An FPTAS for Computing Nash Equilibrium in Resource Graph Games

Hau Chan, Albert Xin Jiang
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We consider the problem of computing a mixed-strategy Nash equilibrium (MSNE) in resource graph games (RGGs), a compact representation for games with an exponential number of strategies. In an RGG, each player's pure strategy is a subset of resources, represented by a binary vector, and her pure strategy set is represented compactly using a set of linear inequality constraints. Given the pure strategies of the players, each player's utility depends on the resource graph and the numbers of times
more » ... the neighboring resources are used. RGGs are general enough to capture a wide variety of games studied in literature, including congestion games and security games.In this paper, we provide the first Fully Polytnomial Time Approximation Scheme (FPTAS) for computing an MSNE in any symmetric multilinear RGG where its constraint moralized resource graph (a graph formed between the moralized resource graph and the constraints defining the strategy polytope) has bounded treewidth. Our FPTAS can be generalized to compute optimal MSNE, and to games with a constant number of player types. As a consequence, our FPTAS provides new approximation results for security games, network congestion games, and bilinear games.
doi:10.24963/ijcai.2018/21 dblp:conf/ijcai/ChanJ18 fatcat:5hs7oh44n5aolnztwrbe6mz4ea