Tort Liability and Unawareness

Unawareness is a form of bounded rationality where a person fails to conceive all feasible acts or consequences or to perceive as feasible all conceivable act-consequence links. We study the implications of unawareness for tort law, where relevant examples include the discovery of a new product or technology (new act), of a new disease or injury (new consequence), or that a product can cause an injury (new link). We argue that negligence has an important advantage over strict liability in a world with unawareness—negligence, through the stipulation of due care standards, spreads awareness about the updated probability of harm

Dynamic Unawareness and Rationalizable Behavior

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance.Unawareness, extensive-form games, extensive-form rationalizability, prudent rationalizability, iterative conditional dominance

Prudent Rationalizability in Generalized Extensive-Form Games

We define an extensive-form analogue of iterated admissibility, called Prudent Rationalizability (PR). In each round of the procedure, for each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. Somewhat surprisingly, prudent rationalizable strategies may not refine the set of Extensive-Form Rationalizable (EFR) strategies (Pearce 1984). However, we prove that the paths induced by PR strategy-profiles (weakly) refine the set of paths induced by EFR strategies. PR applies also to generalized extensive-form games which model mutual unawareness of actions (Heifetz, Meier and Schipper, 2011a). We demonstrate the applicability of PR in the analysis of verifiable communication, and show that it yields the same, full information unraveling prediction as does the unique sequential equilibrium singled out by Milgrom and Roberts (1986); yet, we also show that under unawareness full unraveling might fail.Prudent rationalizability, caution, extensive-form rationalizability, extensive-form games, unawareness, verifiable communication

Reasoning About Knowledge of Unawareness

Awareness has been shown to be a useful addition to standard epistemic logic for many applications. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which he is unaware without there being an explicit fact that the agent knows he is unaware of. We propose a logic for reasoning about knowledge of unawareness, by extending Fagin and Halpern's \emph{Logic of General Awareness}. The logic allows quantification over variables, so that there is a formula in the language that can express the fact that ``an agent explicitly knows that there exists a fact of which he is unaware''. Moreover, that formula can be true without the agent explicitly knowing that he is unaware of any particular formula. We provide a sound and complete axiomatization of the logic, using standard axioms from the literature to capture the quantification operator. Finally, we show that the validity problem for the logic is recursively enumerable, but not decidable.Comment: 32 page

Learning and Discovery

We formulate a dynamic framework for an individual decision-maker within which discovery of previously unconsidered propositions is possible. Using a standard game-theoretic representation of the state space as a tree structure generated by the actions of agents (including acts of nature), we show how unawareness of propositions can be represented by a coarsening of the state space. Furthermore we develop a semantics rich enough to describe the individual's awareness that currently undiscovered propositions may be discovered in the future. Introducing probability concepts, we derive a representation of ambiguity in terms of multiple priors, reflecting implicit beliefs about undiscovered proposition, and derive conditions for the special case in which standard Bayesian learning may be applied to a subset of unambiguous propositions. Finally, we consider exploration strategies appropriate to the context of discovery, comparing and contrasting them with learning strategies appropriate to the context of justification, and sketch applications to scientific research and entrepreneurship.

Unawareness and Implicit Belief

Possible worlds models of belief have difficulties accounting for unawareness, the inability to entertain (and hence believe) certain propositions. Accommodating unawareness is important for adequately modelling epistemic states, and representing the informational content to which agents have in principle access given their explicit beliefs. In this paper, I develop a model of explicit belief, awareness, and informational content, along with an sound and complete axiomatisation. I furthermore defend the model against the seminal impossibility result of Dekel, Lipman and Rustichini, according to which three intuitive conditions preclude non-trivial unawareness on any possible worlds model of belief

Level-k Thinking in the Extensive Form

Level-k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. Player's may learn about levels of opponents' thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l < k to her opponents consistent with the information set. We compare our notion of strong level-k thinking with other solution concepts such as level-k thinking in the associated normal form, strong rationalizability, Delta-rationalizability, iterated admissibility, backward rationalizability, backward level-k thinking, and backward induction. We use strong level-k thinking to reanalyze data from some prior experiments in the literature.Comment: 51 pages, 10 figure

Dynamic Unawareness and Rationalizable Behavior

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. We apply prudent rationalizability to the analysis of verifiable communication with unawareness. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance