This paper is an examination of some modelling problems regarding imperfect recall within the model of extensive games. It is argued that, if the assumption of perfect recall is violated, care must be taken in interpreting the main elements of the model. Interpretations that are inconsequential under perfect recall have important implications in the analysis of games with imperfect recall.

We argue that in extensive decision problems (extensive games with a single player) with imperfect recall care must be taken in interpreting information sets and strategies. Alternative interpretations allow for different kinds of analysis. We address the following issues: 1. randomization at information sets; 2. consistent beliefs; 3. time consistency of optimal plans; 4. the multiselves approach to decision making. We illustrate our discussion through an example that we call the ‘‘paradox of the absentminded driver.’’ Journal of Economic Literature Classification (...) Numbers: C7, D0. 1997 Academic Press. (shrink)

In addition to being uncertain about what the world is like, one can also be uncertain about one’s own spatial or temporal location in the world. My aim is to pose a problem arising from the interaction between these two sorts of uncertainty, solve the problem, and draw two lessons from the solution.

I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...) r. Thus, each conditional in a given family behaves like conditional probability above some specific support level. (shrink)

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.

Journal of Philosophical Logic 34, 97-119, 2005.