We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases
The paper considers an nn-person prisoner’s dilemma game. We present a modification of this model for the network interaction of players. A set of grim trigger strategies is a Nash equilibrium in the repeated nn-person prisoner’s dilemma on a network, just as in the two-player game. However, even a slight deviation leads to the case where players get low payoffs in perpetuity without the possibility of returning to the Pareto optimal payoffs. A solution to this problem is proposed. The players’ payoff functions in a game of an nn-person prisoner’s dilemma type on a network are described. A strategy involving a punishment on a limited interval of the game is proposed. The number of steps required for an effective punishment is found. An example of a network for this game is given. The number of steps for an effective punishment is found for the given example.
The article examines the relationship between power resource and rational behavior in history. It is shown that personal interest is expressed in socially useful economic activities of individuals only if they had no adequate power potential. This general principle is illustrated by examples of Russian medieval history that are associated with the specifics of the trade route «from the Varangians to the Greeks», with land ownership and changing social structure. Further the thesis of the strengthening of the connection between economy and power potential that helps to explain changes in the distribution of power, institutions and economic growth in the Western world in Modern history is elaborated and illustrated. Moreover, the author describes the social dynamics in situations when low social classes expand at social bottoms and, using their monopoly there, exalt.