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Models and solutions of strategic resource allocation problems : approximate equilibrium and online learning in Blotto games

Abstract : Resource allocation problems are broadly defined as situations involving decisions on distributing a limited budget of resources in order to optimize an objective. In particular, many of them involve interactions between competitive decision-makers which can be well captured by game-theoretic models. In this thesis, we choose to investigate resource allocation games. We primarily focus on the Colonel Blotto game (CB game). In the CB game, two competitive players, each having a fixed budget of resources, simultaneously distribute their resources toward n battlefields. Each player evaluates each battlefield with a certain value. In each battlefield, the player who has the higher allocation wins and gains the corresponding value while the other loses and gains zero. Each player's payoff is her aggregate gains from all the battlefields. First, we model several prominent variants of the CB game and their extensions as one-shot complete-information games and analyze players' strategic behaviors. Our first main contribution is a class of approximate (Nash) equilibria in these games for which we prove that the approximation error can be well-controlled. Second, we model resource allocation games with combinatorial structures as online learning problems to study situations involving sequential plays and incomplete information. We make a connection between these games and online shortest path problems (OSP). Our second main contribution is a set of novel regret-minimization algorithms for generic instances of OSP under several restricted feedback settings that provide significant improvements in regret guarantees and running time in comparison with existing solutions.
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Submitted on : Sunday, December 26, 2021 - 1:01:11 AM
Last modification on : Thursday, March 17, 2022 - 5:05:40 PM
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Dong Quan Vu. Models and solutions of strategic resource allocation problems : approximate equilibrium and online learning in Blotto games. Operations Research [cs.RO]. Sorbonne Université, 2020. English. ⟨NNT : 2020SORUS120⟩. ⟨tel-03502593⟩



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