Jean-François Mertens

Equilibria for discounted stochastic games

We prove the existence of subgame-perfect equilibria for discounted stochastic games with general state and action sets, using minimal assumptions(measurability as a function of states, and for each fixed state, compactness of action sets and continuity on those) expect for the rather strong assumption that the transition probabilities are norm-continuous functions of the actions.

The Shapley value in the non-differentiable case

The Shapley value is shown to exist even when there are essential non differentiabilities on the diagonal.

Nonzero-sum stochastic games

Nonzero-sum discounted stochastic games have equilibrium strategies when the state space is uncountable.

Minmax and maxmin of repeated games with incomplete information

AbstractFor a class of 2-Person 0-sum repeated games with incomplete information,Aumann/Masch1er [1967] andStearns [1967] have given a necessary and sufficient condition for the existence of v∞ (the value of the infinitely repeated game).Mertens/Zamir [1971] andMertens [1971/72] have given the formula (and thus proved the existence) of

Absorbing Games with Compact Action Spaces

\mathop {\lim }\limits_{n \to \infty }

The speed of convergence in repeated games with incomplete information on one side

vn, the limit of the values of the games withn repetitions, for a much larger class of games than that treated byAumann/Maschler andSteams. In this paper we extend the Aumann-Maschler-Stearns results to the larger family of games studied byMertens [1971/72].

A note on the characteristic function of supergames

Two examples of strategic equilibrium are given. The first example is a two-person game with a unique dominant strategy for each player where the dominant strategy equilibrium is not extensive form perfect. It is argued that the concept of quasi-perfect equilibria may be superior to that of perfect equilibria. The second example is a two-person game with perfect information, a unique subgame perfect equilibrium, and a unique stable set, but where the latter allows different outcomes. Journal of Economic Literature Classification Number: C72.

Correlated Effectivity Functions

We prove that games with absorbing states with compact action sets have a value.(This abstract was borrowed from another version of this item.)