5,676 research outputs found
Evolution of extortion in structured populations
Extortion strategies can dominate any opponent in an iterated prisoner’s dilemma game. But if players are
able to adopt the strategies performing better, extortion becomes widespread and evolutionary unstable. It may
sometimes act as a catalyst for the evolution of cooperation, and it can also emerge in interactions between two
populations, yet it is not the evolutionarily stable outcome. Here we revisit these results in the realm of spatial
games. We find that pairwise imitation and birth-death dynamics return known evolutionary outcomes. Myopic
best response strategy updating, on the other hand, reveals counterintuitive solutions. Defectors and extortioners
coarsen spontaneously, which allows cooperators to prevail even at prohibitively high temptations to defect.
Here extortion strategies play the role of a Trojan horse. They may emerge among defectors by chance, and
once they do, cooperators become viable as well. These results are independent of the interaction topology, and
they highlight the importance of coarsening, checkerboard ordering, and best response updating in evolutionary
games
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
Zero-determinant strategies in finitely repeated games
Direct reciprocity is a mechanism for sustaining mutual cooperation in
repeated social dilemma games, where a player would keep cooperation to avoid
being retaliated by a co-player in the future. So-called zero-determinant (ZD)
strategies enable a player to unilaterally set a linear relationship between
the player's own payoff and the co-player's payoff regardless of the strategy
of the co-player. In the present study, we analytically study zero-determinant
strategies in finitely repeated (two-person) prisoner's dilemma games with a
general payoff matrix. Our results are as follows. First, we present the forms
of solutions that extend the known results for infinitely repeated games (with
a discount factor w of unity) to the case of finitely repeated games (0 < w <
1). Second, for the three most prominent ZD strategies, the equalizers,
extortioners, and generous strategies, we derive the threshold value of w above
which the ZD strategies exist. Third, we show that the only strategies that
enforce a linear relationship between the two players' payoffs are either the
ZD strategies or unconditional strategies, where the latter independently
cooperates with a fixed probability in each round of the game, proving a
conjecture previously made for infinitely repeated games.Comment: 24 pages, 2 figure
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
Unbending strategies shepherd cooperation and suppress extortion in spatial populations
Evolutionary game dynamics on networks typically consider the competition
among simple strategies such as cooperation and defection in the Prisoner's
Dilemma and summarize the effect of population structure as network
reciprocity. However, it remains largely unknown regarding the evolutionary
dynamics involving multiple powerful strategies typically considered in
repeated games, such as the zero-determinant (ZD) strategies that are able to
enforce a linear payoff relationship between them and their co-players. Here,
we consider the evolutionary dynamics of always cooperate (AllC), extortionate
ZD (extortioners), and unbending players in lattice populations based on the
commonly used death-birth updating. Out of the class of unbending strategies,
we consider a particular candidate, PSO Gambler, a machine-learning-optimized
memory-one strategy, which can foster reciprocal cooperation and fairness among
extortionate players. We derive analytical results under weak selection and
rare mutations, including pairwise fixation probabilities and long-term
frequencies of strategies. In the absence of the third unbending type,
extortioners can achieve a half-half split in equilibrium with unconditional
cooperators for sufficiently large extortion factors. However, the presence of
unbending players fundamentally changes the dynamics and tilts the system to
favor unbending cooperation. Most surprisingly, extortioners cannot dominate at
all regardless of how large their extortion factor is, and the long-term
frequency of unbending players is maintained almost as a constant. Our
analytical method is applicable to studying the evolutionary dynamics of
multiple strategies in structured populations. Our work provides insights into
the interplay between network reciprocity and direct reciprocity, revealing the
role of unbending strategies in enforcing fairness and suppressing extortion.Comment: 21 pages, 6 figure
Conformity enhances network reciprocity in evolutionary social dilemmas
The pursuit of highest payoffs in evolutionary social dilemmas is risky and
sometimes inferior to conformity. Choosing the most common strategy within the
interaction range is safer because it ensures that the payoff of an individual
will not be much lower than average. Herding instincts and crowd behavior in
humans and social animals also compel to conformity on their own right.
Motivated by these facts, we here study the impact of conformity on the
evolution of cooperation in social dilemmas. We show that an appropriate
fraction of conformists within the population introduces an effective surface
tension around cooperative clusters and ensures smooth interfaces between
different strategy domains. Payoff-driven players brake the symmetry in favor
of cooperation and enable an expansion of clusters past the boundaries imposed
by traditional network reciprocity. This mechanism works even under the most
testing conditions, and it is robust against variations of the interaction
network as long as degree-normalized payoffs are applied. Conformity may thus
be beneficial for the resolution of social dilemmas.Comment: 8 two-column pages, 5 figures; accepted for publication in Journal of
the Royal Society Interfac
Impact of Committed Minorities: Unveiling Critical Mass of Cooperation in the Iterated Prisoner's Dilemma Game
The critical mass effect is a prevailing topic in the study of complex
systems. Recent research has shown that a minority of zealots can effectively
drive widespread cooperation in social dilemma games. However, achieving a
critical mass of cooperation in the prisoner's dilemma requires stricter
conditions. The underlying mechanism behind this effect remains unclear,
particularly in the context of repeated interactions. This paper aims to
investigate the influence of a committed minority on cooperation in the
Iterated Prisoner's Dilemma game, a widely studied model of repeated
interactions between individuals facing a social dilemma. In contrast to
previous findings, we identify tipping points for both well-mixed and
structured populations. Our findings demonstrate that a committed minority of
unconditional cooperators can induce full cooperation under weak imitation
conditions. Conversely, a committed minority of conditional cooperators, who
often employ Tit-for-Tat or extortion strategies, can promote widespread
cooperation under strong imitation conditions. These results hold true across
various network topologies and imitation rules, suggesting that critical mass
effects may be a universal principle in social dilemma games. Additionally, we
discover that an excessive density of committed conditional cooperators can
hinder cooperation in structured populations. This research advances our
understanding of the role of committed minorities in shaping social behavior
and provides valuable insights into cooperation dynamics.Comment: 12 pages, 15 figure
- …