arXiv subjects

Nicola Gatti

Publications and source records attributed to Nicola Gatti.

At least 73 records · Page 4Linked to original sources

arXiv2020

Online Posted Pricing with Unknown Time-Discounted Valuations

We study the problem of designing posted-price mechanisms in order to sell a single unit of a single item within a finite period of time. Motivated by real-world problems, such as, e.g., long-term rental of rooms and apartments, we assume that customers arrive online according to a Poisson process, and their valuations are drawn from an unknown distribution and discounted over time. We evaluate our mechanisms in terms of competitive ratio, measuring the worst-case ratio between their revenue and that of an optimal mechanism that knows the distribution of valuations. First, we focus on the identical valuation setting, where all the customers value the item for the same amount. In this setting, we provide a mechanism M_c that achieves the best possible competitive ratio, discussing its dependency on the parameters in the case of linear discount. Then, we switch to the random valuation setting. We show that, if we restrict the attention to distributions of valuations with a monotone hazard rate, then the competitive ratio of M_c is lower bounded by a strictly positive constant that does not depend on the distribution. Moreover, we provide another mechanism, called M_pc, which is defined by a piecewise constant pricing strategy and reaches performances comparable to those obtained with M_c. This mechanism is useful when the seller cannot change the posted price too often. Finally, we empirically evaluate the performances of our mechanisms in a number of experimental settings.

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arXiv2020

Faster Algorithms for Optimal Ex-Ante Coordinated Collusive Strategies in Extensive-Form Zero-Sum Games

We focus on the problem of finding an optimal strategy for a team of two players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate before the game. In that setting, it is known that the best the team can do is sample a profile of potentially randomized strategies (one per player) from a joint (a.k.a. correlated) probability distribution at the beginning of the game. In this paper, we first provide new modeling results about computing such an optimal distribution by drawing a connection to a different literature on extensive-form correlation. Second, we provide an algorithm that computes such an optimal distribution by only using profiles where only one of the team members gets to randomize in each profile. We can also cap the number of such profiles we allow in the solution. This begets an anytime algorithm by increasing the cap. We find that often a handful of well-chosen such profiles suffices to reach optimal utility for the team. This enables team members to reach coordination through a relatively simple and understandable plan. Finally, inspired by this observation and leveraging theoretical concepts that we introduce, we develop an efficient column-generation algorithm for finding an optimal distribution for the team. We evaluate it on a suite of common benchmark games. It is three orders of magnitude faster than the prior state of the art on games that the latter can solve and it can also solve several games that were previously unsolvable.

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arXiv2020

Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive

Persuasion studies how an informed principal may influence the behavior of agents by the strategic provision of payoff-relevant information. We focus on the fundamental multi-receiver model by Arieli and Babichenko (2019), in which there are no inter-agent externalities. Unlike prior works on this problem, we study the public persuasion problem in the general setting with: (i) arbitrary state spaces; (ii) arbitrary action spaces; (iii) arbitrary sender's utility functions. We fully characterize the computational complexity of computing a bi-criteria approximation of an optimal public signaling scheme. In particular, we show, in a voting setting of independent interest, that solving this problem requires at least a quasi-polynomial number of steps even in settings with a binary action space, assuming the Exponential Time Hypothesis. In doing so, we prove that a relaxed version of the Maximum Feasible Subsystem of Linear Inequalities problem requires at least quasi-polynomial time to be solved. Finally, we close the gap by providing a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, in specific settings, yields a QPTAS.

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arXiv2020

Online Joint Bid/Daily Budget Optimization of Internet Advertising Campaigns

Pay-per-click advertising includes various formats (\emph{e.g.}, search, contextual, social) with a total investment of more than 200 billion USD per year worldwide. An advertiser is given a daily budget to allocate over several, even thousands, campaigns, mainly distinguishing for the ad, target, or channel. Furthermore, publishers choose the ads to display and how to allocate them employing auctioning mechanisms, in which every day the advertisers set for each campaign a bid corresponding to the maximum amount of money per click they are willing to pay and the fraction of the daily budget to invest. In this paper, we study the problem of automating the online joint bid/daily budget optimization of pay-per-click advertising campaigns over multiple channels. We formulate our problem as a combinatorial semi-bandit problem, which requires solving a special case of the Multiple-Choice Knapsack problem every day. Furthermore, for every campaign, we capture the dependency of the number of clicks on the bid and daily budget by Gaussian Processes, thus requiring mild assumptions on the regularity of these functions. We design four algorithms and show that they suffer from a regret that is upper bounded with high probability as O(sqrt{T}), where T is the time horizon of the learning process. We experimentally evaluate our algorithms with synthetic settings generated from real data from Yahoo!, and we present the results of the adoption of our algorithms in a real-world application with a daily average spent of 1,000 Euros for more than one year.

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arXiv2020

Election Manipulation on Social Networks: Seeding, Edge Removal, Edge Addition

We focus on the election manipulation problem through social influence, where a manipulator exploits a social network to make her most preferred candidate win an election. Influence is due to information in favor of and/or against one or multiple candidates, sent by seeds and spreading through the network according to the independent cascade model. We provide a comprehensive study of the election control problem, investigating two forms of manipulations: seeding to buy influencers given a social network, and removing or adding edges in the social network given the seeds and the information sent. In particular, we study a wide range of cases distinguishing for the number of candidates or the kind of information spread over the network. Our main result is positive for democracy, and it shows that the election manipulation problem is not affordable in the worst-case except for trivial classes of instances, even when one accepts to approximate the margin of victory. In the case of seeding, we also show that the manipulation is hard even if the graph is a line and that a large class of algorithms, including most of the approaches recently adopted for social-influence problems, fail to compute a bounded approximation even on elementary networks, as undirected graphs with every node having a degree at most two or directed trees. In the case of edge removal or addition, our hardness results also apply to the basic case of social influence maximization/minimization. In contrast, the hardness of election manipulation holds even when the manipulator has an unlimited budget, being allowed to remove or add an arbitrary number of edges.

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arXiv2020

Learning Probably Approximately Correct Maximin Strategies in Simulation-Based Games with Infinite Strategy Spaces

We tackle the problem of learning equilibria in simulation-based games. In such games, the players' utility functions cannot be described analytically, as they are given through a black-box simulator that can be queried to obtain noisy estimates of the utilities. This is the case in many real-world games in which a complete description of the elements involved is not available upfront, such as complex military settings and online auctions. In these situations, one usually needs to run costly simulation processes to get an accurate estimate of the game outcome. As a result, solving these games begets the challenge of designing learning algorithms that can find (approximate) equilibria with high confidence, using as few simulator queries as possible. Moreover, since running the simulator during the game is unfeasible, the algorithms must first perform a pure exploration learning phase and, then, use the (approximate) equilibrium learned this way to play the game. In this work, we focus on two-player zero-sum games with infinite strategy spaces. Drawing from the best arm identification literature, we design two algorithms with theoretical guarantees to learn maximin strategies in these games. The first one works in the fixed-confidence setting, guaranteeing the desired confidence level while minimizing the number of queries. Instead, the second algorithm fits the fixed-budget setting, maximizing the confidence without exceeding the given maximum number of queries. First, we formally prove δ-PAC theoretical guarantees for our algorithms under some regularity assumptions, which are encoded by letting the utility functions be drawn from a Gaussian process. Then, we experimentally evaluate our techniques on a testbed made of randomly generated games and instances representing simple real-world security settings.

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arXiv2020

Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry

Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience of the network users. We focus on Bayesian games with atomic players, where network vagaries are modeled via a (random) state of nature which determines the costs incurred by the players. A third-party entity---the sender---can observe the realized state of the network and exploit this additional information to send a signal to each player. A natural question is the following: is it possible for an informed sender to reduce the overall social cost via the strategic provision of information to players who update their beliefs rationally? The paper focuses on the problem of computing optimal ex ante persuasive signaling schemes, showing that symmetry is a crucial property for its solution. Indeed, we show that an optimal ex ante persuasive signaling scheme can be computed in polynomial time when players are symmetric and have affine cost functions. Moreover, the problem becomes NP-hard when players are asymmetric, even in non-Bayesian settings.

