47,903 research outputs found
The collapse of cooperation in evolving games
Game theory provides a quantitative framework for analyzing the behavior of
rational agents. The Iterated Prisoner's Dilemma in particular has become a
standard model for studying cooperation and cheating, with cooperation often
emerging as a robust outcome in evolving populations. Here we extend
evolutionary game theory by allowing players' strategies as well as their
payoffs to evolve in response to selection on heritable mutations. In nature,
many organisms engage in mutually beneficial interactions, and individuals may
seek to change the ratio of risk to reward for cooperation by altering the
resources they commit to cooperative interactions. To study this, we construct
a general framework for the co-evolution of strategies and payoffs in arbitrary
iterated games. We show that, as payoffs evolve, a trade-off between the
benefits and costs of cooperation precipitates a dramatic loss of cooperation
under the Iterated Prisoner's Dilemma; and eventually to evolution away from
the Prisoner's Dilemma altogether. The collapse of cooperation is so extreme
that the average payoff in a population may decline, even as the potential
payoff for mutual cooperation increases. Our work offers a new perspective on
the Prisoner's Dilemma and its predictions for cooperation in natural
populations; and it provides a general framework to understand the co-evolution
of strategies and payoffs in iterated interactions.Comment: 33 pages, 13 figure
Coevolutionary games - a mini review
Prevalence of cooperation within groups of selfish individuals is puzzling in
that it contradicts with the basic premise of natural selection. Favoring
players with higher fitness, the latter is key for understanding the challenges
faced by cooperators when competing with defectors. Evolutionary game theory
provides a competent theoretical framework for addressing the subtleties of
cooperation in such situations, which are known as social dilemmas. Recent
advances point towards the fact that the evolution of strategies alone may be
insufficient to fully exploit the benefits offered by cooperative behavior.
Indeed, while spatial structure and heterogeneity, for example, have been
recognized as potent promoters of cooperation, coevolutionary rules can extend
the potentials of such entities further, and even more importantly, lead to the
understanding of their emergence. The introduction of coevolutionary rules to
evolutionary games implies, that besides the evolution of strategies, another
property may simultaneously be subject to evolution as well. Coevolutionary
rules may affect the interaction network, the reproduction capability of
players, their reputation, mobility or age. Here we review recent works on
evolutionary games incorporating coevolutionary rules, as well as give a
didactic description of potential pitfalls and misconceptions associated with
the subject. In addition, we briefly outline directions for future research
that we feel are promising, thereby particularly focusing on dynamical effects
of coevolutionary rules on the evolution of cooperation, which are still widely
open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in
BioSystem
Comparing reactive and memory-one strategies of direct reciprocity
Direct reciprocity is a mechanism for the evolution of cooperation based on
repeated interactions. When individuals meet repeatedly, they can use
conditional strategies to enforce cooperative outcomes that would not be
feasible in one-shot social dilemmas. Direct reciprocity requires that
individuals keep track of their past interactions and find the right response.
However, there are natural bounds on strategic complexity: Humans find it
difficult to remember past interactions accurately, especially over long
timespans. Given these limitations, it is natural to ask how complex strategies
need to be for cooperation to evolve. Here, we study stochastic evolutionary
game dynamics in finite populations to systematically compare the evolutionary
performance of reactive strategies, which only respond to the co-player's
previous move, and memory-one strategies, which take into account the own and
the co-player's previous move. In both cases, we compare deterministic strategy
and stochastic strategy spaces. For reactive strategies and small costs, we
find that stochasticity benefits cooperation, because it allows for
generous-tit-for-tat. For memory one strategies and small costs, we find that
stochasticity does not increase the propensity for cooperation, because the
deterministic rule of win-stay, lose-shift works best. For memory one
strategies and large costs, however, stochasticity can augment cooperation.Comment: 18 pages, 7 figure
The Evolution of Extortion in Iterated Prisoner's Dilemma Games
Iterated games are a fundamental component of economic and evolutionary game
theory. They describe situations where two players interact repeatedly and have
the possibility to use conditional strategies that depend on the outcome of
previous interactions. In the context of evolution of cooperation, repeated
games represent the mechanism of reciprocation. Recently a new class of
strategies has been proposed, so called 'zero determinant strategies'. These
strategies enforce a fixed linear relationship between one's own payoff and
that of the other player. A subset of those strategies are 'extortioners' which
ensure that any increase in the own payoff exceeds that of the other player by
a fixed percentage. Here we analyze the evolutionary performance of this new
class of strategies. We show that in reasonably large populations they can act
as catalysts for the evolution of cooperation, similar to tit-for-tat, but they
are not the stable outcome of natural selection. In very small populations,
however, relative payoff differences between two players in a contest matter,
and extortioners hold their ground. Extortion strategies do particularly well
in co-evolutionary arms races between two distinct populations: significantly,
they benefit the population which evolves at the slower rate - an instance of
the so-called Red King effect. This may affect the evolution of interactions
between host species and their endosymbionts.Comment: contains 4 figure
Evolution of cooperation in spatial traveler's dilemma game
Traveler's dilemma (TD) is one of social dilemmas which has been well studied
in the economics community, but it is attracted little attention in the physics
community. The TD game is a two-person game. Each player can select an integer
value between and () as a pure strategy. If both of them select
the same value, the payoff to them will be that value. If the players select
different values, say and (), then the payoff to the
player who chooses the small value will be and the payoff to the other
player will be . We term the player who selects a large value as the
cooperator, and the one who chooses a small value as the defector. The reason
is that if both of them select large values, it will result in a large total
payoff. The Nash equilibrium of the TD game is to choose the smallest value
. However, in previous behavioral studies, players in TD game typically
select values that are much larger than , and the average selected value
exhibits an inverse relationship with . To explain such anomalous behavior,
in this paper, we study the evolution of cooperation in spatial traveler's
dilemma game where the players are located on a square lattice and each player
plays TD games with his neighbors. Players in our model can adopt their
neighbors' strategies following two standard models of spatial game dynamics.
Monte-Carlo simulation is applied to our model, and the results show that the
cooperation level of the system, which is proportional to the average value of
the strategies, decreases with increasing until is greater than the
threshold where cooperation vanishes. Our findings indicate that spatial
reciprocity promotes the evolution of cooperation in TD game and the spatial TD
game model can interpret the anomalous behavior observed in previous behavioral
experiments
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
Small games and long memories promote cooperation
Complex social behaviors lie at the heart of many of the challenges facing
evolutionary biology, sociology, economics, and beyond. For evolutionary
biologists in particular the question is often how such behaviors can arise
\textit{de novo} in a simple evolving system. How can group behaviors such as
collective action, or decision making that accounts for memories of past
experience, emerge and persist? Evolutionary game theory provides a framework
for formalizing these questions and admitting them to rigorous study. Here we
develop such a framework to study the evolution of sustained collective action
in multi-player public-goods games, in which players have arbitrarily long
memories of prior rounds of play and can react to their experience in an
arbitrary way. To study this problem we construct a coordinate system for
memory- strategies in iterated -player games that permits us to
characterize all the cooperative strategies that resist invasion by any mutant
strategy, and thus stabilize cooperative behavior. We show that while larger
games inevitably make cooperation harder to evolve, there nevertheless always
exists a positive volume of strategies that stabilize cooperation provided the
population size is large enough. We also show that, when games are small,
longer-memory strategies make cooperation easier to evolve, by increasing the
number of ways to stabilize cooperation. Finally we explore the co-evolution of
behavior and memory capacity, and we find that longer-memory strategies tend to
evolve in small games, which in turn drives the evolution of cooperation even
when the benefits for cooperation are low
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