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首页> 外文期刊>Automatic Control, IEEE Transactions on >Nash Equilibrium Problems With Scaled Congestion Costs and Shared Constraints
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Nash Equilibrium Problems With Scaled Congestion Costs and Shared Constraints

机译：拥挤成本和共享约束的纳什均衡问题

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摘要

We consider a class of convex Nash games where strategy sets are coupled across agents through a common constraint and payoff functions are linked via a scaled congestion cost metric. A solution to a related variational inequality problem provides a set of Nash equilibria characterized by common Lagrange multipliers for shared constraints. While this variational problem may be characterized by a non-monotone map, it is shown to admit solutions, even in the absence of restrictive compactness assumptions on strategy sets. Additionally, we show that the equilibrium is locally unique both in the primal space as well as in the larger primal-dual space. The existence statements can be generalized to accommodate a piecewise-smooth congestion metric while affine restrictions, surprisingly, lead to both existence and global uniqueness guarantees. In the second part of the technical note, we discuss distributed computation of such equilibria in monotone regimes via a distributed iterative Tikhonov regularization (ITR) scheme. Application to a class of networked rate allocation games suggests that the ITR schemes perform better than their two-timescale counterparts.
机译：我们考虑一类凸纳什博弈，其中策略集通过共同的约束跨代理耦合，收益函数通过规模化的拥塞成本度量进行链接。一个相关的变分不等式问题的解决方案提供了一组Nash均衡，其特征是用于共享约束的通用Lagrange乘数。尽管此变分问题可能以非单调映射为特征，但即使在没有策略集的限制性紧凑性假设的情况下，也显示出它可以接受解。此外，我们证明了平衡在原始空间以及较大的原始对偶空间中都是局部唯一的。存在声明可以被概括为适应分段平滑的拥塞度量，而仿射限制令人惊讶地导致存在和全局唯一性保证。在技​​术说明的第二部分中，我们讨论了通过分布式迭代Tikhonov正则化（ITR）方案在单调范围内进行这种平衡的分布式计算。应用于一类网络速率分配博弈表明，ITR方案的性能要优于两个时间尺度的方案。

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