Real-time water allocation policies calculated with bankruptcy games and genetic programing

Population growth coupled with increased urban and agricultural water use have exacerbated water shortages worldwide. Conflicts among water users frequently arise over scarce water. The application of conflict resolution methods has the potential to resolve such conflicts. Bankruptcy games is a branch of game theory applicable to problems dealing with conflict resolution. This study addresses water allocation to urban-industrial, agricultural, and environmental water uses downstream of the Zarrineh-roud dam, Iran, which diverts water from the Zarrineh-roud River, an important tributary to Lake Urmia. Lake Urmia has been severely stressed by reduction of its water inputs. Water allocation is posed in this study as a bankruptcy game in which the allocation to stakeholders is optimized with proportional (P), adjusted proportional, constrained equal award (CEA), and constrained equal losses methods. The CEA was chosen as the best allocation method based on performance criteria and the Bankruptcy Allocation Sustainability Index. Monthly, real-time, water allocation rule curves were calculated with genetic programming.

Bankruptcy Problem Allocations and the Core of Convex Games

A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.

CONVEXITY OF THE "AIRPORT PROFIT GAME" AND k-CONVEXITY OF THE "BANKRUPTCY GAME"

The topic is two-fold. First, we prove the convexity of Owen's Airport Profit Game (inclusive of revenues and costs). As an adjunct, we characterize the class of 1-convex Airport Profit Games by equivalent properties of the corresponding cost function. Second, we classify the class of 1-convex Bankruptcy Games by solving a minimization problem of its corresponding gap function.