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

Youngsoo Kim, H. Dharma Kwon

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)684-698
Number of pages15
JournalOperations Research
Issue number2
StatePublished - Mar 2024


  • free rider problem
  • impulse control game
  • investment in the common good
  • mixed strategy equilibrium
  • the war of attrition

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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