762 research outputs found
Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players
Game dynamics in which three or more strategies are cyclically competitive,
as represented by the rock-scissors-paper game, have attracted practical and
theoretical interests. In evolutionary dynamics, cyclic competition results in
oscillatory dynamics of densities of individual strategists. In finite-size
populations, it is known that oscillations blow up until all but one strategies
are eradicated if without mutation. In the present paper, we formalize
replicator dynamics with players that have different adaptation rates. We show
analytically and numerically that the heterogeneous adaptation rate suppresses
the oscillation amplitude. In social dilemma games with cyclically competing
strategies and homogeneous adaptation rates, altruistic strategies are often
relatively weak and cannot survive in finite-size populations. In such
situations, heterogeneous adaptation rates save coexistence of different
strategies and hence promote altruism. When one strategy dominates the others
without cyclic competition, fast adaptors earn more than slow adaptors. When
not, mixture of fast and slow adaptors stabilizes population dynamics, and slow
adaptation does not imply inefficiency for a player.Comment: 4 figure
Evolution via imitation among like-minded individuals
In social situations with which evolutionary game is concerned, individuals
are considered to be heterogeneous in various aspects. In particular, they may
differently perceive the same outcome of the game owing to heterogeneity in
idiosyncratic preferences, fighting abilities, and positions in a social
network. In such a population, an individual may imitate successful and similar
others, where similarity refers to that in the idiosyncratic fitness function.
I propose an evolutionary game model with two subpopulations on the basis of
multipopulation replicator dynamics to describe such a situation. In the
proposed model, pairs of players are involved in a two-person game as a
well-mixed population, and imitation occurs within subpopulations in each of
which players have the same payoff matrix. It is shown that the model does not
allow any internal equilibrium such that the dynamics differs from that of
other related models such as the bimatrix game. In particular, even a slight
difference in the payoff matrix in the two subpopulations can make the opposite
strategies to be stably selected in the two subpopulations in the snowdrift and
coordination games.Comment: 3 figure
Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation
Real social interactions occur on networks in which each individual is
connected to some, but not all, of others. In social dilemma games with a fixed
population size, heterogeneity in the number of contacts per player is known to
promote evolution of cooperation. Under a common assumption of positively
biased payoff structure, well-connected players earn much by playing
frequently, and cooperation once adopted by well-connected players is
unbeatable and spreads to others. However, maintaining a social contact can be
costly, which would prevent local payoffs from being positively biased. In
replicator-type evolutionary dynamics, it is shown that even a relatively small
participation cost extinguishes the merit of heterogeneous networks in terms of
cooperation. In this situation, more connected players earn less so that they
are no longer spreaders of cooperation. Instead, those with fewer contacts win
and guide the evolution. The participation cost, or the baseline payoff, is
irrelevant in homogeneous populations but is essential for evolutionary games
on heterogeneous networks.Comment: 4 figures + 3 supplementary figure
Directionality of contact networks suppresses selection pressure in evolutionary dynamics
Individuals of different types, may it be genetic, cultural, or else, with
different levels of fitness often compete for reproduction and survival. A
fitter type generally has higher chances of disseminating their copies to other
individuals. The fixation probability of a single mutant type introduced in a
population of wild-type individuals quantifies how likely the mutant type
spreads. How much the excess fitness of the mutant type increases its fixation
probability, namely, the selection pressure, is important in assessing the
impact of the introduced mutant. Previous studies mostly based on undirected
and unweighted contact networks of individuals showed that the selection
pressure depends on the structure of networks and the rule of reproduction.
Real networks underlying ecological and social interactions are usually
directed or weighted. Here we examine how the selection pressure is modulated
by directionality of interactions under several update rules. Our conclusions
are twofold. First, directionality discounts the selection pressure for
different networks and update rules. Second, given a network, the update rules
in which death events precede reproduction events significantly decrease the
selection pressure than the other rules.Comment: 7 figures, 2 table
Groupwise information sharing promotes ingroup favoritism in indirect reciprocity
Indirect reciprocity is a mechanism for cooperation in social dilemma
situations, in which an individual is motivated to help another to acquire a
good reputation and receive help from others afterwards. Ingroup favoritism is
another aspect of human cooperation, whereby individuals help members in their
own group more often than those in other groups. Ingroup favoritism is a puzzle
for the theory of cooperation because it is not easily evolutionarily stable.
In the context of indirect reciprocity, ingroup favoritism has been shown to be
a consequence of employing a double standard when assigning reputations to
ingroup and outgroup members; e.g., helping an ingroup member is regarded as
good, whereas the same action toward an outgroup member is regarded as bad. We
analyze a model of indirect reciprocity in which information sharing is
conducted groupwise. In our model, individuals play social dilemma games within
and across groups, and the information about their reputations is shared within
each group. We show that evolutionarily stable ingroup favoritism emerges even
if all the players use the same reputation assignment rule regardless of group
(i.e., a single standard). Two reputation assignment rules called simple
standing and stern judging yield ingroup favoritism. Stern judging induces much
stronger ingroup favoritism than does simple standing. Simple standing and
stern judging are evolutionarily stable against each other when groups
employing different assignment rules compete and the number of groups is
sufficiently large. In addition, we analytically show as a limiting case that
homogeneous populations of reciprocators that use reputations are unstable when
individuals independently infer reputations of individuals, which is consistent
with previously reported numerical results.Comment: 25 pages, 7 figures. The Abstract is shortened to fill in arXiv's
abstract for
Evolutionary dynamics and fixation probabilities in directed networks
We investigate the evolutionary dynamics in directed and/or weighted
networks. We study the fixation probability of a mutant in finite populations
in stochastic voter-type dynamics for several update rules. The fixation
probability is defined as the probability of a newly introduced mutant in a
wild-type population taking over the entire population. In contrast to the case
of undirected and unweighted networks, the fixation probability of a mutant in
directed networks is characterized not only by the degree of the node that the
mutant initially invades but by the global structure of networks. Consequently,
the gross connectivity of networks such as small-world property or modularity
has a major impact on the fixation probability.Comment: 7 figure
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