论文标题
半决赛游戏
Semidefinite games
论文作者
论文摘要
我们通过在真实对称矩阵的空间中替换了一个积极的半决赛锥体，从而介绍和研究了半决赛游戏类，该类别概括了bimatrix游戏和有限的$ n $ person游戏。 对于半决赛两人零和游戏，我们表明可以通过半决赛编程来计算最佳策略。此外，我们表明，两人半场零和游戏几乎等同于半决赛编程，从而概括了丹齐格（Dantzig）在Bimatrix游戏和线性编程几乎等同的结果上的结果。 对于一般的两人半场半场比赛，我们证明了纳什均衡的频谱表征。此外，我们提供了许多Nash Equilibria的半决赛游戏的结构。特别是，我们提供了半场游戏的结构，其纳什均衡的连接组件数量超过了Bimatrix游戏中许多Nash Equilibria的长期最著名的结构，该结构是由冯·斯坦格尔（Von Stengel）于1999年提出的。
We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space of real symmetric matrices. For semidefinite two-player zero-sum games, we show that the optimal strategies can be computed by semidefinite programming. Furthermore, we show that two-player semidefinite zero-sum games are almost equivalent to semidefinite programming, generalizing Dantzig's result on the almost equivalence of bimatrix games and linear programming. For general two-player semidefinite games, we prove a spectrahedral characterization of the Nash equilibria. Moreover, we give constructions of semidefinite games with many Nash equilibria. In particular, we give a construction of semidefinite games whose number of connected components of Nash equilibria exceeds the long standing best known construction for many Nash equilibria in bimatrix games, which was presented by von Stengel in 1999.
