Related papers: Hamiltonian Evolutionary Games
This paper presents a class of evolutive Mean Field Games with multiple solutions for all time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T large enough. The phenomenon is analyzed in both the PDE and…
In this paper we introduce the notion of multidimensional multiplicative Poisson vertex algebra, the generalization of the notion of multiplicative Poisson vertex algebra to a difference algebra endowed with D commuting shifts. After…
The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a…
We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical W-algebras and apply it to construct a large class of…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…
The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold…
Evolutionary game theory has become one of the most diverse and far reaching theories in biology. Applications of this theory range from cell dynamics to social evolution. However, many applications make it clear that inherent…
Given a classical $r$-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny…
We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
It is well-known that the problem of recognizing an ESS in a symmetric bimatrix game is coNP-complete. In this paper, we show that recognizing an ESS even in doubly symmetric bimatrix games is also coNP-complete. Our result further implies…
A matrix-based framework for Bayesian games is presented, using semi-tensor product of matrices. Static Bayesian games are considered first. Matrix expression of Bayesian games is proposed. Three kinds of conversions, which convert Bayesian…
Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…
We present alternative explicit forms of the standard Hamiltonian for systems with one degree of freedom. This new class of infinite Hamiltonians is called Newton-equivalent Hamiltonian zoo, producing the same equation of motion. These…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially…
This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie--Hamilton systems. We devise methods to study their superposition rules, time independent constants…
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
In this letter, we deal with evolutionary game theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic,…