Game of Variable Contributions to the Common Good Under Uncertainty

H. Dharma Kwon ()
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H. Dharma Kwon: Department of Business Administration, Gies College of Business, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820; Operations Department, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208

Operations Research, 2022, vol. 70, issue 3, 1359-1370

Abstract: We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games that generalize wars of attrition. Previously known examples of variable concession games in the literature yield equilibria characterized by singular control strategies without any delay of concession. However, these no-delay equilibria are in contrast to mixed-strategy equilibria of canonical wars of attrition in which each player delays concession by a randomized time. We find that a variable contribution game with a single state variable, which extends the Nerlove–Arrow model, possesses an equilibrium characterized by regular control strategies that result in a gradual concession. This equilibrium naturally generalizes the mixed-strategy equilibria from the canonical wars of attrition. Stochasticity of the problem accentuates the qualitative difference between a singular control solution and a regular control equilibrium solution. We also find that asymmetry between the players can mitigate the inefficiency caused by the gradualism.

Keywords: Special Issue: Mathematical Models of Individual and Group Decision Making in Operations Research (in honor of Kenneth Arrow); Nerlove–Arrow model; war of attrition; stochastic control game; free rider problem; gradualism (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:3:p:1359-1370

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