Further Reading

Section 9.1 covered very basic concepts, which can be found in numerous books and on the Internet. For more on Pareto optimality, see [847,909,953,1005]. Section 9.2 is inspired mainly by decision theory books. An excellent introduction is [89]. Other sources include [268,271,673,831]. The ``game against nature'' view is based mainly on [109]. Pattern classification, which is an important form of decision theory, is covered in [19,271,295,711]. Bayesian networks [778] are a popular representation in artificial intelligence research and often provide compact encodings of information for complicated decision-making problems.

Further reading on the game theory concepts of Sections 9.3 and 9.4 can be found in many books (e.g., [59,759]). A fun book that has many examples and intuitions is [917]. For games that have infinite action sets, see [59]. The computation of randomized Nash equilibria remains a topic of active research. A survey of methods appears in [691]; see also [545,699]. The coupled polynomial equations that appear in computing randomized Nash equilibria may seem to suggest applying algorithms from computational algebraic geometry, as were needed in Section 6.4 to solve this kind of problem in combinatorial motion planning. An approach that uses such tools is given in [261]. Contrary to the noncooperative games defined in Section 9.4, cooperative game theory investigates ways in which various players can form coalitions to improve their rewards [779].

Parts of Section 9.5 were inspired by [89]. Utility theory appears in most decision theory books (e.g., [89]) and in some artificial intelligence books (e.g., [839]). An in-depth discussion of Bayesian vs. frequentist issues appears in [831]. For a thorough introduction to constructing cost models for decision making, see [539].