Best response dynamics for continuous zero--sum games | Zendy

Josef Hofbauer | Zendy; Sylvain Sorin | Zendy

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Best response dynamics for continuous zero--sum games

Author(s) -

Josef Hofbauer,

Sylvain Sorin

Publication year - 2006

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2006.6.215

Subject(s) - zero (linguistics) , minimax , convergence (economics) , mathematics , saddle point , regular polygon , saddle , dynamics (music) , best response , set (abstract data type) , mathematical optimization , computer science , nash equilibrium , physics , geometry , economics , philosophy , linguistics , acoustics , programming language , economic growth

We study best response dynamics in continuous time for continuous concave-convex zero-sum games and prove convergence of its trajectories to the set of saddle points, thus providing a dynamical proof of the minmax theorem. Consequences for the corresponding discrete time process with small or diminishing step-sizes are established, including convergence of the fictitious play procedure.

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