game, but a
general Nash Equilibrium model.

Is it reasonable for a player to ignore Nash Equilibria that are not Pareto-
Optimal?

Example, the trivial game with three strategies for each player

0,0 0,0 0,0
0,0 0,0 0,0
0,0 0,0 1,1

There are several pure Nash Equilibrium (and no mixed ones)

2,2
0,0
0,1
1,0
1,1

Of course 2,2 is the only one that seems reasonable (non-pareto equilibrium)
Thus, if such a set of equilibria show up at any ply of the search, we should
just return the equivalent of (2,2). However, what would be the analogous thing
to do in the game tree search when we are presented with a mixed
equilibrium that might include pairs of strategies leading to a non-pareto
optimal pair? Can this occur--theoretically?

Abdallah Saffidine, Hilmar Finnsson, Michael Buro, "Alpha-Beta Pruning
for Games with Simultaneous Moves" Proceedings of the Twenty-Sixth AAAI
Conference on Artificial Intelligence. [Manage messages]