10.1 Introducing Sequential Games Against Nature

This section extends many ideas from Chapter 2 to the case in which nature interferes with the outcome of actions. Section 10.1.1 defines the planning problem in this context, which is a direct extension of Section 2.1. Due to unpredictability, forward projections and backprojections are introduced in Section 10.1.2 to characterize possible future and past states, respectively. Forward projections characterize the future states that will be obtained under the application of a plan or a sequence of actions. In Chapter 2 this concept was not needed because the sequence of future states could always be derived from a plan and initial state. Section 10.1.3 defines the notion of a plan and uses forward projections to indicate how its execution may differ every time the plan is applied.