Savage's Theorem Under Changing Awareness

This paper proposes a simple unified framework of choice under changing awareness, addressing both outcome awareness and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expected-utility rationalization of preferences, in which utilities and probabilities are revised according to three revision rules when awareness changes: (R1) utilities of unaffected outcomes are transformed affinely; (R2) probabilities of unaffected events are transformed proportionally; (R3) enough probabilities 'objectively' never change (they represent revealed objective risk). Savage's Theorem is a special case of the theorem, namely the special case of fixed awareness, in which our axioms reduce to Savage's axioms while R1 and R2 hold trivially and R3 reduces to Savage's requirement of atomless probabilities. Rule R2 parallels Karni and Viero's (2013) 'reverse Bayesianism' and Ahn and Ergin's (2010) 'partition-dependence'. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981)

Bounded Rationality, Indeterminacy, and the Theory of the Firm

Information Systems Working Papers Serie

Towards an epistemic theory of probability.

The main concern of this thesis is to develop an epistemic conception of probability. In chapter one we look at Ramsey's work. In addition to his claim that the axioms of probability ace laws of consistency for partial beliefs, we focus attention on his view that the reasonableness of our probability statements does not consist merely in such coherence, but is to be assessed through the vindication of the habits which give rise to them. In chapter two we examine de Finetti's account, and compare it with Ramsey's. One significant point of divergence is de Finetti's claim that coherence is the only valid form of appraisal for probability statements. His arguments for this position depend heavily on the implementation of a Bayesian model for belief change; we argue that such an approach fails to give a satisfactory account of the relation between probabilities and objective facts. In chapter three we stake out the ground for oar own positive proposals - for an account which is non-objective in so far as it does not require the postulation of probabilistic facts, but non-subjective in the sense that probability statements are open to objective forms of appraisal. we suggest that a certain class of probability statements are best interpreted as recommendations of partial belief; these being measurable by the betting quotients that one judges to be fair. Moreover, we argue that these probability statements are open to three main forms of appraisal (each quantifiable through the use of proper scoring rules), namely: (i) Coherence (ii) Calibration (iii) Refinement. The latter two forms of appraisal are applicable both in an ex ante sense (relative to the information known by the forecaster) and an ex post one (relative to the results of the events forecast). In chapters four and five we consider certain problems which confront theories of partial belief; in particular, (1) difficulties surrounding the justification of the rule to maximise one's information, and (2) problems with the ascription of probabilities to mathematical propositions. Both of these issues seem resolvable; the first through the principle of maximising expected utility (SEU), and the second either by amending the axioms of probability, or by making use of the notion that probabilities are appraisable via scoring rules. There do remain, however, various difficulties with SEU, in particular with respect to its application in real-life situations. These are discussed, but no final conclusion reached, except that an epistemic theory such as ours is not undermined by the inapplicability of SEU in certain situations

Bounded Rationality, Indeterminacy, and the Theory of the Firm

Information Systems Working Papers Serie

Rationality in Econometrics

The idea of rationality enters an econometrician's work in many ways; e.g., in his presuppositions about sample populations, in his model selections and data analyses, and in his choice of projects. I shall consider some of these ways and their ramifications for the econometrician's own life and for the development of econometrics. I begin with a discussion of rationality that I have found in the writings of Aristotle and other leading philosophers. My aim here is to establish the characteristics that we in good faith can expect rational members of a sample population to possess. The characteristics with which I end up have no definite meaning. Instead they are like undefined terms in mathematics that an econometrician can interpret in ways that suit the purposes of his research and seem appropriate for the population he is studying. When interpreted, the pertinent characteristics of the rational members of a given population become hypotheses whose empirical relevance must be tested. In rationally designed econometric studies the interpretation of 'rationality' that seems appropriate for a given study is usually an interpretation that the pertinent econometrician extracts from various economic theories. I look at some of these interpretations and discuss their empirical relevance. The interpretations of particular interest concern consumer choice under certainty, choice under risky and uncertain conditions, and choice in game-theoretic situations. These interpretations appear in various representations in the ways econometricians model rationality. I single out for discussion microeconometric models of consumer choice and macroeconometric rational expectations models. In the last section of the paper I consider two lacunas in Kuhn's and Lakatos' theories, and see how econometricians go about solving puzzles and extending positive heuristics. I begin by discussing the considerations that guide an econometrician in his choice of research projects. Then, I argue about the determinants of rational choice in model selection. Finally, I consider the politics of writing research reports. The contents of these sections concern aspects of an econometrician's rational choice that are relevant for the orderly development of econometrics.

