1,925 research outputs found
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
Linear algebraic structure of zero-determinant strategies in repeated games
Zero-determinant (ZD) strategies, a recently found novel class of strategies
in repeated games, has attracted much attention in evolutionary game theory. A
ZD strategy unilaterally enforces a linear relation between average payoffs of
players. Although existence and evolutional stability of ZD strategies have
been studied in simple games, their mathematical properties have not been
well-known yet. For example, what happens when more than one players employ ZD
strategies have not been clarified. In this paper, we provide a general
framework for investigating situations where more than one players employ ZD
strategies in terms of linear algebra. First, we theoretically prove that a set
of linear relations of average payoffs enforced by ZD strategies always has
solutions, which implies that incompatible linear relations are impossible.
Second, we prove that linear payoff relations are independent of each other
under some conditions. These results hold for general games with public
monitoring including perfect-monitoring games. Furthermore, we provide a simple
example of a two-player game in which one player can simultaneously enforce two
linear relations, that is, simultaneously control her and her opponent's
average payoffs. All of these results elucidate general mathematical properties
of ZD strategies.Comment: 19 pages, 2 figure
Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations
We study the evolution of cooperation in the spatial prisoner's dilemma game,
where besides unconditional cooperation and defection, tit-for-tat,
win-stay-lose-shift and extortion are the five competing strategies. While
pairwise imitation fails to sustain unconditional cooperation and extortion
regardless of game parametrization, myopic updating gives rise to the
coexistence of all five strategies if the temptation to defect is sufficiently
large or if the degree distribution of the interaction network is
heterogeneous. This counterintuitive evolutionary outcome emerges as a result
of an unexpected chain of strategy invasions. Firstly, defectors emerge and
coarsen spontaneously among players adopting win-stay-lose-shift. Secondly,
extortioners and players adopting tit-for-tat emerge and spread via neutral
drift among the emerged defectors. And lastly, among the extortioners,
cooperators become viable too. These recurrent evolutionary invasions yield a
five-strategy phase that is stable irrespective of the system size and the
structure of the interaction network, and they reveal the most unexpected
mechanism that stabilizes extortion and cooperation in an evolutionary setting.Comment: 7 two-column pages, 5 figures; accepted for publication in Scientific
Reports [related work available at http://arxiv.org/abs/1401.8294
Cooperation and control in multiplayer social dilemmas
Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner’s dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups
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