Stable Matching under Forward-Induction Reasoning

A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning. This approach leads to a new definition of stability. The main result shows an equivalence between this notion and “incomplete-information stability”, a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014), for markets with one-sided incomplete information. The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions. In addition, it provides an epistemic foundation for incomplete-information stability. The paper also shows new connections and distinctions between the cooperative and the epistemic approaches in matching markets

Testable Forecasts

Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically. We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. The paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood-ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman-Pearson paradigm of hypothesis testing

The cost of information

We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information.Comment: 52 pages, 4 figure

An Axiomatic Theory of Inductive Inference

This article develops an axiomatic theory of induction that speaks to the recent debate on Bayesian orgulity. It shows the exact principles associated with the belief that data can corroborate universal laws. We identify two types of disbelief about induction: skepticism that the existence of universal laws of nature can be determined empirically, and skepticism that the true law of nature, if it exists, can be successfully identified. We formalize and characterize these two dispositions toward induction by introducing novel axioms for subjective probabilities. We also relate these dispositions to the (controversial) axiom of σ-additivity

Testable Forecasts

Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically. We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. The paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood-ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman-Pearson paradigm of hypothesis testing

The cost of information

We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information

Stable Matching under Forward-Induction Reasoning

A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning. This approach leads to a new definition of stability. The main result shows an equivalence between this notion and “incomplete-information stability”, a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014), for markets with one-sided incomplete information. The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions. In addition, it provides an epistemic foundation for incomplete-information stability. The paper also shows new connections and distinctions between the cooperative and the epistemic approaches in matching markets

Claim Validation

Hume (1748) challenged the idea that a general claim (e.g. "all swans are white") can be validated by empirical evidence, no matter how compelling. We examine this issue from the perspective of a tester who must accept or reject the forecasts of a potential expert. If experts can be skeptical about the validity of claims then they can strategically evade rejection. In contrast, if experts are required to conclude that claims backed by sufficient evidence are likely to be true, then they can be tested and rejected. These results provide an economic rationale for claim validation based on incentive problems