Related papers: An evolutionary view on equilibrium models of tran…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics…
This paper investigates an energy conservation and dissipation -- passivity -- aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise…
Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing…
Applying the concepts and formalisms from Evolutionary Game Theory to the data regime, the fundamental paradigms of Evolutionary Data Theory are introduced. Interpreting data in matrix form as evolutionary entities, input data is mapped to…
We propose a simple dynamic model splitting users of the transport network by type of movement: personal transport and public transport. A distinctive feature proposed in the article is the existence of an evolutionary approach component in…
In the present paper we provide the closed form of the path-like solutions for the logistic and $\theta$-logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their…
We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers'…
In this paper, we present a study of a mobility game with uncertainty in the decision-making of travelers and incorporate prospect theory to model travel behavior. We formulate a mobility game that models how travelers distribute their…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
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…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
In this paper we describe how imitative logit dynamic (rather popular in population games theory) can be interpreted in terms of mirror descent method (well known in convex optimization). We demonstrate the connection of this two type…
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…
Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the…