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arXiv2019

Coordination in Adversarial Sequential Team Games via Multi-Agent Deep Reinforcement Learning

Many real-world applications involve teams of agents that have to coordinate their actions to reach a common goal against potential adversaries. This paper focuses on zero-sum games where a team of players faces an opponent, as is the case, for example, in Bridge, collusion in poker, and collusion in bidding. The possibility for the team members to communicate before gameplay---that is, coordinate their strategies ex ante---makes the use of behavioral strategies unsatisfactory. We introduce Soft Team Actor-Critic (STAC) as a solution to the team's coordination problem that does not require any prior domain knowledge. STAC allows team members to effectively exploit ex ante communication via exogenous signals that are shared among the team. STAC reaches near-optimal coordinated strategies both in perfectly observable and partially observable games, where previous deep RL algorithms fail to reach optimal coordinated behaviors.

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arXiv2019

Learning to Correlate in Multi-Player General-Sum Sequential Games

In the context of multi-player, general-sum games, there is an increasing interest in solution concepts modeling some form of communication among players, since they can lead to socially better outcomes with respect to Nash equilibria, and may be reached through learning dynamics in a decentralized fashion. In this paper, we focus on coarse correlated equilibria (CCEs) in sequential games. First, we complete the picture on the complexity of finding social-welfare-maximizing CCEs by showing that the problem is not in Poly-APX unless P = NP. Furthermore, simple arguments show that CFR - working with behavioral strategies - may not converge to a CCE. However, we devise a simple variant (CFR-S) which provably converges to the set of CCEs, but may be empirically inefficient. Thus, we design a variant of the CFR algorithm (called CFR-Jr) which approaches the set of CCEs with a regret bound sub-linear in the size of the game, and is shown to be dramatically faster than CFR-S and the state-of-the-art algorithms to compute CCEs.

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arXiv2019

Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud

We focus on the following natural question: is it possible to influence the outcome of a voting process through the strategic provision of information to voters who update their beliefs rationally? We investigate whether it is computationally tractable to design a signaling scheme maximizing the probability with which the sender's preferred candidate is elected. We focus on the model recently introduced by Arieli and Babichenko (2019) (i.e., without inter-agent externalities), and consider, as explanatory examples, $k$-voting rule and plurality voting. There is a sharp contrast between the case in which private signals are allowed and the more restrictive setting in which only public signals are allowed. In the former, we show that an optimal signaling scheme can be computed efficiently both under a $k$-voting rule and plurality voting. In establishing these results, we provide two general (i.e., applicable to settings beyond voting) contributions. Specifically, we extend a well known result by Dughmi and Xu (2017) to more general settings, and prove that, when the sender's utility function is anonymous, computing an optimal signaling scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In the public signaling case, we show that the sender's optimal expected return cannot be approximated to within any factor under a $k$-voting rule. This negative result easily extends to plurality voting and problems where utility functions are anonymous.

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arXiv2019

Bayesian Persuasion with Sequential Games

We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the case where the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ in the time at which the receivers commit to following the sender's signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. In contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to a novel algorithm based on the ellipsoid method which we propose.

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arXiv2019

Be a Leader or Become a Follower: The Strategy to Commit to with Multiple Leaders (Extended Version)

We study the problem of computing correlated strategies to commit to in games with multiple leaders and followers. To the best of our knowledge, this problem is widely unexplored so far, as the majority of the works in the literature focus on games with a single leader and one or more followers. The fundamental ingredient of our model is that a leader can decide whether to participate in the commitment or to defect from it by taking on the role of follower. This introduces a preliminary stage where, before the underlying game is played, the leaders make their decisions to reach an agreement on the correlated strategy to commit to. We distinguish three solution concepts on the basis of the constraints that they enforce on the agreement reached by the leaders. Then, we provide a comprehensive study of the properties of our solution concepts, in terms of existence, relation with other solution concepts, and computational complexity.

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arXiv2019

Leadership in Congestion Games: Multiple User Classes and Non-Singleton Actions (Extended Version)

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a complete characterization of hard and easy instances is still lacking. In this paper, we extend the state of the art along two main directions. First, we focus on games where players' actions are made of multiple resources, and we prove that the problem is NP-hard and not in Poly-APX unless P = NP, even in the basic case in which players are symmetric, their actions are made of only two resources, and the cost functions are monotonic. Second, we focus on games with singleton actions where the players are partitioned into classes, depending on which actions they have available. In this case, we provide a dynamic programming algorithm that finds an equilibrium in polynomial time, when the number of classes is fixed and the leader plays pure strategies. Moreover, we prove that, if we allow for leader's mixed strategies, then the problem becomes NP-hard even with only four classes and monotonic costs. Finally, for both settings, we provide mixed-integer linear programming formulations, and we experimentally evaluate their scalability on both random game instances and worst-case instances based on our hardness reductions.

