688 research outputs found
On Relevant Equilibria in Reachability Games
We study multiplayer reachability games played on a finite directed graph
equipped with target sets, one for each player. In those reachability games, it
is known that there always exists a Nash equilibrium (NE) and a subgame perfect
equilibrium (SPE). But sometimes several equilibria may coexist such that in
one equilibrium no player reaches his target set whereas in another one several
players reach it. It is thus very natural to identify "relevant" equilibria. In
this paper, we consider different notions of relevant equilibria including
Pareto optimal equilibria and equilibria with high social welfare. We provide
complexity results for various related decision problems
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
On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
We study turn-based quantitative multiplayer non zero-sum games played on
finite graphs with reachability objectives. In such games, each player aims at
reaching his own goal set of states as soon as possible. A previous work on
this model showed that Nash equilibria (resp. secure equilibria) are guaranteed
to exist in the multiplayer (resp. two-player) case. The existence of secure
equilibria in the multiplayer case remained and is still an open problem. In
this paper, we focus our study on the concept of subgame perfect equilibrium, a
refinement of Nash equilibrium well-suited in the framework of games played on
graphs. We also introduce the new concept of subgame perfect secure
equilibrium. We prove the existence of subgame perfect equilibria (resp.
subgame perfect secure equilibria) in multiplayer (resp. two-player)
quantitative reachability games. Moreover, we provide an algorithm deciding the
existence of secure equilibria in the multiplayer case.Comment: 32 pages. Full version of the FoSSaCS 2012 proceedings pape
The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games
We study multiplayer quantitative reachability games played on a finite
directed graph, where the objective of each player is to reach his target set
of vertices as quickly as possible. Instead of the well-known notion of Nash
equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE),
a refinement of NE well-suited in the framework of games played on graphs. It
is known that there always exists an SPE in quantitative reachability games and
that the constrained existence problem is decidable. We here prove that this
problem is PSPACE-complete. To obtain this result, we propose a new algorithm
that iteratively builds a set of constraints characterizing the set of SPE
outcomes in quantitative reachability games. This set of constraints is
obtained by iterating an operator that reinforces the constraints up to
obtaining a fixpoint. With this fixpoint, the set of SPE outcomes can be
represented by a finite graph of size at most exponential. A careful inspection
of the computation allows us to establish PSPACE membership
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
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