Generalized Nash equilibrium problems are single-shot Nash equilibrium problems, whereby the decisions of all agents are coupled through a shared constraint. Such games are generally challenging to solve as they might give rise to a very large number of solutions. In this context, spanning many equilibria can be interesting to provide meaningful interpretations. In the literature, to compute equilibria, equilibrium problems are classically reformulated as optimization problems, potential games, relaxed and extended games. Applications of these reformulations to an economic dispatch problem under perfect and imperfect competition are provided. Unfortunately, these approaches only enable to describe a very limited part of the equilibrium set. To fill that gap, relying on normalized Nash equilibrium as solution concept, we provide a parametrized decomposition algorithm inspired by the Inexact-ADMM to span many more equilibrium points. Complexifying the setting, we consider an information structure in which the agents can withhold some local information from sensitive data, resulting in private coupling constraints. The convergence of the algorithm and deviations in the players’ strategies at equilibrium are formally analyzed. In addition, the algorithm can be used to coordinate the agents on one specific equilibrium with desirable properties at the system level. The coordination game is formulated as a principal-agent problem, and a procedure is detailed to compute the equilibrium that minimizes a secondary cost function capturing system-level properties. Finally, the Inexact-ADMM is applied to a cellular resource allocation problem, exhibiting better convergence rate than vanilla ADMM, and to compute equilibria that achieve both system-level efficiency and maximum fairness.

广义纳什均衡问题是单次纳什均衡问题，其中所有代理的决策通过共享约束耦合。此类博弈通常难以解决，因为它们可能会产生大量解决方案。在这种情况下，跨越许多平衡点可以提供有意义的解释。在文献中，为了计算均衡，均衡问题被经典地重新表述为优化问题、潜在博弈、松弛和扩展博弈。提供了这些重新公式在完全竞争和不完全竞争下的经济调度问题的应用。不幸的是，这些方法只能描述均衡集的非常有限的一部分。为了填补这个空白，依靠归一化纳什均衡作为解决方案的概念，我们提供了一种受 Inexact-ADMM 启发的参数化分解算法来跨越更多的平衡点。使设置复杂化，我们考虑一种信息结构，其中代理可以从敏感数据中保留一些本地信息，从而导致私有耦合约束。对算法的收敛性和均衡时参与者策略的偏差进行了形式化分析。此外，该算法可用于在一个特定的平衡上协调代理与系统级别的所需属性。协调博弈被公式化为委托代理问题，并详细描述了计算平衡的过程，该过程使捕获系统级属性的二级成本函数最小化。最后，将 Inexact-ADMM 应用于蜂窝资源分配问题，