381 research outputs found
Local Strategy Improvement for Parity Game Solving
The problem of solving a parity game is at the core of many problems in model
checking, satisfiability checking and program synthesis. Some of the best
algorithms for solving parity game are strategy improvement algorithms. These
are global in nature since they require the entire parity game to be present at
the beginning. This is a distinct disadvantage because in many applications one
only needs to know which winning region a particular node belongs to, and a
witnessing winning strategy may cover only a fractional part of the entire game
graph.
We present a local strategy improvement algorithm which explores the game
graph on-the-fly whilst performing the improvement steps. We also compare it
empirically with existing global strategy improvement algorithms and the
currently only other local algorithm for solving parity games. It turns out
that local strategy improvement can outperform these others by several orders
of magnitude
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
We analyse the computational complexity of finding Nash equilibria in simple
stochastic multiplayer games. We show that restricting the search space to
equilibria whose payoffs fall into a certain interval may lead to
undecidability. In particular, we prove that the following problem is
undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium
of G where player 0 wins with probability 1. Moreover, this problem remains
undecidable if it is restricted to strategies with (unbounded) finite memory.
However, if mixed strategies are allowed, decidability remains an open problem.
One way to obtain a provably decidable variant of the problem is restricting
the strategies to be positional or stationary. For the complexity of these two
problems, we obtain a common lower bound of NP and upper bounds of NP and
PSPACE respectively.Comment: 23 pages; revised versio
Imitation in Large Games
In games with a large number of players where players may have overlapping
objectives, the analysis of stable outcomes typically depends on player types.
A special case is when a large part of the player population consists of
imitation types: that of players who imitate choice of other (optimizing)
types. Game theorists typically study the evolution of such games in dynamical
systems with imitation rules. In the setting of games of infinite duration on
finite graphs with preference orderings on outcomes for player types, we
explore the possibility of imitation as a viable strategy. In our setup, the
optimising players play bounded memory strategies and the imitators play
according to specifications given by automata. We present algorithmic results
on the eventual survival of types
Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited
We study nondeterministic strategies in parity games with the aim of
computing a most permissive winning strategy. Following earlier work, we
measure permissiveness in terms of the average number/weight of transitions
blocked by the strategy. Using a translation into mean-payoff parity games, we
prove that the problem of computing (the permissiveness of) a most permissive
winning strategy is in NP intersected coNP. Along the way, we provide a new
study of mean-payoff parity games. In particular, we prove that the opponent
player has a memoryless optimal strategy and give a new algorithm for solving
these games.Comment: 30 pages, revised versio
- …