On the influence of the method of income distribution on the efficiency of collective actions

The paper examines the impact of income sharing methods among collective members on Stackelberg strategy outcomes and the dynamic stability of cooperation within the framework of mathematical modeling of collective actions. It is assumed that the income function and the relative share of each participant in the income are known to everyone before the start of collective actions. Each agent seeks to maximize his own gain, which is represented by the difference between the part of the total income they receive and the monetary equivalent of the amount of effort they exert. When agents independently choose the size of their efforts, the collective falls into the «bad Nash equilibrium». Coordination of efforts based on interpersonal trust, which can develop in a small group of agents (coalition), allows its members to exert the effort required to maximize not individual, but coalition gains. The coalition effect resulting from the complementarity of efforts leads to a Pareto-­preferred outcome relative to the «bad equilibrium». In a sequential game with the coalition of the Stackelberg leader, the coalition effect is enhanced by the Stackelberg strategy. It is shown that if all participants have an equal ability to influence income through their individual efforts and if income is distributed in equal shares, the amount of effort exerted by coalition members is higher, while their gains are lower than those of non-cooperating agents. Accordingly, for the dynamic stability of cooperation, it is necessary to conclude an agreement that provides both conditions of individual rationality for all members of the collective and conditions compatible with incentives for coalition members. Such conditions suppose rejection of equality in income distribution in favor of coalition members. For a sequential Stackelberg game with the coalition as the leader, the interval of coalition share values that meet the necessary conditions was determined.