In this short note, we investigate the framework where agents or players have some uncertainties upon their payoffs or losses, the behavior (or the type, number or any other characteristics) of other players. More specifically, we introduce an extension of the concept of Nash equilibria that generalize different solution concepts called by their authors, and depending on the context, either as robust, ambiguous, partially specified or with uncertainty aversion. We provide a simple necessary and sufficient condition that guarantees its existence and we show that it is actually a selection of conjectural (or self-confirming) equilibria. We finally conclude by how this concept can and should be defined in games with partial monitoring in order to preserve existence properties.
Keywords: robust games, robust Nash equilibria, uncertainties, partial monitoring, conjectural equilibria
@article{RO_2014__48_3_365_0,
author = {Perchet, Vianney},
title = {A note on robust {Nash} equilibria with uncertainties},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {365--371},
year = {2014},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
doi = {10.1051/ro/2014001},
mrnumber = {3264383},
zbl = {1296.91013},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2014001/}
}
TY - JOUR AU - Perchet, Vianney TI - A note on robust Nash equilibria with uncertainties JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 365 EP - 371 VL - 48 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2014001/ DO - 10.1051/ro/2014001 LA - en ID - RO_2014__48_3_365_0 ER -
%0 Journal Article %A Perchet, Vianney %T A note on robust Nash equilibria with uncertainties %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 365-371 %V 48 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2014001/ %R 10.1051/ro/2014001 %G en %F RO_2014__48_3_365_0
Perchet, Vianney. A note on robust Nash equilibria with uncertainties. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 365-371. doi: 10.1051/ro/2014001
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