Simple equilibria in finite games with convexity properties

Tadeusz Radzik, and Piotr Więcek. "Simple equilibria in finite games with convexity properties." Applicationes Mathematicae 42.1 (2015): 83-109. <http://eudml.org/doc/280035>.

@article{TadeuszRadzik2015,
abstract = {This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can be seen as discrete counterparts of classical theorems about the existence of pure (or "almost pure") Nash equilibria in continuous concave (convex) games with compact convex spaces of pure strategies. The paper provides many examples illustrating the results presented and ends with four related open problems.},
author = {Tadeusz Radzik, Piotr Więcek},
journal = {Applicationes Mathematicae},
keywords = {noncooperative game; matrix game; bimatrix game; finite game; game on the unit square; saddle point; Nash equilibrium; convex payoff; pure strategy; two-point strategy},
language = {eng},
number = {1},
pages = {83-109},
title = {Simple equilibria in finite games with convexity properties},
url = {http://eudml.org/doc/280035},
volume = {42},
year = {2015},
}

TY - JOUR
AU - Tadeusz Radzik
AU - Piotr Więcek
TI - Simple equilibria in finite games with convexity properties
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 1
SP - 83
EP - 109
AB - This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can be seen as discrete counterparts of classical theorems about the existence of pure (or "almost pure") Nash equilibria in continuous concave (convex) games with compact convex spaces of pure strategies. The paper provides many examples illustrating the results presented and ends with four related open problems.
LA - eng
KW - noncooperative game; matrix game; bimatrix game; finite game; game on the unit square; saddle point; Nash equilibrium; convex payoff; pure strategy; two-point strategy
UR - http://eudml.org/doc/280035
ER -