344,477 research outputs found
Threshold games and cooperation on multiplayer graphs
Objective: The study investigates the effect on cooperation in multiplayer
games, when the population from which all individuals are drawn is structured -
i.e. when a given individual is only competing with a small subset of the
entire population.
Method: To optimize the focus on multiplayer effects, a class of games were
chosen for which the payoff depends nonlinearly on the number of cooperators -
this ensures that the game cannot be represented as a sum of pair-wise
interactions, and increases the likelihood of observing behaviour different
from that seen in two-player games. The chosen class of games are named
"threshold games", and are defined by a threshold, , which describes the
minimal number of cooperators in a given match required for all the
participants to receive a benefit. The model was studied primarily through
numerical simulations of large populations of individuals, each with
interaction neighbourhoods described by various classes of networks.
Results: When comparing the level of cooperation in a structured population
to the mean-field model, we find that most types of structure lead to a
decrease in cooperation. This is both interesting and novel, simply due to the
generality and breadth of relevance of the model - it is likely that any model
with similar payoff structure exhibits related behaviour.
More importantly, we find that the details of the behaviour depends to a
large extent on the size of the immediate neighbourhoods of the individuals, as
dictated by the network structure. In effect, the players behave as if they are
part of a much smaller, fully mixed, population, which we suggest an expression
for.Comment: in PLOS ONE, 4th Feb 201
The Economics of Small Worlds
We examine a simple economic model of network formation where agents benefit from indirect relationships. We show that small-world featuresâshort path lengths between nodes together with highly clustered link structuresânecessarily emerge for a wide set of parameters
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Chris Cannings: A Life in Games
Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career
Maximum Performance at Minimum Cost in Network Synchronization
We consider two optimization problems on synchronization of oscillator
networks: maximization of synchronizability and minimization of synchronization
cost. We first develop an extension of the well-known master stability
framework to the case of non-diagonalizable Laplacian matrices. We then show
that the solution sets of the two optimization problems coincide and are
simultaneously characterized by a simple condition on the Laplacian
eigenvalues. Among the optimal networks, we identify a subclass of hierarchical
networks, characterized by the absence of feedback loops and the normalization
of inputs. We show that most optimal networks are directed and
non-diagonalizable, necessitating the extension of the framework. We also show
how oriented spanning trees can be used to explicitly and systematically
construct optimal networks under network topological constraints. Our results
may provide insights into the evolutionary origin of structures in complex
networks for which synchronization plays a significant role.Comment: 29 pages, 9 figures, accepted for publication in Physica D, minor
correction
Coalitional Games for Distributed Collaborative Spectrum Sensing in Cognitive Radio Networks
Collaborative spectrum sensing among secondary users (SUs) in cognitive
networks is shown to yield a significant performance improvement. However,
there exists an inherent trade off between the gains in terms of probability of
detection of the primary user (PU) and the costs in terms of false alarm
probability. In this paper, we study the impact of this trade off on the
topology and the dynamics of a network of SUs seeking to reduce the
interference on the PU through collaborative sensing. Moreover, while existing
literature mainly focused on centralized solutions for collaborative sensing,
we propose distributed collaboration strategies through game theory. We model
the problem as a non-transferable coalitional game, and propose a distributed
algorithm for coalition formation through simple merge and split rules. Through
the proposed algorithm, SUs can autonomously collaborate and self-organize into
disjoint independent coalitions, while maximizing their detection probability
taking into account the cooperation costs (in terms of false alarm). We study
the stability of the resulting network structure, and show that a maximum
number of SUs per formed coalition exists for the proposed utility model.
Simulation results show that the proposed algorithm allows a reduction of up to
86.6% of the average missing probability per SU (probability of missing the
detection of the PU) relative to the non-cooperative case, while maintaining a
certain false alarm level. In addition, through simulations, we compare the
performance of the proposed distributed solution with respect to an optimal
centralized solution that minimizes the average missing probability per SU.
Finally, the results also show how the proposed algorithm autonomously adapts
the network topology to environmental changes such as mobility.Comment: in proceedings of IEEE INFOCOM 200
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