Jean-François Mertens

Regarding repeated games and stochastic games, Mertens 1982 and 1986 survey articles, and his 1994 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions. Mertens also made contributions to probability theory and published articles on elementary topology.

Stochastic games were introduced by Lloyd Shapley in 1953. The first paper studied the discounted two-person zero-sum stochastic game with finitely many states and actions and demonstrates the existence of a value and stationary optimal strategies. The study of the undiscounted case evolved in the following three decades, with solutions of special cases by Blackwell and Ferguson in 1968 and Kohlberg in 1974. The existence of an undiscounted value in a very strong sense, both a uniform value and a limiting average value, was proved in 1981 by Jean-François Mertens and Abraham Neyman. The study of the non-zero-sum with a general state and action spaces attracted much attention, and Mertens and Parthasarathy proved a general existence result under the condition that the transitions, as a function of the state and actions, are norm continuous in the actions.

A social welfare function (SWF) maps profiles of individual preferences to social preferences over a fixed set of alternatives. In a seminal paper Arrow (1950) showed the famous "Impossibility Theorem", i.e. there does not exist an SWF that satisfies a very minimal system of axioms: Unrestricted Domain, Independence of Irrelevant Alternatives, the Pareto criterion and Non-dictatorship. A large literature documents various ways to relax Arrow's axioms to get possibility results. Relative Utilitarianism (RU) (Dhillon and Mertens, 1999) is a SWF that consists of normalizing individual utilities between 0 and 1 and adding them, and is a "possibility" result that is derived from a system of axioms that are very close to Arrow's original ones but modified for the space of preferences over lotteries. Unlike classical Utilitarianism, RU does not assume cardinal utility or interpersonal comparability. Starting from individual preferences over lotteries, which are assumed to satisfy the von-Neumann–Morgenstern axioms (or equivalent), the axiom system uniquely fixes the interpersonal comparisons. The theorem can be interpreted as providing an axiomatic foundation for the "right" interpersonal comparisons, a problem that has plagued social choice theory for a long time. The axioms are:

Jean-François Mertens (11 March 1946 – 17 July 2012) was a Belgian game theorist and mathematical economist.