On the possibility of successive approximation towards an equilibrium in a coalition game with reiterating collective action

The study investigates the possibility for the participants of collective action of avoiding a Nash equilibrium trap resulting from a non-coalition game, and of achieving a Pareto-preferable outcome. It is assumed that individual efforts invested by all members of a collective create revenue of which each member is entitled to a certain share. Each agent’s efforts have a positive effect on the value of marginal revenue per effort of any other agent. Each agent aims to maximize their own individual gain. It is further assumed that the lack of trust prevents members of the collective to coordinate their efforts in such a way that allows them to break out of the initial Nash-ineffective equilibrium which occurs in a non-coalition game setting. A small group (coalition) in which agents are united by mutual trust deploys a coalition strategy aimed at maximizing coalitional gains. As a result, not only do gains increase for each member of the larger collective, but also their marginal revenue per effort. The corresponding shift of the individual gain maximum point per each non-cooperated agent towards increasing the volume of effort invested thereby creates the prerequisites for the successive increase of effort invested in a reiterating game not only by coalition members, but also by non-cooperated agents. It is shown that the outcome in each consecutive game dominates over Pareto in the preceding game. Limit of an infinite sequence of outcomes corresponds with a Nash-balanced outcome of a coalition game, where non-cooperated agents assume that all coalition members will necessarily adhere to the coalition strategy.