Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, and Tadeusz Radzik. "Equilibria in constrained concave bimatrix games." Applicationes Mathematicae 40.2 (2013): 167-182. <http://eudml.org/doc/279926>.

@article{WojciechPołowczuk2013,
abstract = {We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete counterpart of the Debreu Theorem about the existence of pure noncooperative equilibria in n-person constrained infinite games. The second one completes the classical theorem on the existence of Nash equilibria in bimatrix games. A wide discussion of the results is given.},
author = {Wojciech Połowczuk, Tadeusz Radzik},
journal = {Applicationes Mathematicae},
keywords = {constrained games; bimatrix games; Debreu theorem; games with infinite payoffs; Nash equilibria},
language = {eng},
number = {2},
pages = {167-182},
title = {Equilibria in constrained concave bimatrix games},
url = {http://eudml.org/doc/279926},
volume = {40},
year = {2013},
}

TY - JOUR
AU - Wojciech Połowczuk
AU - Tadeusz Radzik
TI - Equilibria in constrained concave bimatrix games
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 2
SP - 167
EP - 182
AB - We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete counterpart of the Debreu Theorem about the existence of pure noncooperative equilibria in n-person constrained infinite games. The second one completes the classical theorem on the existence of Nash equilibria in bimatrix games. A wide discussion of the results is given.
LA - eng
KW - constrained games; bimatrix games; Debreu theorem; games with infinite payoffs; Nash equilibria
UR - http://eudml.org/doc/279926
ER -