1,023 research outputs found
The Complexity of Nash Equilibria in Limit-Average Games
We study the computational complexity of Nash equilibria in concurrent games
with limit-average objectives. In particular, we prove that the existence of a
Nash equilibrium in randomised strategies is undecidable, while the existence
of a Nash equilibrium in pure strategies is decidable, even if we put a
constraint on the payoff of the equilibrium. Our undecidability result holds
even for a restricted class of concurrent games, where nonzero rewards occur
only on terminal states. Moreover, we show that the constrained existence
problem is undecidable not only for concurrent games but for turn-based games
with the same restriction on rewards. Finally, we prove that the constrained
existence problem for Nash equilibria in (pure or randomised) stationary
strategies is decidable and analyse its complexity.Comment: 34 page
On approximate and weak correlated equilibria in constrained discounted stochastic games
In this paper, we consider constrained discounted stochastic games with a
countably generated state space and norm continuous transition probability
having a density function. We prove existence of approximate stationary
equilibria and stationary weak correlated equilibria. Our results imply the
existence of stationary Nash equilibrium in stochastic games
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