Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

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.

Peer coordination and communication following disaster warnings: An experimental framework

“…There are various conceptualizations of the role of risk in social dilemmas (Au et al, 2012); perhaps the most relevant to our setting is Van Assen and Snijders 2004, where risk is defined as a person's preference between a sure thing and a gamble with the same expected value. Combining prospect theory and game theory, the authors formally showed that when cooperation is in the loss domain (as in settings where one is asked not to evacuate) the likelihood of cooperation decreases with risk aversion.…”

Behavioural Consistency within the Prisoner'S Dilemma Game: The Role of Personality and Situation

“…Especially interesting, however, is that some prior studies even specifically focused on the PDG. In this regard, Au, Lu, Leung, Yam, and Fung () found that situational variations in the risk associated with cooperation (relative to non‐cooperation) interact with individual differences in risk aversion in shaping cooperative behaviour in the PDG. More specifically, their results showed that risk‐seeking participants cooperated more in risky games, whereas risk‐averse participants cooperated more in less risky games.…”

Expectation and cooperation in prisoner’s dilemmas: The moderating role of game riskiness

“…Glöckner and Hilbig (2012) found that the effect of risk orientation on cooperation depended on environments, such that risk aversion enhanced cooperation in cooperation-friendly environments only, but not in cooperation-unfriendly environments. Au et al (2012) suggested that the inconsistency is due to the ambiguity in defining risk of cooperation and defection in PD. They developed an index of game riskiness (r) such that a PD can be constructed to be more risky or less risky to cooperate.…”

“…Whether cooperation is more or less risky could also depend on whether the outcomes are framed as gains or losses (Raub & Snijders, 1997). Au et al (2012) proposed that in a PD the relative risk of the cooperation choice to that of the defection choice can be calculated as r = (R-S) / [(R−S) + (T−P)], such that the index of game riskiness (r) ranges from 0 to 1. In essence, r is an index of the variance of the cooperation choice outcomes, R and S, relative to the variance of the defection choice outcomes, T and P. A game in which the variance of cooperation outcomes is greater than the variance of defection outcomes will have an r value greater than 0.5 that the cooperation choice is said to be more risky than the defection choice.…”