Achieving symmetric Pareto Nash equilibria using biased replicator dynamics

Abstract

Abstract-Achieving the Nash equilibria for single objective games is known to be a computationally difficult problem. However there is a special class of equilibria called evolutionary robust equilibria which can be obtained through a special type of evolutionary dynamics called the replicator dynamics. This dynamics has special properties over the simplex, which has been studied in optimization theory to solve several combinatorial problems. In this work, we consider the essentially hard combinatorial optimization problem of computing the equilibria in games with multiple objectives. We extend the notion of replicator dynamics to handle such games. We establish proofs of dynamic stability of this modified replicator dynamics and present their relation to the Pareto Nash equilibria in multiobjective games.

Detecting conversational groups in images and sequences: A robust game-theoretic approach

“…Although in "classical" game theory several solution concepts have been proposed during the years, the game theory community has typically given little attention to the evolutionary set-ting. Recently, a solution to this problem has been put forward by Somasundaram and Baras [25] who extended the notion of replicator dynamics and that of an ESS using the concept of Pareto-Nash equilibrium. Another recent attempt towards this direction, though more theoretical in nature, can be found in [55].…”

“…In the work reported in this paper, we follow the idea proposed in [25]. Using concepts from multi-criteria linear programming (MCLP) [56] they proposed a notion of Pareto reply and of Pareto-Nash equilibrium and showed the equivalence with "weighted sum scalarization", a classical technique from multi-objective optimization (see, e.g., [56]).…”

“…To this end, following [25], in our experiments we used the multi-objective simplex method described in [56, Chapter 7] (see also [25] for details).…”

“…The game-theoretic setting provides a conceptual framework which allows us to integrate temporal information in a principled way, in an attempt to reliably extract groups in video sequences under severe noisy conditions. This is done by using a recent approach to integrate multiple payoff functions in an evolutionary game-theoretic setting [25].…”

Detecting Free Standing Conversational Group in Video Using Fuzzy Relations

“…This social representation generates false positives in F-Formation detection. On the other hand, in the fusion step, the affinity matrix sets are integrated in exponential time, in terms of O(2 i ) where i is the number of pivots (Somasundaram and Baras, 2009) (e.g. they use simplex method), the clustering step is O(pce) (Bulò and Pelillo, 2009), where c is the average number of iteration required for converging and e is the amount of social relations.…”