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We study the relations between strategies in game theory and the conformity. The latter is a behavior deemed relevant in social psychology and, as shown in several works, it strongly influences many social dynamics. We consider a population of agents that evolves in accordance with a payoff matrix which embodies two main strategies: cooperation and defection. In particular, agents play a game (e.g., the Prisoner’s Dilemma) by choosing between these two strategies, in order to increase their payoff, i.e., their gain. During the evolution of the system, agents can change strategy according to an update rule, i.e., they can play sometimes as cooperators and sometimes as defectors. Usually, rules to update the strategy are driven by the payoffs of the neighbors of each agent. For instance, an agent imitates its best neighbor, i.e., the one having the highest payoff among the other neighbors. In this context, ‘imitation’ means to adopt the strategy of another agent. In order to study if and how the emergence of cooperation can be affected by a social influence, we provide agents with two different behaviors, i.e., conformity and nonconformity, they use to select their strategy. Numerical simulations show that conformity strongly affects these dynamics, as cooperation emerges in the population, even under conditions of the games that usually lead, almost all agents, to play as defectors.

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).

Competitiveness is a relevant social behavior and in several contexts, from economy to sport activities, has a fundamental role. We analyze this social behavior in the domain of evolutionary game theory, using as reference the Prisoner’s Dilemma. In particular, we investigate whether, in an agent population, it is possible to identify a relation between competitiveness and cooperation. The agent population is embedded both in continuous and in discrete spaces, hence agents play the Prisoner’s Dilemma with their neighbors. In continuous spaces, each agent computes its neighbors by an Euclidean distance-based rule, whereas in discrete spaces agents have as neighbors those directly connected with them. We map competitiveness to the amount of opponents each agent wants to face; therefore, this value is used to define the set of neighbors. Notably, in continuous spaces, competitive agents have a high interaction radius used to compute their neighbors. Instead, since discrete spaces are implemented as directed networks, competitiveness corresponds to the out-degree of each agent, i.e., to the number of arrows starting from the considered agent and directed to those agents it wants to face. Then, we study the evolution of the system with the aim to investigate if, and under which conditions, cooperation among agents emerges. As result, numerical simulations of the proposed model show that competitiveness strongly increases cooperation. Furthermore, we found other relevant phenomena as the emergence of hubs in directed networks.