Tadeusz Płatkowski

Playing minority game

We designed and conducted an experiment to see how people play the standard minority game. The experiment was conducted at the computer lab, using a special software, with a group of 15 students. Collected informations comprise individual choices and individual wealth after each time step. The results, in particular the coordination of the agents, measured by the volatility of the system, are compared for different amount of informations available to the agents.

Drift- or fluctuation-induced ordering and self-organization in driven many-particle systems

According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a cellular-automaton model of interactive motion in space and find an optimal noise strength, while order breaks down at high(er) fluctuation levels. Additionally, we discuss the phenomenon of noise- and drift-induced self-organization in systems that would show disorder in the absence of fluctuations. In the future, related studies may have applications to the control of many-particle systems such as the efficient separation of particles. The rather general formulation of our model in the spirit of game theory may allow to shed some light on several different kinds of noise-induced ordering phenomena observed in physical, chemical, biological, and socio-economic systems (e.g., attractive and repulsive agglomeration, or segregation).

Evolution of populations playing mixed multiplayer games

We study temporal evolution of monomorphic populations of individuals which, at each time step participate in one of the prescribed k-player stage games, k = 2, 3,...,n. We introduce replicator equations for such systems, and investigate the effect of playing different stage games on the number and stability of stationary states of the populations. When the probabilities of the stage games depend on time, we introduce a system of replicator equations in a properly modified simplex of the game, and discuss stationary states for such populations.

An acceleration procedure for discrete velocity approximation of the Boltzmann collision operator

Abstract In this paper, we investigate a method of realization of the discrete velocity approximation of the Boltzmann collision operator studied by Palczewski, Schneider and Bobylev. For this realization, we propose an acceleration procedure, which reduces the computational complexity of the method. The efficiency of the acceleration procedure is demonstrated through a set of numerical tests, which include space homogeneous relaxation problems and space nonhomogeneous problem of shock wave formation.

Enhanced cooperation in prisoner's dilemma with aspiration

Abstract We develop an aspiration-based dynamic model which leads to enhanced cooperation in the Prisoner’s Dilemma game played by the continuous population of agents. The main idea is to limit the aggregate information available to the agents. The model–a system of three nonlinear differential equations–describes the evolution of the aspiration levels of players who use different strategies, and the evolution of the mean frequency of the cooperative strategy in the system of players. The stationary (partial) cooperation level is calculated explicitly. We demonstrate that, contrary to the similar model with only one global aspiration level, the stationary cooperation level can be greater than half.

A mechanism of dynamical interactions for two-person social dilemmas.

We propose a new mechanism of interactions between game-theoretical agents in which the weights of the connections between interacting individuals are dynamical, payoff-dependent variables. Their evolution depends on the difference between the payoff of the agents from a given type of encounter and their average payoff. The mechanism is studied in the frame of two models: agents distributed on a random graph, and a mean field model. Symmetric and asymmetric connections between the agents are introduced. Long time behavior of both systems is discussed for the Prisoners Dilemma and the Snow Drift games.

Entropy profiles in discrete velocity models of the Boltzmann equation

Abstract Entropy profiles in the shock wave solutions of discrete velocity models of the Boltzmann equation are studied. Overshoot of the local entropy in the interior of the shock wave and dependence of the solutions on the Maxwellian limit conditions are discussed.

Aspiration-based full cooperation in finite systems of players

We propose a mathematical model of evolution of a finite well-mixed population of players who change their behavior if the payoff obtained from Prisoners Dilemma based interactions is smaller than a threshold (aspiration level). The threshold can be a fixed constant or a dynamical variable, which depends on some overall dynamically changing characteristics of the system. We investigate the dependence of full cooperation on the group size, game payoffs, aspiration level, and heterogeneity of the system. For endogenous aspirations we find analytically conditions which guarantee full cooperation in the long run for all initial configurations and group sizes. The result is robust to a stochastic choice of strategies by the heterogeneous players, as documented by numerical simulations.

Egalitarian solutions to multiperson social dilemmas in populations

We consider a class of multiperson social dilemma games played in large populations. In particular, the popular games, such as for example the N-person Prisoners Dilemma, the Public Goods, the Tragedy of the Commons, the Volunteers Dilemma, and the Assurance game, are included in the proposed frame. The evolution of such populations is assumed to be governed by the replicator equations. We show that the egalitarian distribution of the social welfare generated in the multiperson social dilemma games fosters the long run cooperation in such populations.

Multimarket Minority Game

We consider a system of heterogeneous agents playing the Minority Game on two markets. At each time step, each agent plays on one of the markets only. The agents can change the market according to some switching scheme. Various switching schemes are investigated: those that depend on the performance of the agents on each of the markets, and those that determine the actual market as a function of the number of games lost on the markets. We discuss the influence of the chosen switching scheme on the overall performance of the system of agents. In particular, we study both aggregate attendance (price returns) and volatilities for various schemes of the market choice.