8 research outputs found
Multiplayer Cost Games with Simple Nash Equilibria
Multiplayer games with selfish agents naturally occur in the design of
distributed and embedded systems. As the goals of selfish agents are usually
neither equivalent nor antagonistic to each other, such games are non zero-sum
games. We study such games and show that a large class of these games,
including games where the individual objectives are mean- or discounted-payoff,
or quantitative reachability, and show that they do not only have a solution,
but a simple solution. We establish the existence of Nash equilibria that are
composed of k memoryless strategies for each agent in a setting with k agents,
one main and k-1 minor strategies. The main strategy describes what happens
when all agents comply, whereas the minor strategies ensure that all other
agents immediately start to co-operate against the agent who first deviates
from the plan. This simplicity is important, as rational agents are an
idealisation. Realistically, agents have to decide on their moves with very
limited resources, and complicated strategies that require exponential--or even
non-elementary--implementations cannot realistically be implemented. The
existence of simple strategies that we prove in this paper therefore holds a
promise of implementability.Comment: 23 page
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
Nash equilibria for reachability objectives in multi-player timed games
We propose a procedure for computing Nash equilibria in multi-player timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use our characterization to compute Nash equilibria in finite concurrent games
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 page