Modelling of collective actions: The significance of cooperative agreements

Abstract

Using mathematical modelling methods, we investigate the collective’s ability to achieve results which are Pareto-dominant over Nash equilibrium. Egoistic urges of the members of the collective, under the law of diminishing returns, give rise to the free-rider problem. Cooperation among agents in an environment where some individuals are characterised by opportunistic tendencies is impaired within a large group due to deficit of trust, yet it is possible within a small group (a coalition) based on interpersonal trust. By deploying a coalitional strategy aimed at maximizing coalitional gains, each individual member of the large group increases their gain. To attain a stable coalition, an agreement must be formed among agents implying adherence to conditions of individual rationality by all members of the collective and compatibility stimuli for all members of the coalition. We further set down the content of such an agreement and calculate side payments that guarantee adherence to conditions necessary for sustainable cooperation, as well as the investment of requisite effort by coalition members.