Allocation games are coalitional games defined in the literature as a way to analyze fair division problems of indivisible goods. The prototypical solution concepts for them are the Shapley value and the Banzhaf value. Unfortunately, their computation is intractable, formally #P-hard. Motivated by this bad news, structural requirements are investigated which can be used to identify islands of tractability. The main result is that, over the class of allocation games, the Shapley value and the Banzhaf value can be computed in polynomial time when interactions among agents can be formalized as graphs of bounded treewidth. This is shown by means of technical tools that are of interest in their own and that can be used for analyzing different kinds of coalitional games. Tractability is also shown for games where each good can be assigned to at most two agents, independently of their interactions.

We study voting games on binary issues, where voters might hold an objective over some issues at stake, while willing to strike deals on the remaining ones, and can influence one another’s voting decision before the vote takes place. We analyse voters’ rational behaviour in the resulting two-phase game, showing under what conditions undesirable equilibria can be removed as an effect of the pre-vote phase.

The Gibbard-Satterthwaite theorem implies the ubiquity of manipulators — voters who could change the election outcome in their favor by unilaterally modifying their vote. In this paper, we ask what happens if a given profile admits several such voters. We model strategic interactions among Gibbard–Satterthwaite manipulators as a normal-form game. We classify the 2-by-2 games that can arise in this setting for two simple voting rules, namely Plurality and Borda, and study the complexity of determining whether a given manipulative vote weakly dominates truth-telling, as well as existence of Nash equilibria.

Preventing attacks in a computer network is the core problem in network security. We introduce a new game-theoretic model of the interaction between a network administrator who uses limited resource to harden a network and an attacker who follows a multi-stage plan to attack the network. The possible plans of the attacker are compactly represented using attack graphs, while the defender adds fake targets (honeypots) to the network to deceive the attacker. The compact representation of the attacker's strategies presents a computational challenge and finding the best response of the attacker is NP-hard. We present a solution method that first translates an attack graph into an MDP and solves it using policy search with a set of pruning techniques. We present an empirical evaluation of the model and solution algorithms, evaluating scalability, the types of solutions that are generated for realistic cases, and sensitivity analysis.

It is known that Nash equilibria and approximate Nash equilibria not necessarily optimize social optima of bimatrix games. In this paper, we show that for every fixed ε > 0, every bimatrix game (with values in [0, 1]) has an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor, (1 − √1 − ε)2, of the optimum. Furthermore, our result can be made algorithmic in the following sense: for every fixed 0 ≤ ε* < ε, if we can find an ε*-approximate Nash equilibrium in polynomial time, then we can find in polynomial time an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor of the optimum. Our analysis is especially tight in the case when ε ≥ 1/2. In this case, we show that for any bimatrix game there is an ε-approximate Nash equilibrium with constant size support whose social welfare is is at least 2√ε − ε ≥ 0.914 times the optimal social welfare. Furthermore, we demonstrate that our bound for the social welfare is tight, that is, for every ε ≥ 1/2 there is a bimatrix game for which every ε-approximate Nash equilibrium has social welfare at most 2√ε − ε times the optimal social welfare.

A key challenge in solving extensive-form games is dealing with large, or even infinite, action spaces. In games of imperfect information, the leading approach is to find a Nash equilibrium in a smaller abstract version of the game that includes only a few actions at each decision point, and then map the solution back to the original game. However, it is difficult to know which actions should be included in the abstraction without first solving the game, and it is infeasible to solve the game without first abstracting it. We introduce a method that combines abstraction with equilibrium finding by enabling actions to be added to the abstraction at run time. This allows an agent to begin learning with a coarse abstraction, and then to strategically insert actions at points that the strategy computed in the current abstraction deems important. The algorithm can quickly add actions to the abstraction while provably not having to restart the equilibrium finding. It enables anytime convergence to a Nash equilibrium of the full game even in infinite games. Experiments show it can outperform fixed abstractions at every stage of the run: early on it improves as quickly as equilibrium finding in coarse abstractions, and later it converges to a better solution than does equilibrium finding in fine-grained abstractions.

We consider discrete protocols for the classical Steinhaus cake cutting problem. Under mild technical conditions, we show that any deterministic strategy-proof protocol for two agents in the standard Robertson-Webb query model is dictatorial, that is, there is a fixed agent to which the protocol allocates the entire cake. For n > 2 agents, a similar impossibility holds, namely there always exists an agent that gets the empty piece (i.e. no cake). In contrast, we exhibit randomized protocols that are truthful in expectation and compute approximately fair allocations.

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given m random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternation, and strict alternation. We present characterizations of the allocations that result respectively from the classes, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.

We consider the computational complexity of computing welfare maximizing partitions for fractional hedonic games — a natural class of coalition formation games that can be succinctly represented by a graph. For such games, welfare maximizing partitions constitute desirable ways to cluster the vertices of the graph. We present both intractability results and approximation algorithms for computing welfare maximizing partitions.