Game theory explains what happened in the Voluntary Agreement negotiations

In 2009, Michael Hanneman and Caitlin Dyckman published a stark assessment:  “The San Francisco Bay-Delta: A failure of decision-making capacity.” A decade later, their game theoretic analysis explains a lot of what happened with the Voluntary Agreement negotiations for the Bay-Delta Water Quality Control Plan Update.

This is the key bit:

A well-known theorem from game theory has application to the bargaining regarding the Delta. The theorem applies to multi-person, cooperative (bargaining) games. A solution concept for such a game is what is known as the core: the core is the set of outcomes with the property that no coalition of players, acting as an independent group, can achieve more for itself than what it would obtain from outcomes in the core. The core is thus the set of bargaining outcomes that cannot be improved on by any coalition acting alone. The theorem states that no core exists when the game is zero-sum. In such a game, any equilibrium leaves at least one group in the position that it can do better for itself by dropping out and going it alone. Hence, any bargaining equilibrium is not stable and cannot be sustained.

Aivazian and Callen (1981) … point out that …  “If the core does not exist, the participants may accept an alternative solution concept; then again they may simply stop negotiating. It is an empirical question as to what happens when the core is empty. We do not know.”

What happened with the Bay-Delta WQCP Voluntary Agreement negotiations was that it was a zero sum game with the environmental groups in the negotiations. And there was thus no “core” of bargaining outcomes that could not be improved on by the water diverters acting alone in a back-room deal. So that ended up being the alternative solution.

Hanneman and Dyckman concluded:

To summarize, our thesis in this paper is that the issue of water diversions and Delta inflows has been unresolved in California for six decades because (1) it involves a fundamental opposition of interests, (2) this opposition of interests makes a voluntary solution unlikely because of the game-theoretic considerations described above, and (3) the SWRCB’s strategy of relying on voluntary agreement to resolve the issue is fundamentally misconceived and is, at some level, an abdication of its responsibility.

Further Reading:

Hanemann, M., Dyckman, C. 2009. The San Francisco Bay-Delta: A failure of decision-making capacity, Environmental Science & Policy, 12(6): 710-725
https://doi.org/10.1016/j.envsci.2009.07.004.