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Consider the single-agent decision problem, where the agent chooses the optimal action a ∈ A to maximize her expected utility. The utility depends on the state of nature θ ∈ Θ, and for the remainder of this lecture, we assume that Θ = {θ1, ..., θN} is a finite set with N elements. Assume also that the (state dependent) utility function u(a, θ) is continuous in a for all θ and A is compact. Let p(i) denote the prior probability of the event {θ = θi}, and p = (p(i), ..., p(N)). We assume w.l.o.g. that p(i) > 0 for all i. The decision maker’s problem is then to