{"type":"ScholarlyArticle","title":"Efficient Computation of Approximate Equilibria in Discrete Colonel Blotto Games","authors":[{"name":"Dong Quan Vu","slug":"dong-quan-vu","given":"Dong Quan","family":"Vu","affiliation":"Nokia Bell Labs , Nokia Paris-Saclay , 91620 Nozay , France"},{"name":"Patrick Loiseau","slug":"patrick-loiseau","given":"Patrick","family":"Loiseau","affiliation":"Univ. Grenoble Alpes , CNRS , Inria , Grenoble INP , LIG , 38000 Grenoble , France; Max Planck Institute for Software Systems (MPI-SWS) , Saarbrücken , Germany"},{"name":"Alonso Silva","slug":"alonso-silva","given":"Alonso","family":"Silva","affiliation":"Nokia Bell Labs , Nokia Paris-Saclay , 91620 Nozay , France"}],"abstract":"The Colonel Blotto game is a famous game commonly used to model resource allocation problems in many domains ranging from security to advertising. Two players distribute a fixed budget of resources on multiple battlefields to maximize the aggregate value of battlefields they win, each battlefield being won by the player who allocates more resources to it. The continuous version of the game---where players can choose any fractional allocation---has been extensively studied, albeit only with partial results to date. Recently, the discrete version---where allocations can only be integers---started to gain traction and algorithms were proposed to compute the equilibrium in polynomial time; but these remain computationally impractical for large (or even moderate) numbers of battlefields. In this paper, we propose an algorithm to compute very efficiently an approximate equilibrium for the discrete Colonel Blotto game with many battlefields. We provide a theoretical bound on the approximation error as a function of the game's parameters. We also propose an efficient dynamic programming algorithm in order to compute for each game instance the actual value of the error. We perform numerical experiments that show that the proposed strategy provides a fast and good approximation to the equilibrium even for moderate numbers of battlefields","doi":"10.24963/ijcai.2018/72","url":"https://ijcai.org/proceedings/2018/72","pdf":"https://ijcai.org/proceedings/2018/0072.pdf","markdown":"https://ijcai.org/proceedings/2018/72.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/72","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":72,"pages":{"first":519,"last":526},"keywords":["Agent-based and Multi-agent Systems: Noncooperative Games","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Resource Allocation"],"videos":[],"references":[{"position":1,"raw":"[Ahmadinejad et al., 2016] AmirMahdi Ahmadinejad, Sina Dehghani, MohammadTaghi Hajiaghayi, Brendan Lucier, Hamid Mahini, and Saeed Seddighin. 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