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.

1. Garfinkel H. (2009). A conception of and experiments with, «trust» as a condition of stable concerted actions. Russian Sociological Review, vol. 8, no. 1, pp. 10–51. (In Russ.)

2. Zak F.L. (2021). On some models of altruistic behavior. Journal of the New Economic Association, no. 1(49), pp. 12–52. (In Russ.)

3. Kapelyushnikov R.I. (2010). The Multiplicity of Institutional Worlds: The Nobel Prize in Economic Sciences 2009. (Part 1). Working paper, WP3/2010/02. Moscow: SU–HSE. (In Russ.)

4. Ostrom E. (2011). Governing the Commons. The Evolution of Institutions for Collective Action. Moscow: IRISEN. (In Russ.)

5. Petrosyan L.A., Zenkevich N.А. (2009). Principles of dynamic stability. Matematicheskaya Teoriya Igr i Еe Prilozheniya, no. 1, pp. 106–123. (In Russ.)

6. Prokhorov A. (2004). Wage-­Levelling as an element of the Russian model of management. Voprosy Ekonomiki, no. 10, pp. 99–113. (In Russ.)

7. Skarzhinskaya E.M., Tsurikov V.I. (2017). The Collective Action Model. Part 1: Equilibrium, Fairness, and Efficiency. Economics and Mathematical Methods, vol. 53, no. 2, pp. 118–133. (In Russ.)

8. Skarzhinskaya E.M., Tsurikov V.I. (2019). On the Significance of Cooperative Agreements for the Efficiency of Collective Action. Russian Management Journal, no. 3, pp. 337–366. (In Russ.)

9. Skarzhinskaya E.M., Tsurikov V.I. (2020). On the Possibility of Successive Approximation towards an Equilibrium in a Coalition Game with Reiterating Collective Action. Economics and Mathematical Methods, vol. 56, no. 4, pp. 103–115. (In Russ.)

10. Skarzhinskaya E.M., Tsurikov V.I. (2021a). Endogenous Stackelberg leadership within a team. The coalition effects. Journal of the New Economic Association, no. 1 (49), pp. 53–79. (In Russ.)

11. Skarzhinskaya E.M., Tsurikov V.I. (2021b). Stackelberg leader in the collective action model. Economics and Mathematical Methods, vol. 57, no. 4, pp. 117–128. (In Russ.)

12. Skarzhinskaya E.M., Tsurikov V.I. (2023). On the issue of stability of a small coalition in a large collective. Part 2. Theoretical Economics, no 5, pp. 43–52. (In Russ.)

13. Skorobogatov А. (2007). Organizational economics and models of incomplete contracts. Voprosy Ekonomiki, no. 12, pp. 71–95. (In Russ.)

14. Tirole J. (2000). The Theory of Industrial Organization. St. Petersburg: Schools of Economics. (In Russ.)

15. Williamson O.E. (1996). The Economic Institutions of Capitalism. Firms, Markets, Relational Contracting. St. Petersburg: Lenizdat. (In Russ.)

16. Furubotn E.G., Richter R. (2005). Institutions and Economic Theory: The Contribution of the New Institutional Economics. St. Petersburg: SPSU Publishing House. (In Russ.)

17. Hart О.D. (2001). Incomplete contracts and the theory of the firm. O.E. Williamson, S.G. Winter (eds). The Nature of the Firm. Origins, Evolution, and Development. Мoscow: Delo, pp. 206–236. (In Russ.)

18. Tsurikov V.I., Skarzhinskaya E.M. (2024). Comparing the Nash and Stackelberg Equilibria in a Collective Action Model. Theoretical Economics, no 1, pp. 75–86. (In Russ.)

19. Shastitko А. (2001). Incomplete Contracts: Problems of Definition and Modeling. Voprosy Ekonomiki, no. 6, pp. 80–99. (In Russ.)

20. Abramitsky R. (2011). Lessons from the kibbutz on the Equality-­Incentives Trade off. Journal of Economics Perspectives, vol. 25, no. 1, pp. 185–208.

21. Grossman S., Hart O. (1986). The cost and benefits of ownership: A theory of vertical and lateral integration. Journal of Political Economy, vol. 94, no. 4, pp. 691–719.

22. Hart O., Moore J. (1988). Incomplete contracts and renegotiation. Econometrics, vol. 56, no. 4, pp. 755–785.

23. Hermalin B. (1998). Toward an Economic Theory of Leadership: Leading by Example. The American Economic Review, vol. 88, no. 5, pp. 1188–1206.

24. Holmstrom B. (1982). Moral Hazard in Teams. The Journal of Economics, vo. 13, no. 2, pp. 324–340.

25. Huck S., Rey-­Biel P. (2006). Endogenous leadership in teams. Journal of Institutional and Theoretical Economics, vol. 162, no. 2, pp. 253–261.

26. Gächter S, Renner E. (2018). Leaders as role models and ‘belief managers’ in social dilemmas. Journal of Economic Behavior and Organization, vol. 154, no. 12, pp. 321–334.

27. Kim J. (2012). Endogenous Leadership in incentive Contracts. Journal of Economic Behavior and Organization, vol. 82, no. 1, pp. 256–266.

28. Sefton, M., Shupp, R., Walker J.M. (2007). The effects of rewards and sanctions in provision of public goods. Economic Inquiry, vol. 45, no. 4, pp. 671–690.

29. Olson M. (1965). The Logic of Collective Action. Public Goods and the Theory of Groups. Cambridge (MA): Harvard University Press.

30. Potters J., Sefton M., Vesterlund L. (2007). Leading-by-example and signaling in voluntary contribution games: an experimental study. Economic Theory, vol. 33, no. 1, pp. 169–182.