Friday, 11:00 - 11:25 h, Room: MA 005

 

Silvia Schwarze
Equilibria in generalized Nash games with applications to games on polyhedra

Coauthors: Justo Puerto, Anita Schöbel

 

Abstract:
In generalized Nash equilibrium (GNE) games, a player’s strategy set depends on the strategy decisions of the competitors. In particular, we consider games on polyhedra, where the strategy space is represented by a polyhedron. We investigate best-reply improvement paths in games on polyhedra and prove the finiteness of such paths for special cases. In particular, under the assumption of a potential game, we prove existence of equilibria for strictly convex payoffs.
In addition, we study multiobjective characterizations of equilibria for general (nonpolyhedral) GNE games for the case of monotone payoffs. We show that nondominated points in the decision space are equilibria. Moreover, the equivalence of the sets of equilibria and nondominated points is ensured by establishing an additional restriction on the feasible strategy sets, leading to the new definition of comprehensive sets. As a result, multiobjective optimization techniques carry over to GNE games with monotone payoffs. In addition, we discuss the relation to efficient solutions in the payoff space. Applying those results to games on polyhedra, we yield linear programming formulations for finding equilibria.

 

Talk 2 of the contributed session Fri.1.MA 005
"New models and solution concepts II" [...]
Cluster 8
"Game theory" [...]

 

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