Comparing the Nash and Stackelberg Equilibria in a Collective Action Model

Vladimir Tsurikov; Elena M. Skarzhinskaya

COMPARING THE NASH AND STACKELBERG EQUILIBRIA IN A COLLECTIVE ACTION MODEL Comparing the Nash and Stackelberg Equilibria in a Collective Action Model

АА Аа

Published in Theoretical economics · Issue 1 · Pages 75–86 · Rubric: NEW INDUSTRIALIZATION: THEORETICAL AND ECONOMIC ASPECT

Received: 09.12.2023 Accepted: 22.12.2023 Published: 30.03.2024

Authors

Vladimir Tsurikov

ORCID

Elena M. Skarzhinskaya

ORCID

Vladimir Tsurikov

Academic degree: doctor of economic sciences

Science rang: professor

Kostroma State Agricultural Academy Russian Federation · Kostroma

ORCID

Elena M. Skarzhinskaya

Kostroma State University Russian Federation · Kostroma

ORCID

ABSTRACT

This study compares collective action outcomes under varying coordination conditions using mathematical modeling. The assumption is that the collective’s members receive a cumulative income, which increases with the escalation of their efforts and adheres to the law of diminishing returns. The impact of coordination on the effectiveness of their actions is attributed to the complementarity of efforts, which implies that an increase in the effort made y each agent results in an increase in the marginal income from the efforts of any other agent. The formation of a coalition (small group), whose members strive to maximize coalition gains, allows the collective to avoid the Nash bad equilibrium trap, into which it falls when each member chooses the scope of their effort autonomously. We analyze and compare the outcomes of two games involving a coalition: a simultaneous game where Nash equilibrium is achieved, and a sequential game where Stackelberg equilibrium is achieved. In the sequential game, coalition members assume the leader’s role and are therefore the first to implement their efforts. All non-cooperative agents act as followers and decide on their effort scope depending on the efforts already made by coalition members. Consequently, considering each non-cooperative agent’s aim to maximize their individual gain given their knowledge about the relative size of coalition efforts, coalition members determine the optimal scope of their efforts using backward induction. As a result of the coalition’s Stackelberg strategy, the aggregate revenue and each team member’s payoff in the sequential game is greater than in the simultaneous coalition game.

KEYWORDS

Collective action, coalition, Nash equilibrium, Stackelberg strategy, Pareto efficiency

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