Stackelberg leader in a collective action model

Within a mathematical modelling framework, we analyze the conditions allowing a self-governedcollective to achieve Stackelberg equilibrium. It is assumed that members of the collective generate common income through individual effort, which income is then distributed among all members of the collective according to their predetermined share. Effort invested by each agent wields (imposes) a positive influence on the marginal income resulting from the effort invested by any other agent. Each member of the collective aims to maximize their individual gain. Within a model built on the most general principles, it is shown that a Stackelberg equilibrium outcome is preferable over Nash equilibrium. The model, utilizing the special case of income function and private costs functions; helps identify the correlation between the agents’ efforts and their individual characteristics such as the agent’s share in the income, income elasticity by effort, and subjective valuation of private costs. It is shown that additional income generatedby the move (transition) from Nash to Stackelberg equilibrium depends only on the elasticity of income vs. the leader’s effort, and the sum of elasticity indexes for all members of the collective. We introduce the definition and the conditions for the existence of a distinctive agent, who acts as a Stackelberg leader and ensures maximum individual gain for each member of the collective (including their own). The absence of a distinctive agent in a collective gives rise to the Stackelberg leadership problem, as each member of the collective is only able to obtain maximum gains when acting as a follower.

Keywords

collective action, leader, followers, Nash equilibrium, Stackelberg equilibrium, Pareto efficiency

Received

18.11.2021

Publication date

13.12.2021

Number of characters

35845

Cite

GOST	Skarzhinsky Y., Tsurikov V. Stackelberg leader in a collective action model // Ekonomika i matematicheskie metody – 2021. – V. 57. – Issue 4 C. 117-128 [Electronic resource]. URL: https://emm.jes.su/S042473880017519-9-1 (circulation date: 02.05.2024). DOI: 10.31857/S042473880017519-9
MLA	Skarzhinsky, Yelena, Tsurikov, Vladimir I "Stackelberg leader in a collective action model." Ekonomika i matematicheskie metody 57.4 (2021):117-128. DOI: 10.31857/S042473880017519-9
APA	Skarzhinsky Y., Tsurikov V. (2021). Stackelberg leader in a collective action model. Ekonomika i matematicheskie metody 57(4), pp.117-128 DOI: 10.31857/S042473880017519-9

100 rub.

When subscribing to an article or issue, the user can download PDF, evaluate the publication or contact the author. Need to register.

Number of purchasers: 0, views: 451

Readers community rating: votes 0

1. Anderson S., Engers M. (1992). Stacelberg versus Cournot oligopoly equilibrium. International Journal of Industrial Organization, 1, 127–135.

2. Arbak E., Villeval V. (2013). Voluntary leadership: Motivation and influence. Social Choice and Welfare, 3, 635–662.

3. Furubotn E.G., Richter R. (2005). Institutions and economic theory: The contribution of the new institutional economics. St. Petersburg: Publishing house of St. Petersburg State University (in Russian).

4. Gächter S, Renner E. (2018). Leaders as role models and ‘belief managers’ in social dilemmas. Journal of Economic Behavior & Organization, 154 (C), 321–334.

5. Gervais S., Goldstein I. (2007). The positive effects of biased self-perceptions in firms. Review of Finance, 3, 453–496.

6. Grossman S., Hart O. (1986). The cost and benefits of ownership: A theory of vertical and lateral integration. Journal of Political Economy, 4, 691–719.

7. Hamilton J., Slutsky S. (1990). Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior, 2, 29–46.

8. Hart O.D. (2001). Incomplete contracts and the theory of the firm. In: Nature of the firm. Moscow, Delo, 206–236 (in Russian).

9. Hart O.D., Moore J. (1988). Incomplete contracts and renegotiation. Econometrics, 4, 755–785.

10. Hermalin B. (1998). Toward an economic theory of leadership: Leading by example. The American Economic Review, 88, 1188–1206.

11. Holmstrom B. (1982). Moral hazard in teams. The Bell Journal of Economics, 2, 324–340.

12. Huck S., Rey-Biel P. (2006). Endogenous leadership in teams. Journal of Institutional and Theo-retical Economics, 2, 253–261.

13. Ino H., Matsumura T. (2012). How many firms should be leaders? Beneficial concentrations revisited. International Economic Review, 4, 1323–1340.

14. Julien L. (2018). Stackelberg games. In: Handbook of Game Theory and Industrial Organization, 1, 10, 261–311.

15. Kapeyushnikov R. (2010). The multiplicity of institutional worlds: The Nobel Prize in economic sciences 2009. Working paper WP3/2010/02. Part 1. Moscow: National Research University “Higher School of Economics” (in Russian).

16. Kim J. (2012). Endogenous leadership in incentive contracts. Journal of Economic Behavior & Organization, 1, 256–266.

17. Linster B. (1993). Stackelberg rent-seeking. Public Choice, 2, 307–321.

18. Olson M. (1965). The logic of collective action. Public goods and the theory of groups. Cambridge: Harvard University Press.

19. Ostrom E. (2011). Governing the commons. The evolution of collective institutions for collective action. Moscow: IRISEN, Mysl’ (in Russian).

20. Potters J., Sefton M., Vesterlund L. (2007). Leading-by-example and signaling in voluntary con-tribution games: an experimental study. Economic Theory, 33, 169–182.

21. Préget R., Nguyen-Van P., Willinger M. (2016). Who are the Voluntary leaders? Experimental evidence from a sequential contribution game. Theory and Decision, 4, 581–599.

22. Shastitko A. (2001). Incomplete contracts: Problems of definition and modeling. Voprosy Ekono-miki, 6, 80–99 (in Russian).

23. Skarzhinskaya E.M., Tsurikov V.I. (2014). On the issue of the effectiveness of collective action. Russian Management Journal, 12, 3, 87–106 (in Russian).

24. Skarzhinskaya E.M., Tsurikov V.I. (2017b). Model of collective action. Part 2: The leading coali-tion. Economics and Mathematical Methods, 53, 4, 89–104 (in Russian).

25. Skarzhinskaya E.M., Tsurikov V.I. (2017c). Economic-mathematical analysis of the efficiency conditions of the principle “from each according to his ability, to each according to his work”. Russian Journal of Economic Theory, 2, 110–122 (in Russian).

26. Skarzhinskaya E.M., Tsurikov V.I. (2020). On the possibility of successive approximation to-wards an equilibrium in a coalition game with reiterating collective action. Economics and Mathematical Methods, 56, 4, 103–115 (in Russian).

27. Skorobogatov A. (2007). Organization theory and models of incomplete contracts. Voprosy Ekonomiki, 12, 71–95 (in Russian).

28. Stackelberg H. (1934). Marktform und Gleichgewicht. Wien; Berlin: J. Springer.

29. Tirole J. (2000). Markets and market power of the theory of industrial organization. Vol. 1. St. Petersburg: The School of Economics (in Russian).