6 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 Admissibility in Omega-Regular Games
Iterated admissibility is a well-known and important concept in classical
game theory, e.g. to determine rational behaviors in multi-player matrix games.
As recently shown by Berwanger, this concept can be soundly extended to
infinite games played on graphs with omega-regular objectives. In this paper,
we study the algorithmic properties of this concept for such games. We settle
the exact complexity of natural decision problems on the set of strategies that
survive iterated elimination of dominated strategies. As a byproduct of our
construction, we obtain automata which recognize all the possible outcomes of
such strategies