Friday, 11:30 - 11:55 h, Room: MA 005

 

Yin Chen
Computing perfect equilibria of finite n-person games in normal form with an interior-point path-following method

Coauthor: Chuangyin Dang

 

Abstract:
For any given sufficiently small positive number ε, we show that the imposition of a minimum probability ε on each pure strategy in a Nash equilibrium leads to an ε-perfect equilibrium of a finite n-person game in normal form. To compute such an ε-perfect equilibrium, we introduce a homotopy parameter to combine a weighted logarithmic barrier term with each player's payoff function and devise a new game. When the parameter varies from 0 to 1, the new game deforms from a trivial game to the original game. With the help of a perturbation term, it is proved that there exists a smooth interior-point path that starts from an unique Nash equilibrium of the trivial game and leads to an ε-perfect equilibrium of the original game at its limit. A predictor-corrector method is presented to follow the path. As an application of this result, we derive a scheme to compute a perfect equilibrium. Numerical results show that the scheme is effective and efficient.

 

Talk 3 of the contributed session Fri.1.MA 005
"New models and solution concepts II" [...]
Cluster 8
"Game theory" [...]

 

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