Related papers: Fictitious Play in $3\times 3$ games: chaos and di…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
We study an ensemble of individuals playing the two games of the so-called Parrondo paradox. In our study, players are allowed to choose the game to be played by the whole ensemble in each turn. The choice cannot conform to the preferences…
We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in…
We analyze the pedestrian evacuation of a rectangular room with a single door considering a Lattice Gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational…
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…
We consider an example of cyclic competition bimatrix game which is a Rock-Scissors-Paper game with assumption about perfect memory of the playing agents. At first we investigate the dynamics in the neighbourhood of the Nash equilibrium as…
In this paper, we introduce a couple of dynamical systems that are related to the Chaos Game. We begin by discussing different methods of generating the Sierpinski gasket. Then we show how the transition from random to uniform selection…
This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…
Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full…
Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be…
We investigate chaotic scattering on an attractive step potential with a quadrupolar deformation. The phase space features of the bound billiard are studied by using the notion of symmetry lines to find periodic orbits. We show that the…
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this…
We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of…
The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…
The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no…
A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…
A new model of population dynamics on lattices is proposed. The model consists of players on lattice points, each of which plays the RSP game with neighboring players. Each player copies the next hand from the hand of the neighbouring…
We present a novel algorithm for game-theoretic trajectory planning, tailored for settings in which agents can only observe one another in specific regions of the state space. Such problems arise naturally in the context of multi-robot…
With evolutionary game theory, mathematicians, physicists and theoretical biologists usually show us beautiful figures of population dynamic patterns. 2x2 game (matching pennies game) is one of the classical cases. In this letter, we report…
We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new…