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

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.     

Parental Involvement in Primary School Education: its Relationship with Children’s Academic Performance and Psychosocial Competence through Engaging Children with School

The benefits of parental involvement in children’s education have been well established but increasing evidence suggests that overparenting may have adverse effects on children. The question of whether excessive parental involvement hinders children’s academic and psychosocial development warrants further investigations. This study examined the associations of parental educational involvement at home and in school with academic performance and psychological health of 507 Chinese Grade 3 schoolchildren in Hong Kong. Parents reported on their level of involvement in children’s schooling and their children’s psychosocial issues. Children were surveyed to determine their school engagement, and their Chinese language and mathematics attainment was assessed. We also explored the underlying mechanism by testing children’s engagement with school as a mediator of the relationships. Our results showed that home-based parental educational involvement was positively associated with children’s language competence and psychosocial wellbeing, and the associations were linked through engaging children with school. However, the benefits reached a plateau at higher level of parental involvement in children’s learning at home. School-based parental involvement had an indirect effect on children’s prosocial behavior through school engagement. These findings highlight the significance of optimal level of parental involvement in children’s education at home for children’s development.     

A Probabilistic Model of Criticality in a Sequential Public Good Dilemma

A public good (PG) is a commodity or service made available to all members of a group: its provision depends on the voluntary contribution of its members. Once provided, all members can enjoy the benefits of the PG, regardless of whether they contributed or not; hence, there is a temptation to “free-ride” in the hope that others will contribute. Rapoport (1987) showed that an important factor that affects cooperation (contribution) in a PG dilemma is the extent to which a group member is critical in providing it. Erev and Rapoport (1990) tested a game-theoretic model that yields deterministic predictions about the effects of criticality on cooperation in public good dilemmas. Based on research by Chen, Au, and Komorita (1996), we propose a probabilistic model of criticality. The model is tested and found to fit empirical data. Extensions of the model to situations with uncertain group size or provision point are discussed.     

Time complexity and consistency issues in using the AHP for making group decisions

Two different ways of using the AHP in making group decisions are compared and evaluated. The first method combines different experts’ opinions before applying an eigenvalue method to obtain final weights for decision alternatives. The second, in contrast, derives each expert's rating for the decision alternatives before combining them. Both methods take into account the relative importance of different experts in making decisions. Comparison and evaluation of these two methods are made by using two criteria: time complexity and consistency indices. A numerical example is provided to illustrate the use of these two methods, and results of a mathematical simulation are presented for comparing the time complexity in different-sized problems. © 1998 John Wiley & Sons, Ltd.     

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

This paper investigated the effect of risk orientation, game riskiness, and expectation of cooperation on cooperation in one-shot prisoner’s dilemmas (PD). Participants in pairs played PD games that varied on game riskiness such that for half of the games cooperation was more risky than defection (more risky games) while for another half cooperation was less risky (less risky games). They estimated how likely it was that the other player was going to cooperate (expectation of cooperation) before they made their cooperation/defection decision on each game. Supporting the Goal/Expectation Hypothesis, we replicated the effect that expectation of cooperation enhanced cooperation. We also found that risk-seeking individuals cooperated more in more risky games whereas risk-averse individuals cooperated more in less risky games. More importantly, we found that game riskiness moderated the effect of expectation of cooperation on cooperation. The positive effect of expectation of cooperation on cooperation was stronger for more risky games than for less risky games. Our results illustrated how the relation between expectation and cooperation as stipulated by the Goal/Expectation Hypothesis was moderated by riskiness of the situations.     

Developmental patterns of emotion regulation in toddlerhood: Examining predictors of change and long‐term resilience

Emotion regulation is critical for optimal functioning across a wide range of domains and may be even more important for individuals in high‐risk environments. While evidence suggests that childhood is generally a period of emotion regulation growth and development, research is needed to examine factors that may contribute to deviations from a typical trajectory. In a prospective study of 1,905 children, latent class growth analysis (LCGA) was used to identify trajectory groups of emotion regulation across toddlerhood (age 14–36 months), examine predictors of those trajectory groups from child temperament, parenting behaviors, and environmental risk, and explore predictions of resilience in 5th grade from the identified groups. LGCA supported a three‐class model, with a Stable Incline group, a Decline group, and a Catch‐Up group. Child negative emotionality, positive and negative parenting, and environmental risk predicted group membership. These trajectory groups in toddlerhood were predictive of child resilient functioning in the 5th grade. Our findings highlight the importance of utilizing developmental models of emotion regulation and provide implications for prevention and early intervention services to enhance emotion regulation development in early childhood.     

Bonus and Penalty in Common Pool Resource Dilemmas under Uncertainty

Common pool resource (CPR) dilemmas constitute a class of social dilemmas in which equilibrium behavior results in Pareto deficient outcomes that are not at all desirable by the group. We focus on a class of CPR dilemmas that, in addition to strategic uncertainty about the harvesting behavior of the other group members, include environmental uncertainty about the size of the CPR. In an attempt to decrease the rate of requests from the common pool, and thereby increase individual payoffs, we extend previous research-both theoretically and experimentally-in two different directions. In the bonus treatment, a reward is given to the agent(s) who requests the least, and in the penalty treatment, a charge is imposed on the agent(s) who requests the most. We show that under equilibrium play the bonus treatment decreases total group request, whereas the penalty treatment increases it. Our experimental results do not support this prediction. Rather, both treatments considerably decrease the rate of request and, therefore, increase the rate of provision. The penalty treatment is shown to be more effective in reducing individual requests and enhancing provision rates than the bonus treatment. Copyright 2001 Academic Press.     

Child sex moderates the association between negative parenting and childhood conduct problems

Although multiple dimensions of negative parenting behavior are associated with childhood conduct problems (CP), there is relatively little research on whether the association is equally robust in boys and girls. To improve the specificity of current models of negative parenting and offspring CP, we explored the potential moderating role of child sex in a sample of 179 5- to 10-year-old ethnically diverse boys and girls with and without attention-deficit/hyperactivity disorder (ADHD) who were assessed using multiple methods (i.e., rating scales, semistructured interviews) and informants (i.e., parents, teachers). Controlling for children's age, race-ethnicity, and ADHD diagnostic status (i.e., ADHD vs. non-ADHD), inconsistent discipline was positively associated with offspring aggression and rule-breaking behavior, whereas harsh punishment was positively associated with aggression, rule-breaking behavior, and oppositional defiant disorder symptoms. Furthermore, child sex significantly moderated the association of inconsistent discipline and aggression and rule-breaking behavior, such that inconsistent discipline was positively associated with CP for boys, but not for girls. Given the centrality of negative parenting to theories of and efficacious interventions for aggression and CP, we discuss these findings within a developmental psychopathology framework and consider their implications for intervention.