Recently, algorithms for computing game-theoretic solutions have been deployed in real-world security applications, such as the placement of checkpoints and canine units at Los Angeles International Airport. These algorithms assume that the defender (security personnel) can commit to a mixed strategy, a so-called Stackelberg model. As pointed out by Kiekintveld et al. (2009), in these applications, generally, multiple resources need to be assigned to multiple targets, resulting in an exponential number of pure strategies for the defender. In this paper, we study how to compute optimal Stackelberg strategies in such games, showing that this can be done in polynomial time in some cases, and is NP-hard in others.

Many computational problems in game theory, such as finding Nash equilibria, are algorithmically hard to solve. This limitation forces analysts to limit attention to restricted subsets of the entire strategy space. We develop algorithms to identify rationally closed subsets of the strategy space under given size constraints. First, we modify an existing family of algorithms for rational closure in two-player games to compute a related rational closure concept, called formations , for n -player games. We then extend these algorithms to apply in cases where the utility function is partially specified, or there is a bound on the size of the restricted profile space. Finally, we evaluate the performance of these algorithms on a class of random games.

Security games, and important class of Stackelberg games, are used in deployed decision-support tools in use by LAX police and the Federal Air Marshals Service. The algorithms used to solve these games find optimal randomized schedules to allocate security resources for infrastructure protection. Unfortunately, the state of the art algorithms either fail to scale or to provide a correct solution for large problems with arbitrary scheduling constraints. We introduce ASPEN, a branch-and-price approach that overcomes these limitations based on two key contributions: (i) A column-generation approach that exploits a novel network flow representation, avoiding a combinatorial explosion of schedule allocations; (ii) A branch-and-bound algorithm that generates bounds via a fast algorithm for solving security games with relaxed scheduling constraints. ASPEN is the first known method for efficiently solving massive security games with arbitrary schedules.

Intentions have been widely studied in AI, both in the context of decision-making within individual agents and in multi-agent systems. Work on intentions in multi-agent systems has focused on joint intention models, which characterise the mental state of agents with a shared goal engaged in teamwork. In the absence of shared goals, however, intentions play another crucial role in multi-agent activity: they provide a basis around which agents can mutually coordinate activities. Models based on shared goals do not attempt to account for or explain this role of intentions. In this paper, we present a formal model of multi-agent systems in which belief-desire-intention agents choose their intentions taking into account the intentions of others. To understand rational mental states in such a setting, we formally define and investigate notions of multi-agent intention equilibrium, which are related to equilibrium concepts in game theory.

We consider problems where several individuals each need to make a yes/no choice regarding a number of issues and these choices then need to be aggregated into a collective choice. Depending on the application at hand, different combinations of yes/no may be considered rational. We can describe such rationality assumptions in terms of a propositional formula. The question then arises whether or not a given aggregation procedure will lift the rationality assumptions from the individual to the collective level, i.e., whether the collective choice will be rational whenever all individual choices are. To address this question, for each of a number of simple fragments of the language of propositional logic, we provide an axiomatic characterisation of the class of aggregation procedures that will lift all rationality assumptions expressible in that fragment.

We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied by Conitzer, Rognlie, and Xia, and the distance rationalizability (DR) framework of Elkind, Faliszewski, and Slinko. The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.

We consider the problem of manipulating elections via cloning candidates. In our model, a manipulator can replace each candidate c by one or more clones, i.e., new candidates that are so similar to  c  that each voter simply replaces  c  in his vote with the block of  c 's clones. The outcome of the resulting election may then depend on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of prominent voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with the related problem of control via adding candidates.

In some voting situations, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. Focusing on scoring rules, we give complexity results for the above possible winner problem.

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of cutting a cake in a way that is truthful and fair, where for the first time our notion of dominant strategy truthfulness is the ubiquitous one in social choice and computer science. We design both deterministic and randomized cake cutting algorithms that are truthful and fair under different assumptions with respect to the valuation functions of the agents.

We develop an efficient algorithm for computing pure strategy Nash equilibria that satisfy various criteria (such as the utilitarian or Nash-Bernoulli social welfare functions) in games with sparse interaction structure. Our algorithm, called Valued Nash Propagation (VNP), integrates the optimisation problem of maximising a criterion with the constraint satisfaction problem of finding a game's equilibria to construct a criterion that defines a c -semiring. Given a suitably compact game structure, this criterion can be efficiently optimised using message-passing. To this end, we first show that VNP is complete in games whose interaction structure forms a hypertree. Then, we go on to provide theoretic and empirical results justifying its use on games with arbitrary structure; in particular, we show that it computes the optimum >82% of the time and otherwise selects an equilibrium that is always within 2% of the optimum on average.