当前位置: 首页 > 科学研究 > 学术交流 > 正文
学术交流

Two-Stage Quadratic Games under Uncertainty and their Solution by Progressive Hedging Algorithms

2019-09-02 09:53

报告人: 张敏

报告人单位: 中国科学院新疆生态与地理研究所

时间: 2019-09-06 10:30-11:30

地点: 卫津路校区14号楼202教

开始时间: 10:30

报告人简介: 副研究员

年: 2019

日月: 09.06

A model of a two-stage N-person noncooperative game under uncertainty is studied, in which at the first stage each player solves a quadratic program parameterized by other players' decisions and then at the second stage the player solves a recourse quadratic program parameterized by the realization of a random vector, the second-stage decisions of other players, and the first-stage decisions of all players. The problem of finding a Nash equilibrium of this game is shown to be equivalent to a stochastic linear complementarity problem. A linearly convergent progressive hedging algorithm is proposed for finding a Nash equilibrium if the resulting complementarity problem is monotone. For the nonmonotone case, it is shown that, as long as the complementarity problem satisfies an additional elicitability condition, the progressive hedging algorithm can be modified to find a local Nash equilibrium at a linear rate. The elicitability condition is reminiscent of the sufficient second-order optimality condition in nonlinear programming. Various numerical experiments indicate that the progressive hedging algorithms are efficient for mid-sized problems. In particular, the numerical results include a comparison with the best response method that is commonly adopted in the literature.

联系我们

地址:天津市海河教育园区雅观路135号32号教学楼,300350
邮箱: maths@tju.edu.cn
电话:+86(0)22 27402850
传真:+86(0)22 27402850

扫码关注学院最新动态