A. S. Hegazi

On dynamical multi-team and signaling games

Abstract Dynamic multi-team games are introduced. In these games Pareto optimality is used within the team but Nash equilibrium is sought between different teams. Puu’s approach to dynamic standard games is generalized to multi-team Cournot game. Multi-team Hawk–Dove game is introduced. Dynamic signaling game is studied.

An Epidemic Model on Small-World Networks and Ring Vaccination

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the probability of infection is high enough. Also an analytical approximation for this model is studied.

On discrete dynamical systems associated to games

Dynamical systems corresponding to continuous strategy games are introduced. The steady of the systems corresponding to continuous prisoners dilemma, hawk-dove and rock-scissors-paper games are found and their stability are discussed. A discrete imitation equation is derived. Smales payoff memory game formulation is generalized.

On Spatial Asymmetric Games

The stability of some spatial asymmetric games is discussed. Both linear and nonlinear asymptotic stability of asymmetric hawk-dove and prisoners dilemma are studied. Telegraph reaction diffusion equations for the asymmetric spatial games are presented. Asymmetric games of parental investment is studied in the presence of both ordinary and cross diffusions.

Sato–Crutchfield Formulation For Some Evolutionary Games

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoners dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoners dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

Infinitesimally deformed field and string theories

The infinitesimally deformed oscillator algebra is used to derive the infinitesimally deformed Heisenberg algebra. Hence, the infinitesimally deformed field theories and string theories are constructed. The physical meaning of these theories is discussed.

ON PERSISTENCE AND STABILITY OF SOME BIOLOGICAL SYSTEMS WITH CROSS DIFFUSION

The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without delay), hawk–dove–retaliate and prisoners dilemma games are given.

On some variants of dynamical systems

Abstract A dynamical system motivated by discrete physics is studied. Fuzzy dynamical systems are used to study fuzzy discrete replicator dynamics of hawk–dove (HD) and prisoners dilemma (PD) games. New solutions are obtained. Finally a preliminary study for fuzzy predator–prey model is studied and a new equilibrium is found.

A dynamic model for e-commerce taxation

A dynamic model for e-commerce taxation is given. Stability conditions impose constraints on taxation parameters both in the conventional and the electronic sectors. A model is used to derive a condition on the number of e-commerce firms to avoid market instability. This may explain the overexpansion (too many firms) phenomena observed in the e-commerce sector.

On some variants of prisoner's dilemma dynamics

In this work two variants of Prisoners dilemma game are given. The first one is related to spite. Spite is the willingness to harm oneself in order to cause more harm to another. An extreme case is when one goes as far as killing himself to harm his enemy. This behavior sometimes occurs in humans. To model it, the standard replicator dynamics is replaced by imitation dynamics. We study the spite replicator dynamics for the prisoners dilemma game and derive a case where cooperation may arise. The second variant is the prisoners dilemma loner game. Smales memory formulation for game is used to study it.