The Impartial Observer Theorem of Social Ethics

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument, using a simple mathematical formalism, as well as a conceptual critique of each its premisses.Utilitarianism, Impartiality, Sympathy, Von Neumann- Morgenstern Utility Theory, Subjective Probability.

Non-cooperative game theory

This is the first draft of the entry “Game Theory” to appear in the Sage Handbook of the Philosophy of Social Science (edited by Ian Jarvie & Jesús Zamora Bonilla), Part III, Chapter 16.game theory, epstemic foundations, incomplete information,epstemic foundations, incomplete information

The ignorant observer

We propose an extension of Harsanyi's Impartial Observer Theorem based on the representation of ignorance as the set of all possible probability distributions over individuals. We obtain a characterization of the observer's preferences that, under our most restrictive conditions, is a convex combination of Harsanyi's utilitarian and Rawls' egalitarian criteria. This representation is ethically meaningful, in the sense that individuals' utilities are cardinally measurable and fully comparable. This allows us to conclude that the impartiality requirement cannot be used to decide between Rawls' and Harsanyi's positions.Impartiality, Justice, Utilitarianism, Egalitarianism, Decision under ignorance.

Proper Rationalizability and Belief Revision in Dynamic Games

In this paper we develop an epistemic model for dynamic games in which players may revise their beliefs about the opponents'' preferences (including the opponents'' utility functions) as the game proceeds. Within this framework, we propose a rationalizability concept that is based upon the following three principles: (1) at every instance of the game, a player should believe that his opponents are carrying out optimal strategies, (2) a player should only revise his belief about an opponent''s relative ranking of two strategies if he is certain that the opponent has decided not to choose one of these strategies, and (3) the players'' initial beliefs about the opponents'' utility functions should agree on a given profile u of utility functions. Common belief about these events leads to the concept of persistent rationalizability for the profile u of utility functions. It is shown that for a given profile u of utility functions, every properly rationalizable strategy for ``types with non-increasing type supports'''' is a persistently rationalizable strategy for u. This result implies that persistently rationalizable strategies always exist for all game trees and all profiles of utility functions.mathematical economics;

Half empty, half full and the possibility of agreeing to disagree

Aumann (1976) derives his famous we cannot agree to disagree result under the assumption of rational Bayesian learning. Motivated by psychological evidence against this assumption, we develop formal models of optimistically, resp. pessimistically, biased Bayesian learning within the framework of Choquet expected utility theory. As a key feature of our approach the posterior subjective beliefs do, in general, not converge to "true" probabilities. Moreover, the posteriors of different people can converge to different beliefs even if these people receive the same information. As our main contribution we show that people may well agree to disagree if their Bayesian learning is psychologically biased in our sense. Remarkably, this finding holds regardless of whether people with identical priors apply the same psychologically biased Bayesian learning rule or not. A simple example about the possibility of ex-post trading in a financial asset illustrates our formal findings. Finally, our analysis settles a discussion in the no-trade literature (cf. Dow, Madrigal, and Werlang 1990, Halevy 1998) in that it clarifies that ex-post trade between agents with common priors and identical learning rules is only possible under asymmetric information.Common Knowledge, No-Trade Results, Rational Bayesian Learning, Bounded Rationality, Choquet Expected Utility Theory, Bayesian Updating, Dynamic Inconsistency

Are conventions solutions ? Contrasting visions of the relationship between convention and uncertainty

This paper maps out different conceptions and dynamic accounts of convention developed within game theory, Post Keynesian economics and the économie des conventions. These accounts are distinguished in terms of the way in which they conceive of uncertainty (as probabilistic or radical).