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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 actors’ geographical locations i on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for all of the 20 involved actors in atomized interactions when β = 0.9, 0.6 and 0.3 respectively; (d, e, f) Vim for all of the 20 involved actors in imperfectly embedded interactions when β = 0.9, 0.6 and 0.3 respectively. The curves provide a comparison in terms of motivation for cooperation for all actors who are located at different positions on the river. Each actor’s motivation for cooperation is also compared in every subplot when the interactions take place under different levels of asymmetries φ = 0.1, 0.5, 1, 2 and 3.
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pone-0073793-g003: The effect of actors’ geographical locations i on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for all of the 20 involved actors in atomized interactions when β = 0.9, 0.6 and 0.3 respectively; (d, e, f) Vim for all of the 20 involved actors in imperfectly embedded interactions when β = 0.9, 0.6 and 0.3 respectively. The curves provide a comparison in terms of motivation for cooperation for all actors who are located at different positions on the river. Each actor’s motivation for cooperation is also compared in every subplot when the interactions take place under different levels of asymmetries φ = 0.1, 0.5, 1, 2 and 3.

Mentions: Figure 3 indicates how Va and Vim would change as an actor’s geographical location i moves gradually from the source to the end of the river. We select three scenarios in which the continuing probability β is set to 0.3, 0.6 and 0.9. In each subplot, we also compare how each actor reacts to variations of the levels of asymmetric payoff under the circumstances when φ equals to 0.1, 0.5, 1, 2 and 3. Two remarks can be drawn from this figure. First, Va and Vim increase with i at the beginning and then decrease after Va and Vim reach their apexes. Although the position of the apexes varies with φ and β, it implies that relative up-midstream actors are more likely to cooperate than the others when the remaining variables are held invariant. Second, the upstream curves in each subplot become steeper as φ increases. It shows that greater individual differences exist among upstream actors with higher levels of asymmetries.


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 actors’ geographical locations i on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for all of the 20 involved actors in atomized interactions when β = 0.9, 0.6 and 0.3 respectively; (d, e, f) Vim for all of the 20 involved actors in imperfectly embedded interactions when β = 0.9, 0.6 and 0.3 respectively. The curves provide a comparison in terms of motivation for cooperation for all actors who are located at different positions on the river. Each actor’s motivation for cooperation is also compared in every subplot when the interactions take place under different levels of asymmetries φ = 0.1, 0.5, 1, 2 and 3.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0073793-g003: The effect of actors’ geographical locations i on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for all of the 20 involved actors in atomized interactions when β = 0.9, 0.6 and 0.3 respectively; (d, e, f) Vim for all of the 20 involved actors in imperfectly embedded interactions when β = 0.9, 0.6 and 0.3 respectively. The curves provide a comparison in terms of motivation for cooperation for all actors who are located at different positions on the river. Each actor’s motivation for cooperation is also compared in every subplot when the interactions take place under different levels of asymmetries φ = 0.1, 0.5, 1, 2 and 3.
Mentions: Figure 3 indicates how Va and Vim would change as an actor’s geographical location i moves gradually from the source to the end of the river. We select three scenarios in which the continuing probability β is set to 0.3, 0.6 and 0.9. In each subplot, we also compare how each actor reacts to variations of the levels of asymmetric payoff under the circumstances when φ equals to 0.1, 0.5, 1, 2 and 3. Two remarks can be drawn from this figure. First, Va and Vim increase with i at the beginning and then decrease after Va and Vim reach their apexes. Although the position of the apexes varies with φ and β, it implies that relative up-midstream actors are more likely to cooperate than the others when the remaining variables are held invariant. Second, the upstream curves in each subplot become steeper as φ increases. It shows that greater individual differences exist among upstream actors with higher levels of asymmetries.

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