1,576 research outputs found
Optimal cooperation-trap strategies for the iterated Rock-Paper-Scissors game
In an iterated non-cooperative game, if all the players act to maximize their
individual accumulated payoff, the system as a whole usually converges to a
Nash equilibrium that poorly benefits any player. Here we show that such an
undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game
involving two players X and Y. Player X has the option of proactively adopting
a cooperation-trap strategy, which enforces complete cooperation from the
rational player Y and leads to a highly beneficial as well as maximally fair
situation to both players. That maximal degree of cooperation is achievable in
such a competitive system with cyclic dominance of actions may stimulate
creative thinking on how to resolve conflicts and enhance cooperation in human
societies.Comment: 5 pages including 3 figure
Loop-corrected belief propagation for lattice spin models
Belief propagation (BP) is a message-passing method for solving probabilistic
graphical models. It is very successful in treating disordered models (such as
spin glasses) on random graphs. On the other hand, finite-dimensional lattice
models have an abundant number of short loops, and the BP method is still far
from being satisfactory in treating the complicated loop-induced correlations
in these systems. Here we propose a loop-corrected BP method to take into
account the effect of short loops in lattice spin models. We demonstrate,
through an application to the square-lattice Ising model, that loop-corrected
BP improves over the naive BP method significantly. We also implement
loop-corrected BP at the coarse-grained region graph level to further boost its
performance.Comment: 11 pages, minor changes with new references added. Final version as
published in EPJ
Solving the undirected feedback vertex set problem by local search
An undirected graph consists of a set of vertices and a set of undirected
edges between vertices. Such a graph may contain an abundant number of cycles,
then a feedback vertex set (FVS) is a set of vertices intersecting with each of
these cycles. Constructing a FVS of cardinality approaching the global minimum
value is a optimization problem in the nondeterministic polynomial-complete
complexity class, therefore it might be extremely difficult for some large
graph instances. In this paper we develop a simulated annealing local search
algorithm for the undirected FVS problem. By defining an order for the vertices
outside the FVS, we replace the global cycle constraints by a set of local
vertex constraints on this order. Under these local constraints the cardinality
of the focal FVS is then gradually reduced by the simulated annealing dynamical
process. We test this heuristic algorithm on large instances of Er\"odos-Renyi
random graph and regular random graph, and find that this algorithm is
comparable in performance to the belief propagation-guided decimation
algorithm.Comment: 6 page
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