Asymmetric Payoff Mechanism and Information Effects in Water Sharing Interactions: A Game Theoretic Model of Collective Cooperation

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"General theoretic studies of collective action in common-pool resources (CPRs) dilemmas have been usually established on an assumption that actors all share symmetric access and position with regard to the commons. However, in real situations, most actors in a complex social-ecological system are heterogeneous in terms of their power, wealth, influence and so forth. The heterogeneity is also greatly attributed to diverse geographies, social hierarchies, skills, knowledge, and other features which are attached to those actors. Thus, analyses of internal and external asymmetric mechanisms are thus required to facilitate cooperation and achieve social optimum in CPR dilemmas. This paper uses surface water as an example to give a preliminary attempt to cope with the key issues mentioned above. We present an iterative N-Person Prisoner's Dilemma (PD) game theoretic model to quantitatively address the equilibrium conditions for collective cooperation in water sharing interactions. With a modified PD game payoff matrix and a simple evolutionary approach, asymmetric mechanism and information effects are incorporated into the model simultaneously. Numerical simulations are carried out in Matlab environment. The results demonstrate asymmetric mechanism leads to individual variations in terms of motivation to cooperate amongst different upstream and downstream actors. Tail-end actor is the one with least motivation to cooperate and up-midstream actors are more willing to cooperate. Moreover, higher level of asymmetries would increase upstream actors' incentives to cooperate yet downstream actors are barely affected by the asymmetric mechanism. 'The shadow of the future' again is confirmed to increase the chances of universal cooperation, yet with the asymmetric mechanism, stronger motivation to cooperate is produced for downstream actors than upstream actors. The results also show greater level of information exchange relaxes overall equilibrium conditions, yet there is a negative effect on all actors' incentive to cooperate with the increase of total number of actors."
IASC, game theory, modeling, cooperation