21,626 research outputs found
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
Games on graphs with a public signal monitoring
We study pure Nash equilibria in games on graphs with an imperfect monitoring
based on a public signal. In such games, deviations and players responsible for
those deviations can be hard to detect and track. We propose a generic
epistemic game abstraction, which conveniently allows to represent the
knowledge of the players about these deviations, and give a characterization of
Nash equilibria in terms of winning strategies in the abstraction. We then use
the abstraction to develop algorithms for some payoff functions.Comment: 28 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
Thin Games with Symmetry and Concurrent Hyland-Ong Games
We build a cartesian closed category, called Cho, based on event structures.
It allows an interpretation of higher-order stateful concurrent programs that
is refined and precise: on the one hand it is conservative with respect to
standard Hyland-Ong games when interpreting purely functional programs as
innocent strategies, while on the other hand it is much more expressive. The
interpretation of programs constructs compositionally a representation of their
execution that exhibits causal dependencies and remembers the points of
non-deterministic branching.The construction is in two stages. First, we build
a compact closed category Tcg. It is a variant of Rideau and Winskel's category
CG, with the difference that games and strategies in Tcg are equipped with
symmetry to express that certain events are essentially the same. This is
analogous to the underlying category of AJM games enriching simple games with
an equivalence relations on plays. Building on this category, we construct the
cartesian closed category Cho as having as objects the standard arenas of
Hyland-Ong games, with strategies, represented by certain events structures,
playing on games with symmetry obtained as expanded forms of these arenas.To
illustrate and give an operational light on these constructions, we interpret
(a close variant of) Idealized Parallel Algol in Cho
Solving Stochastic B\"uchi Games on Infinite Arenas with a Finite Attractor
We consider games played on an infinite probabilistic arena where the first
player aims at satisfying generalized B\"uchi objectives almost surely, i.e.,
with probability one. We provide a fixpoint characterization of the winning
sets and associated winning strategies in the case where the arena satisfies
the finite-attractor property. From this we directly deduce the decidability of
these games on probabilistic lossy channel systems.Comment: In Proceedings QAPL 2013, arXiv:1306.241
Games with Delays. A Frankenstein Approach
We investigate infinite games on finite graphs where the information flow is
perturbed by nondeterministic signalling delays. It is known that such
perturbations make synthesis problems virtually unsolvable, in the general
case. On the classical model where signals are attached to states, tractable
cases are rare and difficult to identify.
Here, we propose a model where signals are detached from control states, and
we identify a subclass on which equilibrium outcomes can be preserved, even if
signals are delivered with a delay that is finitely bounded. To offset the
perturbation, our solution procedure combines responses from a collection of
virtual plays following an equilibrium strategy in the instant- signalling game
to synthesise, in a Frankenstein manner, an equivalent equilibrium strategy for
the delayed-signalling game
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