Decision theory is the science of rational choice in situations in which there is uncertainty about the outcome. Rational choice theory asserts that individuals whose behavior satisfies a few plausible conditions (such as transitivity, which means that if A is preferred to B and B is preferred to C, then A is preferred to C) will behave as though they are maximizing a preference function defined over the choice outcomes. For instance, consider an agent with the preference function u(a, n) defined over two goods, Apples and Nuts, and with an amount of money M to spend. Thus, u(2, 5) is the "utility" the agent derives from consuming two apples and five nuts (for this reason, economists call a preference function a utility function). If the prices of Apples and Nuts are p_a and p_n, the individual will choose the amount of Apples a...