We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either games and, thus, leads -- via our first algorithm -- to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd [2016].

翻译：我们研究两种经典资源分配游戏的平衡计算问题:原子分裂式拥堵游戏和多市场Cournot 寡头垄断游戏。对于使用单顿战略和针对玩家的折叠式成本函数的原子分裂式拥堵游戏,我们设计了第一个计算纯纳什均衡的多元时间算法。我们的算法是组合式的,并计算了假定合理投入的准确平衡。我们的想法是计算一个相关的可整体分割单吨拥堵游戏的平衡,在这个游戏中,玩家只能用共同包大小的组合组合组合来分割他们的需求。虽然在文献中曾经考虑过一体化游戏,但是没有已知的单一时间算法计算平衡。同样,我们设计了第一个多元时间算法,并将它作为我们主要算法的建筑块块。然后我们开发了一个多元时间可比较式折算法,绘制一个多市场Cournot竞争游戏,配有上述公司特有的近价函数和四分解式与相关的原子分解式拥堵游戏之间的成本。在文献中保留了两种游戏中的平衡,因此,导致最近的平衡。我们的第一个混合时间算法是我们最后的定式算法,它意味着我们最后的固定的固定的固定定局。