@techreport{834facb88e334046a452715719ef244e,
title = "Entangled Equilibria for Bimatrix Games",
abstract = "This paper proposes a new refinement of Nash equilibria. Where most existing refinements are based on a thought experiment which imposes a certain {\textquoteleft}imperfection{\textquoteright} on the choices of individual players, we consider a thought experiment in which the imperfections occur on a global, {\textquoteleft}system{\textquoteright} level. If an imperfection occurs, the actions as prescribed by the players{\textquoteright} strategic choices are blocked for all players simultaneously, rather than for individual players. The idea behind this is that after players submit their strategies, some entity or system converts these strategies into actions leading to payoffs. In this new thought experiment, with small probability, this entity makes an error that blocks the chosen combination of actions instead of implementing them, and chooses a random combination of the remaining actions. We refer to an equilibrium based on this thought experiment as an entangled equilibrium. Focusing on bimatrix games, we show that the set of entangled equilibria is non-empty and the union of a finite number of polytopes. Finally, we discuss a geometriccombinatorial approach to efficiently determine all entangled equilibria of 2 × n bimatrix games, gaining practical insight in the exact workings of the underlying thought experiment.",
keywords = "entangled equilibrium, Nash equilibrium refinement, bimatrix game",
author = "{van Beek}, Andries and Peter Borm",
note = "CentER Discussion Paper Nr. 2024-016",
year = "2024",
month = jul,
day = "10",
language = "English",
volume = "2024-016",
series = "CentER Discussion Paper",
publisher = "CentER, Center for Economic Research",
type = "WorkingPaper",
institution = "CentER, Center for Economic Research",
}