top
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.
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 -