Investment in the Common Good: Free Rider Effect and the Stability of Mixed Strategy Equilibria

Youngsoo Kim () and H. Dharma Kwon ()
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Youngsoo Kim: Culverhouse College of Business, University of Alabama, Tuscaloosa, Alabama 35487
H. Dharma Kwon: Gies College of Business, Department of Business Administration, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820

Operations Research, 2024, vol. 72, issue 2, 684-698

Abstract: In the game of investment in the common good, the free rider problem can delay the stakeholders’ actions in the form of a mixed strategy equilibrium. However, it has been recently shown that the commonly known form of mixed strategy equilibria of the stochastic war of attrition is destabilized by even the slightest degree of asymmetry between the players. Such extreme instability is contrary to the widely accepted notion that a mixed strategy equilibrium is the hallmark of the war of attrition. Motivated by this quandary, we search for a mixed strategy equilibrium in a stochastic game of investment in the common good. Our results show that, despite asymmetry, a mixed strategy equilibrium exists if the model takes into account the repeated investment opportunities. This class of mixed strategy equilibria disappear only if the asymmetry is sufficiently high. Because the mixed strategy equilibrium is less efficient than pure strategy equilibria, it behooves policy makers to prevent it by promoting a sufficiently high degree of asymmetry between the stakeholders through, for example, asymmetric subsidy.

Keywords: Decision Analysis; investment in the common good; impulse control game; the war of attrition; free rider problem; mixed strategy equilibrium (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:2:p:684-698

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