Emergence of Cooperation in Competitive Environments

We study the Prisoner's Dilemma in competitive environments with the aim to investigate if, and under which conditions, a cooperative behavior emerges in an agent population. In particular, agents are embedded in two different regions of space, i.e., A continuous space and a discrete space. The former is represented by a simple square, whereas the latter by a directed network. In both spaces, agents face by playing the Prisoner's Dilemma with their neighbors. In the continuous space, neighbors are identified by a rule based on the Euclidean distance among agents. Instead, in the network, agents have as neighbors those connected with them. In the proposed model, the competitiveness corresponds to the number of opponents each agent decides to face, i.e., Competitive agents faces many agents at each time step. Therefore, in the continuous space, the competitiveness is represented by the radius of each agent within it finds its opponents. Instead, in the discrete space, the competitiveness corresponds to the agent's out-degree, i.e., The number of neighbors connected with an arrow starting from the considered agent an directed to its neighbors. We study the evolution of the system over time in both spaces, analyzing also the degree distribution (both the in-degree and the out-degree) of the resulting directed network. It is worth to highlight that, as main result, we found the competitiveness strongly improves cooperation among agents in both domains. Furthermore, as cooperation emerges when the Prisoner's Dilemma is played over a network, several agents become hubs (i.e., Agents with a high out-degree).