3,856 research outputs found
Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game
It is well known that in contrast to the Prisoner's Dilemma, the snowdrift
game can lead to a stable coexistence of cooperators and cheaters. Recent
theoretical evidence on the snowdrift game suggests that gradual evolution for
individuals choosing to contribute in continuous degrees can result in the
social diversification to a 100% contribution and 0% contribution through
so-called evolutionary branching. Until now, however, game-theoretical studies
have shed little light on the evolutionary dynamics and consequences of the
loss of diversity in strategy. Here we analyze continuous snowdrift games with
quadratic payoff functions in dimorphic populations. Subsequently, conditions
are clarified under which gradual evolution can lead a population consisting of
those with 100% contribution and those with 0% contribution to merge into one
species with an intermediate contribution level. The key finding is that the
continuous snowdrift game is more likely to lead to assimilation of different
cooperation levels rather than maintenance of diversity. Importantly, this
implies that allowing the gradual evolution of cooperative behavior can
facilitate social inequity aversion in joint ventures that otherwise could
cause conflicts that are based on commonly accepted notions of fairness.Comment: 30 pages, 3 tables, 5 figure
Cycles in adversarial regularized learning
Regularized learning is a fundamental technique in online optimization,
machine learning and many other fields of computer science. A natural question
that arises in these settings is how regularized learning algorithms behave
when faced against each other. We study a natural formulation of this problem
by coupling regularized learning dynamics in zero-sum games. We show that the
system's behavior is Poincar\'e recurrent, implying that almost every
trajectory revisits any (arbitrarily small) neighborhood of its starting point
infinitely often. This cycling behavior is robust to the agents' choice of
regularization mechanism (each agent could be using a different regularizer),
to positive-affine transformations of the agents' utilities, and it also
persists in the case of networked competition, i.e., for zero-sum polymatrix
games.Comment: 22 pages, 4 figure
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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
Fixation and escape times in stochastic game learning
Evolutionary dynamics in finite populations is known to fixate eventually in
the absence of mutation. We here show that a similar phenomenon can be found in
stochastic game dynamical batch learning, and investigate fixation in learning
processes in a simple 2x2 game, for two-player games with cyclic interaction,
and in the context of the best-shot network game. The analogues of finite
populations in evolution are here finite batches of observations between
strategy updates. We study when and how such fixation can occur, and present
results on the average time-to-fixation from numerical simulations. Simple
cases are also amenable to analytical approaches and we provide estimates of
the behaviour of so-called escape times as a function of the batch size. The
differences and similarities with escape and fixation in evolutionary dynamics
are discussed.Comment: 19 pages, 9 figure
Mean Field Equilibrium in Dynamic Games with Complementarities
We study a class of stochastic dynamic games that exhibit strategic
complementarities between players; formally, in the games we consider, the
payoff of a player has increasing differences between her own state and the
empirical distribution of the states of other players. Such games can be used
to model a diverse set of applications, including network security models,
recommender systems, and dynamic search in markets. Stochastic games are
generally difficult to analyze, and these difficulties are only exacerbated
when the number of players is large (as might be the case in the preceding
examples).
We consider an approximation methodology called mean field equilibrium to
study these games. In such an equilibrium, each player reacts to only the long
run average state of other players. We find necessary conditions for the
existence of a mean field equilibrium in such games. Furthermore, as a simple
consequence of this existence theorem, we obtain several natural monotonicity
properties. We show that there exist a "largest" and a "smallest" equilibrium
among all those where the equilibrium strategy used by a player is
nondecreasing, and we also show that players converge to each of these
equilibria via natural myopic learning dynamics; as we argue, these dynamics
are more reasonable than the standard best response dynamics. We also provide
sensitivity results, where we quantify how the equilibria of such games move in
response to changes in parameters of the game (e.g., the introduction of
incentives to players).Comment: 56 pages, 5 figure
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
Evolutionary consequences of behavioral diversity
Iterated games provide a framework to describe social interactions among
groups of individuals. Recent work stimulated by the discovery of
"zero-determinant" strategies has rapidly expanded our ability to analyze such
interactions. This body of work has primarily focused on games in which players
face a simple binary choice, to "cooperate" or "defect". Real individuals,
however, often exhibit behavioral diversity, varying their input to a social
interaction both qualitatively and quantitatively. Here we explore how access
to a greater diversity of behavioral choices impacts the evolution of social
dynamics in finite populations. We show that, in public goods games, some
two-choice strategies can nonetheless resist invasion by all possible
multi-choice invaders, even while engaging in relatively little punishment. We
also show that access to greater behavioral choice results in more "rugged "
fitness landscapes, with populations able to stabilize cooperation at multiple
levels of investment, such that choice facilitates cooperation when returns on
investments are low, but hinders cooperation when returns on investments are
high. Finally, we analyze iterated rock-paper-scissors games, whose
non-transitive payoff structure means unilateral control is difficult and
zero-determinant strategies do not exist in general. Despite this, we find that
a large portion of multi-choice strategies can invade and resist invasion by
strategies that lack behavioral diversity -- so that even well-mixed
populations will tend to evolve behavioral diversity.Comment: 26 pages, 4 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
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
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