3,536 research outputs found
Rational Verification in Iterated Electric Boolean Games
Electric boolean games are compact representations of games where the players
have qualitative objectives described by LTL formulae and have limited
resources. We study the complexity of several decision problems related to the
analysis of rationality in electric boolean games with LTL objectives. In
particular, we report that the problem of deciding whether a profile is a Nash
equilibrium in an iterated electric boolean game is no harder than in iterated
boolean games without resource bounds. We show that it is a PSPACE-complete
problem. As a corollary, we obtain that both rational elimination and rational
construction of Nash equilibria by a supervising authority are PSPACE-complete
problems.Comment: In Proceedings SR 2016, arXiv:1607.0269
Absoluteness via Resurrection
The resurrection axioms are forcing axioms introduced recently by Hamkins and
Johnstone, developing on ideas of Chalons and Velickovi\'c. We introduce a
stronger form of resurrection axioms (the \emph{iterated} resurrection axioms
for a class of forcings and a given
ordinal ), and show that implies generic
absoluteness for the first-order theory of with respect to
forcings in preserving the axiom, where is a
cardinal which depends on ( if is any
among the classes of countably closed, proper, semiproper, stationary set
preserving forcings).
We also prove that the consistency strength of these axioms is below that of
a Mahlo cardinal for most forcing classes, and below that of a stationary limit
of supercompact cardinals for the class of stationary set preserving posets.
Moreover we outline that simultaneous generic absoluteness for
with respect to and for with respect to
with is in principle
possible, and we present several natural models of the Morse Kelley set theory
where this phenomenon occurs (even for all simultaneously). Finally,
we compare the iterated resurrection axioms (and the generic absoluteness
results we can draw from them) with a variety of other forcing axioms, and also
with the generic absoluteness results by Woodin and the second author.Comment: 34 page
Multi-player games with LDL goals over finite traces
Linear Dynamic Logic on finite traces (LDLF) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLF. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLF goals are considered, in the settings we study—Reactive Modules games and iterated Boolean games with goals over finite traces—players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLF objectives is regular, and provides complexity results for the associated automata constructions
Multi-Player Games with LDL Goals over Finite Traces
Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning
about the behaviour of concurrent and multi-agent systems.
In this paper, we investigate techniques for both the characterisation and
verification of equilibria in multi-player games with goals/objectives
expressed using logics based on LDLf. This study builds upon a generalisation
of Boolean games, a logic-based game model of multi-agent systems where players
have goals succinctly represented in a logical way.
Because LDLf goals are considered, in the settings we study -- Reactive
Modules games and iterated Boolean games with goals over finite traces --
players' goals can be defined to be regular properties while achieved in a
finite, but arbitrarily large, trace.
In particular, using alternating automata, the paper investigates
automata-theoretic approaches to the characterisation and verification of (pure
strategy Nash) equilibria, shows that the set of Nash equilibria in
multi-player games with LDLf objectives is regular, and provides complexity
results for the associated automata constructions
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
Metabolism of Social System: N-Person Iterated Prisoner’s Dilemma Analysis In Random Boolean Network
Random Boolean Network has been used to find out regulation patterns of genes in organism. This approach is very interesting to use in a game such as N-Person Prisoner’s Dilemma. Here we assume that agent’s action is influenced by input in the form of choices of cooperate or defect she accepted from other agent or group of agents in the system. Number of cooperators, pay-off value received by each agent, and average value of the group, are observed in every state, from initial state chosen until it reaches its state-cycle attractor. In simulation performed here, we gain information that a system with large number agents based on action on input K equals to two, will reach equilibrium and stable condition over strategies taken out by its agents faster than higher input, that is K equals to three. Equilibrium reached in longer interval, yet it is stable over strategies carried out by agents
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