Jean-François Mertens

Jean-François Mertens
Born	(1946-03-11)March 11, 1946 Antwerp, Belgium
Died	July 17, 2012(2012-07-17) (aged 66)
Nationality	Belgium
Fields	Game Theory Mathematical economics
Alma mater	Université Catholique de Louvain Docteur ès Sciences 1970
Doctoral advisor	José Paris Jacques Neveu
Influences	Robert Aumann Reinhard Selten John Harsanyi John von Neumann
Influenced	Claude d'Aspremont Bernard De Meyer Amrita Dhillon Francoise Forges Jean Gabszewicz Srihari Govindan Abraham Neyman Anna Rubinchik Sylvain Sorin
Notable awards	Econometric Society Fellow von Neumann Lecturer of Game Theory Society

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, 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 , 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 and Zamir 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.

Repeated games with incomplete information, were pioneered by Aumann and Maschler. Two of Jean-François Mertens contributions to the field are the extensions of repeated two person zero-sum games with incomplete information on both sides for both (1) the type of information available to players and (2) the signalling structure.

In those set-ups Jean-François Mertens provided an extension of the characterization of the minmax and maxmin value for the infinite game in the dependent case with state independent signals. Additionally with Shmuel Zamir, Jean-François Mertens showed the existence of a limiting value. Such a value can be thought either as the limit of the values ${\displaystyle v_{n}}$ of the ${\displaystyle n}$ stage games, as ${\displaystyle n}$ goes to infinity, or the limit of the values ${\displaystyle v_{\lambda }}$ of the ${\displaystyle {\lambda }}$-discounted games, as agents become more patient and ${\displaystyle {\lambda }\to 1}$.

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