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The aim of this paper is to build a computational model that presents the effects of social dynamics such as evolution on populations applying the theory of Hobbesian Social Contract, social learning and norm diffusion. The phenomenon we are studying is the so-called tragedy of the commons, in which individual agents, having open access to a resource unconstrained by common social structures, act according to their own self-interest, seeking to maximise their own profits. Developing the theoretical framework and agent-based model, we applied to our artificial environment the norm associated with altruism, which modifies agents' behaviour during the simulation, which in turn affects the distribution of wealth. Through the behavioural space, we show that under certain circumstances specified in the parameter, it is possible to obtain a social contract and, as a result, a state of equilibrium. We show that individuals who have obtained the norm are able to enter into a contract, resulting in a rising wealth of the population and a more equilibrium distribution, while if they do not, more inequalities emerge. However, our model is a simplification of Hobbes' theory, admittedly, our agents can spontaneously establish cooperation but there are no complex structures, such as psychological ones, or moral cognition. We believe that this is a skeletal description of the Hobbesian social contract, in which self-interested individuals without obligation to cooperate agree to abide by a norm and its benefits. Depending on how profitable cooperation is (due to the redistribution) and the number of altruistic agents, the community members work for the common good.