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.

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.

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.

In cooperative multiagent systems an alternative that maximizes the social welfare — the sum of utilities — can only be selected if each agent reports its full utility function. This may be infeasible in environments where communication is restricted. Employing a voting rule to choose an alternative greatly reduces the communication burden, but leads to a possible gap between the social welfare of the optimal alternative and the social welfare of the one that is ultimately elected. Procaccia and Rosenschein have introduced the concept of distortion to quantify this gap. In this paper, we present the notion of embeddings into voting rules: functions that receive an agent's utility function and return the agent's vote. We establish that very low distortion can be obtained using randomized embeddings, especially when the number of agents is large compared to the number of alternatives. We investigate our ideas in the context of three prominent voting rules with low communication costs: Plurality, Approval, and Veto. Our results arguably provide a compelling reason for employing voting in cooperative multiagent systems.

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in repeated games with discounting. The process starts with a single hypercube approximation of the set of SPE payoff profiles. Then the initial hypercube is gradually partitioned on to a set of smaller adjacent hypercubes, while those hypercubes that cannot contain any SPE point are gradually withdrawn. Whether a given hypercube can contain an equilibrium point is verified by an appropriate mixed integer program. A special attention is paid to the question of extracting players' strategies and their representability in form of finite automata.

For many election systems, bribery (and related) attacks have been shown NP-hard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central political-science model of electorates — single-peaked preferences — those protections vanish. By using single-peaked preferences to simplify combinatorial covering challenges, we show that NP-hard bribery problems — including those for Kemeny and Llull elections- — fall to polynomial time. By using single-peaked preferences to simplify combinatorial partition challenges, we show that NP-hard partition-of-voters problems fall to polynomial time. We furthermore show that for single-peaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ 2 p -complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in single-peaked electorates.

Connecting between standard AI planning constructs and a classical cooperative model of transferable-utility coalition games, we introduce the notion of transferable-utility (TU) planning games. The key representational property of these games is that coalitions are valued implicitly based on their ability to carry out efficient joint plans. On the side of the expressiveness, we show that existing succinct representations of monotonic TU games can be efficiently compiled into TU planning games. On the side of computation, TU planning games allow us to provide some of the strongest to date tractability results for core-existence and core-membership queries in succinct TU coalition games.

We consider optimizing the coalition structure in Coalitional Skill Games (CSGs), a succinct representation of coalitional games. In CSGs, the value of a coalition depends on the tasks its members can achieve. The tasks require various skills to complete them, and agents may have different skill sets. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that CSGs can represent any characteristic function, and consider optimal coalition structure generation in this representation. We provide hardness results, showing that in general CSGs, as well as in very restricted versions of them, computing the optimal coalition structure is hard. On the positive side, we show that the problem can be reformulated as constraint satisfaction on a hyper graph, and present an algorithm that finds the optimal coalition structure in polynomial time for instances with bounded tree-width and number of tasks.

Previous work on machine scheduling has considered the case of agents who control the scheduled jobs and attempt to minimize their own completion time. We argue that in cloud and grid computing settings, different machines cannot be considered to be fully cooperative as they may belong to competing economic entities, and that agents can easily move their jobs between competing providers. We therefore consider a setting in which the machines are also controlled by selfish agents, and attempt to maximize their own gains by strategically selecting their scheduling policy. We analyze the equilibria that arise due to competition in this 2-sided setting. In particular, not only do we require that the jobs will be in equilibrium with one another, but also that the schedulers' policies will be in equilibrium. We also consider different mixtures of classic deterministic scheduling policies and random scheduling policies.