Limited lookahead has been studied for decades in perfect-information games. This paper initiates a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. The question of how one should act when facing an opponent whose lookahead is limited is studied along multiple axes: lookahead depth, whether the opponent(s), too, have imperfect information, and how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard or NP-hard. We proceed to design algorithms for computing optimal commitment strategies for when the opponent breaks ties 1) favorably, 2) according to a fixed rule, or 3) adversarially. The impact of limited lookahead is then investigated experimentally. The limited-lookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium, but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths. This uncovers a lookahead pathology.

Our work deals with the important problem of globally characterizing truthful mechanisms where players have multi-parameter, additive valuations, like scheduling unrelated machines or additive combinatorial auctions. Very few mechanisms are known for these settings and the question is: Can we prove that no other truthful mechanisms exist? We characterize truthful mechanisms for n players and 2 tasks or items, as either task-independent, or a player-grouping minimizer, a new class of mechanisms we discover, which generalizes affine minimizers. We assume decisiveness, strong monotonicity and that the truthful payments (The (normalized) payments are uniquely determined by the allocation function of the mechanism; thus the assumptions concern properties of the allocation.) are continuous functions of players' bids.

We study the tournament fixing problem (TFP), which asks whether a tournament organizer can rig a single-elimination (SE) tournament such that their favorite player wins, simply by adjusting the initial seeding. Prior results give two perspectives of TFP: on the one hand, deciding whether an arbitrary player can win any SE tournament is known to be NP-complete; on the other hand, there are a number of known conditions, under which a player is guaranteed to win some SE tournament. We extend and connect both these lines of work. We show that for a number of structured variants of the problem, where our player is seemingly strong, deciding whether the player can win any tournament is still NP-complete. Dual to this hardness result, we characterize a new set of sufficient conditions for a player to win a tournament. Further, we give an improved exact algorithm for deciding whether a player can win a tournament.

They concluded that UCT quickly finds Self-play Monte Carlo Tree Search (MCTS) has a good but suboptimal policy, while Outcome Sampling initially been successful in many perfect-information twoplayer learns more slowly but converges to the optimal policy games. Although these methods have been over time. In this paper, we address the question whether the extended to imperfect-information games, so far inability of UCT to converge to a Nash equilibrium can be they have not achieved the same level of practical overcome while retaining UCT's fast initial learning rate. We success or theoretical convergence guarantees focus on the full-game MCTS setting, which is an important as competing methods. In this paper we step towards developing sound variants of online MCTS in introduce Smooth UCT, a variant of the established imperfect-information games. Upper Confidence Bounds Applied to Trees In particular, we introduce Smooth UCT, which combines (UCT) algorithm.

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.

A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely characterize an influence measure: a function that, given a set of classified points, outputs a value for each feature corresponding to its influence in determining the classification outcome. We show that our influence measure takes on an intuitive form when the unknown classifier is linear. Finally, we employ our influence measure in order to analyze the effects of user profiling on Google’s online display advertising.

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.