Narrow Results

In contrast to the usual models using the prisoner's dilemma to study the development of cooperation, the present paper studies renewable resource exploitation, where possible degrees of cooperation of resource users can be selected from a continuous spectrum. The evolutionary dynamics of the system is based on the so-called lumberjacks' dilemma game, where renewable resources (e.g. a biomass) with a continuous logistic growth are harvested at discrete intervals. A player – lumberjack proposes the percentage of resources to be harvested and his goal is to maximize his sustainable yield. In the multi – player game the greatest proposed percentage is harvested and the players share it in the proportion to their proposed percentage. Excessive greed would however exhaust the resource. The ideal solution determined by a mathematical analysis is compared with the results of locally optimizing agents and evolutionary computations, where the influence of other lumberjacks is included into the “environment”, so that there exist no “conscious” cooperation. Despite this lack of information, couples of players develop a very good cooperation.

We propose a stochastic dynamic model of migration and economic aggregation in a system of employed (immobile) and unemployed (mobile) agents which respond to local wage gradients. Dependent on the local economic situation described by a production function which includes cooperative effects employed agents can become unemployed and vice versa. The spatio-temporal distribution of employed and unemployed agents is investigated both analytically and by means of stochastic computer simulations. We find the establishment of distinct economic centers out of a random initial distribution. The evolution of these centers occurs in two different stages: (i) small economic centers are formed based on the positive feedback of mutual stimulation/cooperation among the agents, (ii) some of the small centers grow at the expense of others, which finally leads to the concentration of the labor force in different extended economic regions. This crossover to large-scale production is accompanied by an increase in the unemployment rate. We observe a stable coexistence between these regions, although they exist in an internal quasistationary non-equilibrium state and still follow a stochastic eigendynamics.