Existence of Secure Equilibrium in Multi-Player Games with Perfect Information

Julie De Pril
UMONS
Friday, 6 June, 2014 - 16:00
NO Building, room 2NO9.06

Secure equilibrium is a refinement of Nash equilibrium, which provides
some security to the players against deviations when a player changes
his strategy to another best response strategy. The concept of secure
equilibrium is specifically developed for assume-guarantee synthesis
and has already been applied in this context. Yet, not much is known
about its existence in games with more than two players. In this
paper, we establish the existence of secure equilibrium in two classes
of multi-player perfect information turn-based games: (1) in games
with possibly probabilistic transitions, having countable state and
finite action spaces and bounded and continuous payoff functions, and
(2) in games with only deterministic transitions, having arbitrary
state and action spaces and Borel payoff functions with a finite range
(in particular, qualitative Borel payoff functions). We show that
these results apply to several types of games studied in the
literature.