50,936 research outputs found
Understanding the shape of the mixture failure rate (with engineering and demographic applications)
Mixtures of distributions are usually effectively used for modeling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications. We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behavior as t tends to infty. Some demographic and engineering examples are considered. The corresponding inverse problem is discussed.
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
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
Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
Agent-based stochastic models for finite populations have recently received
much attention in the game theory of evolutionary dynamics. Both the ultimate
fixation and the pre-fixation transient behavior are important to a full
understanding of the dynamics. In this paper, we study the transient dynamics
of the well-mixed Moran process through constructing a landscape function. It
is shown that the landscape playing a central theoretical "device" that
integrates several lines of inquiries: the stable behavior of the replicator
dynamics, the long-time fixation, and continuous diffusion approximation
associated with asymptotically large population. Several issues relating to the
transient dynamics are discussed: (i) multiple time scales phenomenon
associated with intra- and inter-attractoral dynamics; (ii) discontinuous
transition in stochastically stationary process akin to Maxwell construction in
equilibrium statistical physics; and (iii) the dilemma diffusion approximation
facing as a continuous approximation of the discrete evolutionary dynamics. It
is found that rare events with exponentially small probabilities, corresponding
to the uphill movements and barrier crossing in the landscape with multiple
wells that are made possible by strong nonlinear dynamics, plays an important
role in understanding the origin of the complexity in evolutionary, nonlinear
biological systems.Comment: 34 pages, 4 figure
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