16,063 research outputs found
Instability in spatial evolutionary games
We investigate the aspects that influence the instability of
spatial evolutionary games, namely the Prisoner's Dilemma and the
Snowdrift games. In this paper instability is defined as the proportion of
strategy changes in the asymptotic period of the evolutionary process.
The results show that with the Prisoner's Dilemma, when the level of
noise present in the decision process is very low, the instability decreases
as the synchrony rate decreases. With the Snowdrift this pattern of behavior
depends strongly on the interaction topology and arises only for
random and scale-free networks. However, for large noise values, the instability
in both games depends only on the proportion of cooperators
present in the population: it increases as the proportion of cooperators
approaches 0.5. We advance an explanation for this behavior
Survival of the Fittest and Zero Sum Games
Competition for available resources is natural amongst coexisting species,
and the fittest contenders dominate over the rest in evolution. The dynamics of
this selection is studied using a simple linear model. It has similarities to
features of quantum computation, in particular conservation laws leading to
destructive interference. Compared to an altruistic scenario, competition
introduces instability and eliminates the weaker species in a finite time.Comment: 6 pages, formatted according to journal style. Special Issue on Game
Theory and Evolutionary Processes. (v2) Published version. Some
clarifications added. Topological interpretation pointed ou
Pattern formation for reactive species undergoing anisotropic diffusion
Turing instabilities for a two species reaction-diffusion systems is studied
under anisotropic diffusion. More specifically, the diffusion constants which
characterize the ability of the species to relocate in space are direction
sensitive. Under this working hypothesis, the conditions for the onset of the
instability are mathematically derived and numerically validated. Patterns
which closely resemble those obtained in the classical context of isotropic
diffusion, develop when the usual Turing condition is violated, along one of
the two accessible directions of migration. Remarkably, the instability can
also set in when the activator diffuses faster than the inhibitor, along the
direction for which the usual Turing conditions are not matched
"Stability of Spatial Equilibrium"
This paper focuses on externalities between economic agents. We consider spatial dis- tribution of economic activities in a multiregional dynamical system, where regions may be interpreted as clubs, social subgroups, species, or strategies. Our dynamics includes gravity models and replicator dynamics as special cases. Assuming that other variables, such as prices are solved as a function of the population distribution, we analyze both interior and corner equilibria of spatial distribution in a general class of dynamics, including the replicator dynamics and the gravity model. We derive the exact conditions for stable equilibrium and give some interpretations of the stability conditions. We show that interior equilibria are stable in the presence of strong agglomeration economies, but unstable in the presence of strong congestion diseconomies.
Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power
Evolutionary game theory has been successfully used to investigate the
dynamics of systems, in which many entities have competitive interactions. From
a physics point of view, it is interesting to study conditions under which a
coordination or cooperation of interacting entities will occur, be it spins,
particles, bacteria, animals, or humans. Here, we analyze the case, where the
entities are heterogeneous, particularly the case of two populations with
conflicting interactions and two possible states. For such systems, explicit
mathematical formulas will be determined for the stationary solutions and the
associated eigenvalues, which determine their stability. In this way, four
different types of system dynamics can be classified, and the various kinds of
phase transitions between them will be discussed. While these results are
interesting from a physics point of view, they are also relevant for social,
economic, and biological systems, as they allow one to understand conditions
for (1) the breakdown of cooperation, (2) the coexistence of different
behaviors ("subcultures"), (2) the evolution of commonly shared behaviors
("norms"), and (4) the occurrence of polarization or conflict. We point out
that norms have a similar function in social systems that forces have in
physics
- …