A paper by Deng and Conitzer in AAAI'17 introduces disarmament games, in which players alternatingly commit not to play certain pure strategies. However, in practice, disarmament usually does not consist in removing a strategy, but rather in removing a resource (and doing so rules out all the strategies in which that resource is used simultaneously). In this paper, we introduce a model of disarmament games in which resources, rather than strategies, are removed. We prove NP-completeness of several formulations of the problem of achieving desirable outcomes via disarmament. We then study the case where resources can be fractionally removed, and prove a result analogous to the folk theorem that all desirable outcomes can be achieved. We show that we can approximately achieve any desirable outcome in a polynomial number of rounds, though determining whether a given outcome can be obtained in a given number of rounds remains NP-complete.

Much recent work in the AI community concerns algorithms for computing optimal mixed strategies to commit to, as well as the deployment of such algorithms in real security applications. Another possibility is to commit not to play certain actions. If only one player makes such a commitment, then this is generally less powerful than completely committing to a single mixed strategy. However, if players can alternatingly commit not to play certain actions and thereby iteratively reduce their strategy spaces, then desirable outcomes can be obtained that would not have been possible with just a single player committing to a mixed strategy. We refer to such a setting as a disarmament game. In this paper, we study disarmament for two-player normal-form games. We show that deciding whether an outcome can be obtained with disarmament is NP-complete (even for a fixed number of rounds), if only pure strategies can be removed. On the other hand, for the case where mixed strategies can be removed, we provide a folk theorem that shows that all desirable utility profiles can be obtained, and give an efficient algorithm for (approximately) obtaining them.