Richard Posner (United States Court of Appeal and University of Chicago) has posted What Do Deities Maximize? on SSRN. Here is the abstract:
This article presents a positive economic theory of the behavior of supernatural beings or deities. The essay addresses a well known problem in the conventional theological account of a supreme being that is omnipotent and omniscient. Given omnipotence, the state of the world should be identical with the state most favored by the preference structure of the deity. But rational choice theory is the positive theory that a rational actor will act so as to maximize the satisfaction of its preferences. Given omnipotence and omniscience, it follows that all states of affairs already accord with the preferences of an omnipotent and omniscient deity, leading to the paradoxical conclusion that rational action by such an entity is impossible.
The model proposed in this article resolves this paradox by invoking the familiar notion of "free will." By creating beings with free will, a rational deity creates conditions in which it is possible for the deity to act rationally by interacting with creatures that it creates which have free will (who thus can act in ways that do not accord with the the deity's preferences). On this model, a deity acts rationally when it acts in ways that induce creatures with free will to satisfy the deity's preferences. For example, a deity might demand some act of sacrifice, reverence, or obedience and then threaten to punish creatures that do not satisfy these demands. Such threats might be made credible by actions that demonstrate the power of the deity to create plagues, floods, and other natural disasters visited upon those who are disobedient or irreverent.
This model provides a theoretical alternative to the common view of divine beings as Prometheans or saints, and it suggests new ways of looking at such practical issues as the design of religious institutions that can produce human behavior that will avoid the deleterious consequences that attend punitive actions by omnipotent deities. The author expresses no opinion on the question whether such entities actually exist.