Dynamic Games with Nature: Designing Policy under Ambiguity

Environmental and resource economics is permeated by economic and environmental uncertainties. The expected utility framework founded by von Neumann and Morgenstern and later extended to subjective probability by Savage is the traditional framework for dealing with risk in economics. Frank Knight suggested the need to distinguish between risk and uncertainty for situations where there is ignorance or not enough information to assign probabilities — objective or subjective — to events. Knightian uncertainty, or ambiguity, is an appropriate framework for studying environmental management issues, given the complexities and the multiple sources of underlying uncertainties. Decision-making under ambiguity has been based on the maxmin expected utility. Robust control, by using maxmin rules and by introducing a fictitious adversarial agent referred to as Nature, provides policies under ambiguity. In robust rules the lower bounds to the rule's performance are determined by Nature, and management can be regarded as a game between the regulator and Nature. The regulator maximizes her/his objective, while Nature "tries" to minimize the regulator's objective. The outcome of this game determines regulation under ambiguity. This paper presents methods for studying environmental and resource management issues and designing robust policies under ambiguity or Knightian uncertainty and ambiguity aversion. In particular, robust control methods are applied to a differential game associated with a problem of international pollution control. Optimal robust feedback rules and state variable paths are derived. The differential game framework is also extended to recently developed deterministic robust control methods which allow direct comparisons between cooperative and noncooperative outcomes.