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Jean-François Mertens
Jean-François Mertens (11 March 1946 – 17 July 2012) was a Belgian game theorist and mathematical economist.〔
Jean-François Mertens made some contributions to probability theory and published articles on elementary topology,〔Mertens, Jean-François, 1992. "Essential Maps and Manifolds," Proceedings of the American Mathematical Society, 115(2), 1992.〕〔Mertens, Jean-François, 2003. "Localization of the Degree on Lower-dimensional Sets," International Journal of Game Theory, 32: 379–386. ()〕 but he was mostly active in economic theory. In particular, he contributed to order-book of market games, cooperative games, noncooperative games, repeated games, epistemic models of strategic behavior, and refinements of Nash equilibrium (see solution concept).
In cooperative game theory he contributed to the solution concepts called the core and the Shapley value. Regarding repeated games and stochastic games, Mertens 1982〔Mertens, Jean-François, 1982. "Repeated Games: An Overview of the Zero-sum Case," Advances in Economic Theory, edited by W. Hildenbrand, Cambridge University Press, London and New York.〕 and 1986〔Mertens, Jean-François, 1986. "Repeated Games," International Congress of Mathematicians. ()〕 survey articles, and his 1994〔Mertens, Jean-François, and Sylvain Sorin, and Shmuel Zamir, 1994. "Repeated Games," Parts A, B, C; Discussion Papers 1994020, 1994021, 1994022; Université Catholique de Louvain, Center for Operations Research and Econometrics (CORE). () ()〕 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions.
==Epistemic models==
Mertens and Zamir〔Mertens, Jean-François, and Shmuel Zamir, 1985. "Formulation of Bayesian analysis for games with incomplete information," International Journal of Game Theory, 14(1): 1–29. ()〕〔An exposition for the general reader is by Shmuel Zamir, 2008: "Bayesian games: Games with incomplete information," Discussion Paper 486, Center for Rationality, Hebrew University.()〕 implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types. They constructed a universal space of types in which, subject to specified consistency conditions, each type corresponds to the infinite hierarchy of his probabilistic beliefs about others' probabilistic beliefs. They also showed that any subspace can be approximated arbitrarily closely by a finite subspace, which is the usual tactic in applications.〔A popular version in the form of a sequence of dreams about dreams appears in the film "Inception." () The logical aspects of players' beliefs about others' beliefs is related to players' knowledge about others' knowledge; see Prisoners and hats puzzle for an entertaining example, and Common knowledge (logic) for another example and a precise definition.〕
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