Equilibrium computation in resource allocation games

Abstract We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For with singleton strategies player-specific affine cost functions, we devise first polynomial time algorithm computing a pure Nash equilibrium. Our is combinatorial computes exact assuming rational input. The idea to compute an associated integrally-splittable game in which players can only split their demands integral multiples of common packet size. While have been considered literature before, no was known. Also this class, use it as building block our main algorithm. then develop computable transformation mapping competition firm-specific price functions quadratic costs described above. preserves equilibria either and, thus, leads – via equilibria. Finally, analysis implies new bounds on difference between real be seen generalization recent single market oligopolies obtained by Todd (Math Op Res 41(3):1125–1134 2016, 10.1287/moor.2015.0771 ).