Chaotic and deterministic switching in a two-person game

We study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to behaviour ranging from almost deterministic actions to chaotic-like dynamics. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning.learning process, dynamics, switching, chaos

On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background

The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality criterion is set up and it is used to determine uniquely the set of solutions as well as to show that even-parity solutions do not exist.Comment: 10 page

The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps

We probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the Discrete Markus-Yamabe Question are those possessing Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map

Public Firms in a Dynamic Third Market Model

We set the third market model in a dynamic context to decide whether a country can achieve benefits by subsidizing a public rm's exports. We use calculus of variations with the constraint that the welfare is either maximized or grows at constant rate, reflecting the public concern of the firm. We conclude that a subsidy can be a good strategy for the country in some instances, even though only over a finite period of time. The duration of this period depends on the output strategy of the public firm as well as on exogenous factors.public firms, strategic trade policy, third market model, calculus of variations