Rational Cooperation In One-Shot Simultaneous Pd-Situations

The paper shows that being able to forecast another player's actual cooperation better than pure chance can change players' strategic incentives in a one-shot simultaneous PD-situation. In particular, it is shown that if both players have such ability (to forecast each others' actual choices better than pure chance), then "conditionally cooperative" Nash equilibria may exist in addition to the "always defect" equilibrium. By "conditionally cooperative" we mean that players do not cooperate because of a behavioral "disposition" to act cooperatively, but cooperate rather selectively contingent on their forecasting of the opponent's cooperation (cooperate if and only if each other is forecasted to cooperate). -- Der Beitrag zeigt, daß Spieler, die in der Lage sind, die Aktionen ihrer Gegenspieler eher richtig als falsch zu prognostizieren, in einer prototypischen Gefangenendilemmasituation einen Anreiz haben, sich kooperativ zu verhalten. Insbesondere wird nachgewiesen, daß es neben dem aus der tradtitionellen Analyse bekannten Ergebnis der allseitigen Defektion auch zu sogenannten "bedingt kooperativen" Nash-Gleichgewichten kommen kann, falls beide Spieler diese Prognosefähigkeit besitzen. Die Spieler kooperieren dabei nicht aufgrund einer Disposition für kooperatives Verhalten, sondern vielmehr selektiv und bedingt auf ihre Vorhersagefähigkeit.prisoner's dilemma,reliability condition,forecasting ability,trust

Managed Floats to Damp Shocks like 1982-5 and 2006-9: Field and Laboratory Evidence for Chinese Interest in a Single World Currency

This paper’s field evidence is: (1) many official sectors rapidly forget the damage of the 1982-85 exchange rate liquidity crisis and reverted to what caused that crisis, namely a closed economy clean floats perspective; and (2) the 2006-2008/9 exchange rate liquidity shock would have been more drastic but for central bank currency swaps. This evidence is bolstered by a laboratory experiment that incorporates more aspects of real world complexity and more different sorts of official and private sector agents than are feasible in econometric or algebraic investigations and employs a new central bank cooperation-conflict model of exchange rate determination , and is within an umbrella theory of Pope, namely SKAT, the Stages of Knowledge Ahead Theory. SKAT allows for risk effects from stages omitted in normal models, including those from (a) difficulties of agents in evaluating alternatives in a complex environment in which the assumed maximization of expected utility is impossible; and (b) preference for safety and reliability is not trivialized. Our joint field plus laboratory evidence indicates that official sectors should maintain an international exchange rate oriented perspective, or better yet, a single world currency as recommended by Zhou Xiaochuan, head of the People’s Bank of China. To avoid rapid forgetting of havoc from isolationist clean floats and the value of stable exchange rates, a new syllabus, as under the SKAT umbrella, is fundamental in the education of official sector members in order to furnish them with a coherent alternative intellectual framework to current university education that excludes liquidity crises.clean float, managed float, IMF imposed conditions, exchange rate regime, exchange rate volatility, experiment, SKAT the Stages of Knowledge Ahead Theory, monetary policy, transparent policy, exchange rate shocks, central bank cooperation, central bank conflict

Modeling Relevance

During the past decade, particularly during the years immediately following the California Supreme Court\u27s decision in People v. Collins, a number of articles have appeared suggesting ways in which jurors might use certain mathematical techniques of decision theory as aids in the rational evaluation of circumstantial evidence. Professor Tribe, in an important response to the post-Collins articles, argues against introducing these techniques into the factfinding process. Problems that Tribe foresees include the necessary imprecision of the probabilistic estimates that these techniques require, the dwarfing of soft variables by those that are more readily quantified, and the potential dehumanization of the trial in the name of rational factfinding. In this article I try to show the utility of two simple models, Bayes\u27 Theorem and regret matrices, for thinking about the meaning of relevance and for analyzing those evidentiary rules, which I call the relevance rules, generally associated with this topic. The discussion assumes that the factfinder is a jury and, unless otherwise noted, that the issue to be resolved is a defendant\u27s guilt. However, the analysis may be readily generalized to the situation where the factfinder is a judge and/ or a question other than guilt is at issue. The first section of this article applies the two models to a simplified situation where the factfinder must evaluate only one item of indisputably accurate testimony. The second section explores complexities that can arise when a case involves two or more items of possibly unreliable evidence

Essays on General Equilibrium with Asymmetric Information

Dissertação de Doutoramento em Economia, área de especialização em Economia, apresentada à Faculdade de Economia da Universidade do Port