5,703 research outputs found
Evolutionary Multiplayer Games
Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to
social evolution. However, many applications make it clear that inherent
non-linearities of natural systems need to be taken into account. One way of
introducing such non-linearities into evolutionary games is by the inclusion of
multiple players. An example is of social dilemmas, where group benefits could
e.g.\ increase less than linear with the number of cooperators. Such
multiplayer games can be introduced in all the fields where evolutionary game
theory is already well established. However, the inclusion of non-linearities
can help to advance the analysis of systems which are known to be complex, e.g.
in the case of non-Mendelian inheritance. We review the diachronic theory and
applications of multiplayer evolutionary games and present the current state of
the field. Our aim is a summary of the theoretical results from well-mixed
populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology,
social sciences and population genetics. In closing, we probe certain future
directions which can be explored using the complexity of multiplayer games
while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape
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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
Aspiration Dynamics of Multi-player Games in Finite Populations
Studying strategy update rules in the framework of evolutionary game theory,
one can differentiate between imitation processes and aspiration-driven
dynamics. In the former case, individuals imitate the strategy of a more
successful peer. In the latter case, individuals adjust their strategies based
on a comparison of their payoffs from the evolutionary game to a value they
aspire, called the level of aspiration. Unlike imitation processes of pairwise
comparison, aspiration-driven updates do not require additional information
about the strategic environment and can thus be interpreted as being more
spontaneous. Recent work has mainly focused on understanding how aspiration
dynamics alter the evolutionary outcome in structured populations. However, the
baseline case for understanding strategy selection is the well-mixed population
case, which is still lacking sufficient understanding. We explore how
aspiration-driven strategy-update dynamics under imperfect rationality
influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under which a
strategy is more abundant than the other in the weak selection limiting case.
This approach has a long standing history in evolutionary game and is mostly
applied for its mathematical approachability. Hence, we also explore strong
selection numerically, which shows that our weak selection condition is a
robust predictor of the average abundance of a strategy. The condition turns
out to differ from that of a wide class of imitation dynamics, as long as the
game is not dyadic. Therefore a strategy favored under imitation dynamics can
be disfavored under aspiration dynamics. This does not require any population
structure thus highlights the intrinsic difference between imitation and
aspiration dynamics
Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback
We study the evolutionary dynamics of games under environmental feedback
using replicator equations for two interacting populations. One key feature is
to consider jointly the co-evolution of the dynamic payoff matrices and the
state of the environment: the payoff matrix varies with the changing
environment and at the same time, the state of the environment is affected
indirectly by the changing payoff matrix through the evolving population
profiles. For such co-evolutionary dynamics, we investigate whether convergence
will take place, and if so, how. In particular, we identify the scenarios where
oscillation offers the best predictions of long-run behavior by using
reversible system theory. The obtained results are useful to describe the
evolution of multi-community societies in which individuals' payoffs and
societal feedback interact.Comment: 7 pages, submitted to a conferenc
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
A New Mathematical Model for Evolutionary Games on Finite Networks of Players
A new mathematical model for evolutionary games on graphs is proposed to
extend the classical replicator equation to finite populations of players
organized on a network with generic topology. Classical results from game
theory, evolutionary game theory and graph theory are used. More specifically,
each player is placed in a vertex of the graph and he is seen as an infinite
population of replicators which replicate within the vertex. At each time
instant, a game is played by two replicators belonging to different connected
vertices, and the outcome of the game influences their ability of producing
offspring. Then, the behavior of a vertex player is determined by the
distribution of strategies used by the internal replicators. Under suitable
hypotheses, the proposed model is equivalent to the classical replicator
equation. Extended simulations are performed to show the dynamical behavior of
the solutions and the potentialities of the developed model.Comment: 26 pages, 7 figures, 1 tabl
Dynamics in atomic signaling games
We study an atomic signaling game under stochastic evolutionary dynamics.
There is a finite number of players who repeatedly update from a finite number
of available languages/signaling strategies. Players imitate the most fit
agents with high probability or mutate with low probability. We analyze the
long-run distribution of states and show that, for sufficiently small mutation
probability, its support is limited to efficient communication systems. We find
that this behavior is insensitive to the particular choice of evolutionary
dynamic, a property that is due to the game having a potential structure with a
potential function corresponding to average fitness. Consequently, the model
supports conclusions similar to those found in the literature on language
competition. That is, we show that efficient languages eventually predominate
the society while reproducing the empirical phenomenon of linguistic drift. The
emergence of efficiency in the atomic case can be contrasted with results for
non-atomic signaling games that establish the non-negligible possibility of
convergence, under replicator dynamics, to states of unbounded efficiency loss
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