Cifre PhD Proposal: “Learning in Blotto games and applications to modeling attention in social networks”

The Colonel Blotto game is a fundamental model of strategic resource allocation: two players allocate a fixed amount of resources to a fixed number of battlefields with given values, each battlefield is then won by the player who allocated more resources to it, and each player maximizes the aggregate value of battlefields he wins. It recently gained a very high interest in theoretical and applied research communities because of its potential to model many important problems of resource allocation in strategic settings ranging from international war to computer security. In particular, it provides a good model of competition for attention of users in social networks. There, battlefields correspond to users and their values correspond to the value of convincing the users (e.g., in advertisement, it would be the value of the product bought by the user). Theoretical solutions of the Colonel Blotto game could therefore enable important progresses in designing strategies to allocate resources optimally to capture the attention of users in a social network, a topic of high importance in the online world with applications for instance to advertisement campaigns or information propagation. Applications of the Colonel Blotto game, however, have remained limited so far mostly due to the lack of solutions of the game in realistic cases. Indeed, although it was originally proposed by Borel in 1921 [2], the first Nash equilibrium solution of the game was given in 1950 [6] in a simple case (2 or 3 battlefields). In 2006, a Nash equilibrium solution was given for an arbitrary number of battlefields [9] (see also a survey in [10]), but only if all battlefields have the same value, which is not realistic in applications. In our recent work, we proposed first ideas towards a Nash equilibrium solution for arbitrary battlefields values [11], and towards a Nash equilibrium solution of the Blotto