15 research outputs found
Games with recurring certainty
Infinite games where several players seek to coordinate under imperfect
information are known to be intractable, unless the information flow is
severely restricted. Examples of undecidable cases typically feature a
situation where players become uncertain about the current state of the game,
and this uncertainty lasts forever. Here we consider games where the players
attain certainty about the current state over and over again along any play.
For finite-state games, we note that this kind of recurring certainty implies a
stronger condition of periodic certainty, that is, the events of state
certainty ultimately occur at uniform, regular intervals. We show that it is
decidable whether a given game presents recurring certainty, and that, if so,
the problem of synthesising coordination strategies under w-regular winning
conditions is solvable.Comment: In Proceedings SR 2014, arXiv:1404.041
Distributed Synthesis in Continuous Time
We introduce a formalism modelling communication of distributed agents
strictly in continuous-time. Within this framework, we study the problem of
synthesising local strategies for individual agents such that a specified set
of goal states is reached, or reached with at least a given probability. The
flow of time is modelled explicitly based on continuous-time randomness, with
two natural implications: First, the non-determinism stemming from interleaving
disappears. Second, when we restrict to a subclass of non-urgent models, the
quantitative value problem for two players can be solved in EXPTIME. Indeed,
the explicit continuous time enables players to communicate their states by
delaying synchronisation (which is unrestricted for non-urgent models). In
general, the problems are undecidable already for two players in the
quantitative case and three players in the qualitative case. The qualitative
undecidability is shown by a reduction to decentralized POMDPs for which we
provide the strongest (and rather surprising) undecidability result so far
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
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Alternating-time temporal logic with finite-memory strategies
Model-checking the alternating-time temporal logics ATL and ATL* with
incomplete information is undecidable for perfect recall semantics. However,
when restricting to memoryless strategies the model-checking problem becomes
decidable. In this paper we consider two other types of semantics based on
finite-memory strategies. One where the memory size allowed is bounded and one
where the memory size is unbounded (but must be finite). This is motivated by
the high complexity of model-checking with perfect recall semantics and the
severe limitations of memoryless strategies. We show that both types of
semantics introduced are different from perfect recall and memoryless semantics
and next focus on the decidability and complexity of model-checking in both
complete and incomplete information games for ATL/ATL*. In particular, we show
that the complexity of model-checking with bounded-memory semantics is
Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete
information games just as in the memoryless case. We also present a proof that
ATL and ATL* model-checking is undecidable for n >= 3 players with
finite-memory semantics in incomplete information games.Comment: In Proceedings GandALF 2013, arXiv:1307.416