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Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization
Author(s) -
Au Wing Tung,
Lu Su,
Leung Hildie,
Yam Paton,
Fung Jane M. Y.
Publication year - 2012
Publication title -
journal of behavioral decision making
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.136
H-Index - 76
eISSN - 1099-0771
pISSN - 0894-3257
DOI - 10.1002/bdm.743
Subject(s) - cooperativeness , dilemma , risk seeking , economics , prisoner's dilemma , microeconomics , index (typography) , function (biology) , expected utility hypothesis , mathematical economics , social psychology , psychology , game theory , computer science , mathematics , geometry , personality , evolutionary biology , world wide web , temperament , biology
Abstract We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r , to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation ( K ), our formulation of risk allows us to construct games that vary in risk (as indexed by r ) while controlling for cooperativeness (as indexed by K ). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.