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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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The effect of continuing probability β on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) 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 continuing probability β.
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pone-0073793-g005: The effect of continuing probability β on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) 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 continuing probability β.

Mentions: Figure 5 indicates how Va and Vim would change as the continuing probability β increases. We consider three scenarios in which the level of asymmetries φ is set to 0.4, 1 and 3. In each subplot, we compare the motivation for cooperation of five different actors (head-end, mid-upstream, mid, mid-downstream, tail-end). The value of β is generally referred as “the shadow of the future” which indicates the possibility of future interactions between all involved actors. Hence, the larger β is the more likely the game can continue. We can draw two remarks from Figure 5. On one hand, for a particular actor, Va and Vim increase with β when is φ constant. It confirms that an actor is more likely to cooperate when “the shadow of the future” is more significant. On the other hand, the slope of the curves for downstream actors becomes steeper than upstream actors when β is relatively large; the situation is reversed when β is relatively small. It implies that downstream actors’ motivation for cooperation increase faster than upstream actors when there is a higher possibility that future interactions will continue taking place. To the contrary, upstream actors are more motivated to cooperate than downstream actors even when there is a greater chance that the game could quickly end. An intuitive explanation for the joint effects of β and i is actors’ vision for their long-term interactions. For the downstream actors, assurance of future interactions will reduce their risks by giving them more control over other actors. They will therefore more likely to provide cooperation. This effect is amplified by the level of asymmetries. Whereas upstream actors are less exposed to others hence direct reciprocate behavior would not reduce their motivation for cooperation.


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 continuing probability β on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) 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 continuing probability β.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0073793-g005: The effect of continuing probability β on the conditions for cooperative NE when the group size is fixed to 20.(a, b, c) Va for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) in atomized interactions when φ = 0.4, 1 and 3 respectively; (d, e, f) Vim for five involved actors (head-end, mid-upstream, mid, mid-downstream, tail-end) 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 continuing probability β.
Mentions: Figure 5 indicates how Va and Vim would change as the continuing probability β increases. We consider three scenarios in which the level of asymmetries φ is set to 0.4, 1 and 3. In each subplot, we compare the motivation for cooperation of five different actors (head-end, mid-upstream, mid, mid-downstream, tail-end). The value of β is generally referred as “the shadow of the future” which indicates the possibility of future interactions between all involved actors. Hence, the larger β is the more likely the game can continue. We can draw two remarks from Figure 5. On one hand, for a particular actor, Va and Vim increase with β when is φ constant. It confirms that an actor is more likely to cooperate when “the shadow of the future” is more significant. On the other hand, the slope of the curves for downstream actors becomes steeper than upstream actors when β is relatively large; the situation is reversed when β is relatively small. It implies that downstream actors’ motivation for cooperation increase faster than upstream actors when there is a higher possibility that future interactions will continue taking place. To the contrary, upstream actors are more motivated to cooperate than downstream actors even when there is a greater chance that the game could quickly end. An intuitive explanation for the joint effects of β and i is actors’ vision for their long-term interactions. For the downstream actors, assurance of future interactions will reduce their risks by giving them more control over other actors. They will therefore more likely to provide cooperation. This effect is amplified by the level of asymmetries. Whereas upstream actors are less exposed to others hence direct reciprocate behavior would not reduce their motivation for cooperation.

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