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Coordination of Collective Actions by Using the Stackelberg Strategy

  • CONTROL IN SOCIAL ECONOMIC SYSTEMS
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Abstract

The paper deals with a theoretical study of the coordination of actions of members of a self-managed team using the Stackelberg strategy aimed at increasing their individual gains. It is assumed that the team creates a total income that increases with the growth of efforts made by each agent and obeys the diminishing return law. The unique Nash equilibrium that exists under the conditions of complete autonomy of all agents is Pareto inefficient. It is shown that for the transition to a Pareto-preferential outcome it suffices to form a small group (coalition) in the team whose members trust each other and are not prone to opportunistic behavior. Following a coalition strategy aimed at achieving the maximum coalition gain, the coalition members increase their efforts; this leads to an increase in the total income. Conditions are found under which the coalition can use the Stackelberg leadership strategy. It is shown that the Stackelberg equilibrium outcome dominates in the sense of Pareto over Nash equilibrium outcomes both in noncooperative and coalitional games.

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Notes

  1. This conclusion is completely consistent with the conclusion obtained in Holmström paper [3], in the “prisoners’ dilemma” model, and in incomplete contract models [4,5,6,7].

  2. To make sure that the total payoff \( U \) is higher in the outcome \( P \) than in the outcome \( N \), it suffices to refer to the gradient of the function \( U \). At the Nash equilibrium point \( N \), each coordinate of \( \mathrm {grad}\thinspace U \) is greater than zero; it follows that the function \( U \) reaches higher values at effort levels that exceed the equilibrium.

  3. A rigorous proof of the theorem on the increase of all variables that form the solution of system (6) with a decrease in the value of at least one of the parameters that represent its right-hand sides is given in [25].

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Authors and Affiliations

  1. Kostroma State University, Kostroma, 156005, Russia

    E. M. Skarzhinskaya

  2. Kostroma State Agricultural Academy, Karavaevo, Kostroma oblast, 156530, Russia

    V. I. Tsurikov

Authors
  1. E. M. Skarzhinskaya
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  2. V. I. Tsurikov
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Correspondence to E. M. Skarzhinskaya or V. I. Tsurikov.

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Translated by V. Potapchouck

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Skarzhinskaya, E.M., Tsurikov, V.I. Coordination of Collective Actions by Using the Stackelberg Strategy. Autom Remote Control 83, 1093–1107 (2022). https://doi.org/10.1134/S0005117922070062

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