Ray Dacey: Learning, Knowledge and Adaptation
Analyses of human decision making generally characterize the decision problem as a pair <S,A> with state-space S and act-space A, and the decision-maker as a triple <M,P,U> with outcome mapping M, probability measure P, and utility function U. In a decision-theoretic account, S is the set of states from which Nature stochastically selects and A is the set of actions from which the human decision-maker purposefully selects. In a game-theoretic account, S is the set of actions from which the rational adversary purposefully or stochastically selects, and A is the set of actions from which the decision-maker purposefully or stochastically selects.
The epistemic problems associated with decision making focus on two issues - the selection of the outcome mapping M and the specification of the probability measure P. The former is an instance of inference to laws and the latter is an instance of the specification of a probability measure. We will deal with these classes of problems as they arise. Here I wish to note that one of the great contributions of traditional decision theory is the economic theory of information. Due in large measure to Jacob Marschak (1974), the economic theory of information provides a Bayes-rational account of inference
In a traditional decision-theoretic account, the outcome mapping M is composed in much the same way as in the physical sciences. The world is presumed to be coherent, in the style of a deterministic system, and can be represented by (perhaps complex) mapping M which specifies the outcome for each act-state pair
In a non-traditional decision-theoretic account, the states of nature are presumed to be dependent upon the human's selection of an act. This seemingly minor addition requires the specification of an additional probability measure. In Jeffrey's account, this additional measure is a component of the primary system and is modeled as the decision-maker's probability distribution over the act space A (Jeffrey 1983). In the end, this additional probability measure leads to the loss of the economic theory of information (Dacey 1981). Decision theory meets game theory in the analysis of Newcomb's Problem. It is not my aim to spend time rehashing this well-known problem. I wish only to do three things here. First, I will show how traditional inference can be given a role in "resolving" a decision-theoretic account of Newcomb's Problem (Dacey, et al., 1977). Second, I will make a connection with the e coli of game theory, the Prisoner's Dilemma problem. Third, I will use a result (Skyrms, 1994) to make a connection between decision theory and modern game theory.
Traditional game theory provides the standard account of human decision making when the adversary is a purposeful decision-maker. Typically, the adversary is presumed to be another human. However, as employed in contemporary biology, game theory does not require this assumption - the adversary merely must be purposeful (Maynard Smith, 1982, 1999). Uncertainty, and the related epistemic problems, arises in game theory in three ways. First, the decision-maker can be uncertain about the game being played. Second, the decision-maker can be uncertain about the adversary's selection of an act (or acts). This case is most immediately similar to the traditional decision-theoretic account of human choice. Third, the decision-maker can be uncertain about his/her own selection of an act. In this case, the decision-maker, and perhaps the adversary, has adopted a mixed strategy, i.e., a probability mixture of the acts in A. This case is most immediately similar to Jeffrey's decision-theoretic account of human choice. In all three cases, the decision-maker is uncertain about the outcome mapping M.
Modern Game theory has focused on three forms of learning - fictitious play, the best response dynamic, and the replicator dynamic (Fudenberg and Levine, 1998). These forms of learning provide a natural connection with evolutionary theory. This connection can be viewed as an extension of the connection, made by Skyrms (1994), between decision theory and evolution. Another connection can be made between these forms of learning and the institutions that arise in societies. This connection is made explicit in the work of Young (1998).
Finally, the advent of low cost computing has produced many sophisticated analyses based on rational agent modeling (Epstein and Axtel, 1996; Santa Fe Institute, 1999; Tesfatsion, 1999). This, in turn, has two interesting results. First, it has led to interesting epistemic issues pertaining to the status of the findings of computer modeling. Second, it has led, at the hands of Kelly (1996) and his colleagues, to a very modern account of epistemology itself.
Session 1: Traditional Decision-Theoretic Analyses
Session 2: Jeffrey's Decision-Theoretic Analysis
Session 3: Decision-Theoretic Analysis and Game-Theoretic Analysis
Session 4: Traditional Game-Theoretic Analyses
Session 5: Modern Game-Theoretic Analyses
Session 6: Computer-Based Analyses
Ray Dacey's Course