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Joint effects of asymmetric payoff and reciprocity mechanisms on collective cooperation in water sharing interactions: a game theoretic perspective.

Ng CN, Wang RY, Zhao T - PLoS ONE (2013)

Bottom Line: We present an iterative N-person game theoretic model to investigate the joint effects of these two mechanisms in a linear fully connected river system under three information assumptions.Meanwhile, various upstream and downstream actors manifest individual disparities as a result of the direct reciprocity and asymmetric payoff mechanisms.The upstream actors also display weak sensitivity to an increase in the total number of actors, which generally results in a reduction in the other actors' motivation for cooperation.

View Article: PubMed Central - PubMed

Affiliation: Department of Geography, The University of Hong Kong, Pokfulam, Hong Kong.

ABSTRACT
Common-pool resource (CPR) dilemmas distinguish themselves from general public good problems by encompassing both social and physical features. This paper examines how a physical mechanism, namely asymmetric payoff; and a social mechanism, reciprocity; simultaneously affect collective cooperation in theoretical water sharing interactions. We present an iterative N-person game theoretic model to investigate the joint effects of these two mechanisms in a linear fully connected river system under three information assumptions. From a simple evolutionary perspective, this paper quantitatively addresses the conditions for Nash Equilibrium in which collective cooperation might be established. The results suggest that direct reciprocity increases every actor's motivation to contribute to the collective good of the river system. Meanwhile, various upstream and downstream actors manifest individual disparities as a result of the direct reciprocity and asymmetric payoff mechanisms. More specifically, the downstream actors are less willing to cooperate unless there is a high probability that long-term interactions are ensured; however, a greater level of asymmetries is likely to increase upstream actors' incentives to cooperate even though the interactions could quickly end. The upstream actors also display weak sensitivity to an increase in the total number of actors, which generally results in a reduction in the other actors' motivation for cooperation. It is also shown that the indirect reciprocity mechanism relaxes the overall conditions for cooperative Nash Equilibrium.

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Related in: MedlinePlus

The effect of total number of actors n on the conditions for cooperative NE.(a, b, c) Va for the head-end, mid-stream and tail-end actors in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for the head-end, mid-stream and tail-end actors in imperfectly embedded interactions when φ = 0.4, 1 and 3 respectively. The curves provide each actor’s general response to the increase of the group size. Each actor’s motivation for cooperation is represented by two curves β = 0.3 and 0.9 in every subplot.
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pone-0073793-g002: The effect of total number of actors n on the conditions for cooperative NE.(a, b, c) Va for the head-end, mid-stream and tail-end actors in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for the head-end, mid-stream and tail-end actors in imperfectly embedded interactions when φ = 0.4, 1 and 3 respectively. The curves provide each actor’s general response to the increase of the group size. Each actor’s motivation for cooperation is represented by two curves β = 0.3 and 0.9 in every subplot.

Mentions: Figure 2 indicates how Va and Vim would change as the total number of actors n increases. We considered three scenarios in which the level of asymmetry φ is set to 0.4, 1 and 3.We select the head-end, tail-end and midstream actors as examples to illustrate. In each subplot, we also compare Va and Vim under two different continuing probability 0.3 and 0.9. In general, the results demonstrate a descending trend of Va and Vim in most scenarios. The results correspond to Olson’s influential argument about “the logic of collective action” which states that the larger a group is, the less likely they are to create social incentives which lead its members to provide collective goods [11]. Nonetheless, we also discover that the head-end actor’s incentive to cooperate is hardly affected by the group size when a high level of asymmetries exists during the course of interactions. An intuitive explanation for this phenomenon is that the head-end actor has most control over his potential loss. Greater level of asymmetries reduces his dependence on other actors’ behavior. Hence his risk of being defected by others does not increase with the number of actors involved.


Joint effects of asymmetric payoff and reciprocity mechanisms on collective cooperation in water sharing interactions: a game theoretic perspective.

Ng CN, Wang RY, Zhao T - PLoS ONE (2013)

The effect of total number of actors n on the conditions for cooperative NE.(a, b, c) Va for the head-end, mid-stream and tail-end actors in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for the head-end, mid-stream and tail-end actors in imperfectly embedded interactions when φ = 0.4, 1 and 3 respectively. The curves provide each actor’s general response to the increase of the group size. Each actor’s motivation for cooperation is represented by two curves β = 0.3 and 0.9 in every subplot.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3755971&req=5

pone-0073793-g002: The effect of total number of actors n on the conditions for cooperative NE.(a, b, c) Va for the head-end, mid-stream and tail-end actors in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for the head-end, mid-stream and tail-end actors in imperfectly embedded interactions when φ = 0.4, 1 and 3 respectively. The curves provide each actor’s general response to the increase of the group size. Each actor’s motivation for cooperation is represented by two curves β = 0.3 and 0.9 in every subplot.
Mentions: Figure 2 indicates how Va and Vim would change as the total number of actors n increases. We considered three scenarios in which the level of asymmetry φ is set to 0.4, 1 and 3.We select the head-end, tail-end and midstream actors as examples to illustrate. In each subplot, we also compare Va and Vim under two different continuing probability 0.3 and 0.9. In general, the results demonstrate a descending trend of Va and Vim in most scenarios. The results correspond to Olson’s influential argument about “the logic of collective action” which states that the larger a group is, the less likely they are to create social incentives which lead its members to provide collective goods [11]. Nonetheless, we also discover that the head-end actor’s incentive to cooperate is hardly affected by the group size when a high level of asymmetries exists during the course of interactions. An intuitive explanation for this phenomenon is that the head-end actor has most control over his potential loss. Greater level of asymmetries reduces his dependence on other actors’ behavior. Hence his risk of being defected by others does not increase with the number of actors involved.

Bottom Line: We present an iterative N-person game theoretic model to investigate the joint effects of these two mechanisms in a linear fully connected river system under three information assumptions.Meanwhile, various upstream and downstream actors manifest individual disparities as a result of the direct reciprocity and asymmetric payoff mechanisms.The upstream actors also display weak sensitivity to an increase in the total number of actors, which generally results in a reduction in the other actors' motivation for cooperation.

View Article: PubMed Central - PubMed

Affiliation: Department of Geography, The University of Hong Kong, Pokfulam, Hong Kong.

ABSTRACT
Common-pool resource (CPR) dilemmas distinguish themselves from general public good problems by encompassing both social and physical features. This paper examines how a physical mechanism, namely asymmetric payoff; and a social mechanism, reciprocity; simultaneously affect collective cooperation in theoretical water sharing interactions. We present an iterative N-person game theoretic model to investigate the joint effects of these two mechanisms in a linear fully connected river system under three information assumptions. From a simple evolutionary perspective, this paper quantitatively addresses the conditions for Nash Equilibrium in which collective cooperation might be established. The results suggest that direct reciprocity increases every actor's motivation to contribute to the collective good of the river system. Meanwhile, various upstream and downstream actors manifest individual disparities as a result of the direct reciprocity and asymmetric payoff mechanisms. More specifically, the downstream actors are less willing to cooperate unless there is a high probability that long-term interactions are ensured; however, a greater level of asymmetries is likely to increase upstream actors' incentives to cooperate even though the interactions could quickly end. The upstream actors also display weak sensitivity to an increase in the total number of actors, which generally results in a reduction in the other actors' motivation for cooperation. It is also shown that the indirect reciprocity mechanism relaxes the overall conditions for cooperative Nash Equilibrium.

Show MeSH
Related in: MedlinePlus