Game Equilibrium Models II

pp 188-262

Irrigation Institutions and the Games Irrigators Play: Rule Enforcement Without Guards

  • Franz Weissing
  • , Elinor Ostrom

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This is the first of three efforts examining how irrigation institutions affect equilibrium stealing and enforcement rates. In this chapter, we examine rule—following and rule—enforcement rates of behavior adopted by irrigators on systems where rules are self—enforced rather than enforced by formal guards. To do this, we assume that irrigators rotate into the position of a turntaker. When in the position of a turntaker, they choose between taking a legal amount of water and taking more water than authorized (stealing). The other irrigators are turnwaiters who must decide whether to expend resources to monitor the behavior of the turntaker or not. In all our models, we find no combination of parameters where the rate of stealing by the turntaker falls to zero. In other words, there is always some stealing going on.

We give a complete equilibrium analysis for the situation where all irrigators have the same payoffs, monitoring efficiencies, and norms of behavior. Then, we examine how stealing and monitoring rates are affected by changes in parameters including: number of irrigators. cost of monitoring, detection probabilities, relative benefits of stealing, losses felt when stealing occurs, and the reward for successful discovery of a stealing event. Our final analysis addresses how the introduction of asymmetries in payoffs, monitoring efficiencies, and/or norms of behavior affects the distribution of equilibrium outcomes. One consequence of asymmetry is that there is no longer a unique Nash equilibrium. We find both paradoxical and non—paradoxical equilibria. In the paradoxical equilibria, just those turnwaiters monitor less who are inherently in a better position to monitor. In the non—paradoxical equilibria, one class of turnwaiters sticks to a pure strategy while the turntaker adjusts his stealing rate to the cost—benefit ratio of the others who are monitoring at an intermediate rate.

Several of our results are counterintuitive at first sight and reflect the interactive nature of the situation and the interdependence of the players. Our findings also contribute to a more general understanding of the relative weight of ‘primary’ and ‘secondary’ interaction effects in a mixed—strategy context.