49 research outputs found
Monadic Second-Order Logic with Arbitrary Monadic Predicates
We study Monadic Second-Order Logic (MSO) over finite words, extended with
(non-uniform arbitrary) monadic predicates. We show that it defines a class of
languages that has algebraic, automata-theoretic and machine-independent
characterizations. We consider the regularity question: given a language in
this class, when is it regular? To answer this, we show a substitution property
and the existence of a syntactical predicate.
We give three applications. The first two are to give very simple proofs that
the Straubing Conjecture holds for all fragments of MSO with monadic
predicates, and that the Crane Beach Conjecture holds for MSO with monadic
predicates. The third is to show that it is decidable whether a language
defined by an MSO formula with morphic predicates is regular.Comment: Conference version: MFCS'14, Mathematical Foundations of Computer
Science Journal version: ToCL'17, Transactions on Computational Logi
A note on wage differentials, fixed-wages and adverse selection.
Using a substitution property of worker’s types (productivity and time preference), we propose an explanation for both fixed-wages and wage differentials. Fixed-wages result in bunching at the optimum. Equally productive workers with different time preference accept different wages.Wage differentials; Fixed-wages; Labor contracts; Adverse selection; Heterogeneous time preference;
Preference for Information
What is the relationship between an agent’s attitude towards information, and her attitude towards risk? If an agent always prefers more information, does this imply that she obeys the independence axiom? We provide a substitution property on preferences that is equivalent to the agent (intrinsically) liking information in the absence of contingent choices. We use this property to explore both questions, first in general, then for recursive smooth preferences, and then in specific recursive non-expected utility models. Given smoothness, for both the rank dependence and betweenness models, if an agent is information-loving then her preferences can depart from Kreps and Porteus’s (1978) temporal expected utility model in at most one stage. This result does not extend to quadratic utility. Finally, we give several conditions such that, provided the agent intrinsically likes information, Blackwell’s (1953) result holds; that is, she will always prefer more informative signals, whether or not she can condition her subsequent behavior on the signal
Infinite-horizon choice functions
We analyze infinite-horizon choice functions within the setting of a simple technology. Efficiency and time consistency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes-Sen, Pigou-Dalton, and resource monotonicity. We show that Suppes-Sen and Pigou-Dalton imply that the consumption and inheritance functions are monotone with respect to time - thus justifying sustainability - while resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource. Examples illustrate the characterization results.Intergenerational resource allocation, infinite-horizon choice
Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior, Second Version
Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker (DM) who has recursive, non-expected utility preferences over compound lotteries. DM has preferences for one-shot resolution of uncertainty (PORU) if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic PORU and static preferences that are identified with commonly observed behavior in Allais-type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium. In an intertemporal context, PORU captures “loss aversion with narrow framing.”Recursive preferences over compound lotteries, resolution of uncertainty, Allais paradox, narrow framing, negative certainty independence