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arXiv2019

Election Manipulation on Social Networks with Messages on Multiple Candidates

We study the problem of election control through social influence when the manipulator is allowed to use the locations that she acquired on the network for sending \emph{both} positive and negative messages on \emph{multiple} candidates, widely extending the previous results available in the literature that study the influence of a single message on a single candidate. In particular, we provide a tight characterization of the settings in which the maximum increase in the margin of victory can be efficiently approximated and of those in which any approximation turns out to be impossible. We also show that, in simple networks, a large class of algorithms, mainly including all approaches recently adopted for social-influence problems, fail to compute a bounded approximation even on very simple networks, as undirected graphs with every node having a degree at most two or directed trees. Finally, we investigate various extensions and generalizations of the model.

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arXiv2019

Computing Optimal Coarse Correlated Equilibria in Sequential Games

We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the hardness results on the computation of normal-form correlated equilibria, we introduce the notion of normal-form coarse correlated equilibrium, extending the definition of coarse correlated equilibrium to sequential games. We show that, in two-player games without chance moves, an optimal (e.g., social welfare maximizing) normal-form coarse correlated equilibrium can be computed in polynomial time, and that in general multi-player games (including two-player games with Chance), the problem is NP-hard. For the former case, we provide a polynomial-time algorithm based on the ellipsoid method and also propose a more practical one, which can be efficiently applied to problems of considerable size. Then, we discuss how our algorithm can be extended to games with Chance and games with more than two players.

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arXiv2018

Quasi-Perfect Stackelberg Equilibrium

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasi-perfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings---that is, settings where a leader can commit to a strategy---which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

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arXiv2018

Leadership in Singleton Congestion Games: What is Hard and What is Easy

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of them acts as leader. In particular, we address the cases where the players either have the same action spaces (i.e., the set of resources they can choose is the same for all of them) or different ones, and where their costs are either monotonic functions of the resource congestion or not. We show that, in the case where the players have different action spaces, the cost the leader incurs in a Stackelberg equilibrium cannot be approximated in polynomial time up to within any polynomial factor in the size of the game unless P = NP, independently of the cost functions being monotonic or not. We show that a similar result also holds when the players have nonmonotonic cost functions, even if their action spaces are the same. Differently, we prove that the case with identical action spaces and monotonic cost functions is easy, and propose polynomial-time algorithm for it. We also improve an algorithm for the computation of a socially optimal equilibrium in singleton congestion games with the same action spaces without leadership, and extend it to the computation of a Stackelberg equilibrium for the case where the leader is restricted to pure strategies. For the cases in which the problem of finding an equilibrium is hard, we show how, in the optimistic setting where the followers break ties in favor of the leader, the problem can be formulated via mixed-integer linear programming techniques, which computational experiments show to scale quite well.

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arXiv2018

Computing a Pessimistic Leader-Follower Equilibrium with Multiple Followers: the Mixed-Pure Case

The search problem of computing a \textit{leader-follower equilibrium} has been widely investigated in the scientific literature in, almost exclusively, the single-follower setting. Although the \textit{optimistic} and \ textit{pessimistic} versions of the problem are solved with different methodologies, both cases allow for efficient, polynomial-time algorithms based on linear programming. The situation is different with multiple followers, where results are only sporadic and depend strictly on the nature of the followers' game. In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader's commitment, play a Nash equilibrium. The corresponding search problem, both in the optimistic and pessimistic versions, is known to be not in Poly-$\textsf{APX}$ unless $\textsf{P}=\textsf{NP}$ and exact algorithms are known only for the optimistic case. We focus on the case where the followers play in pure strategies under the assumption of pessimism. After casting this search problem as a \italic{pessimistic bilevel programming problem}, we show that, with two followers, the problem is $\textsf{NP}$-hard and, with three or more followers, it is not in Poly-$\textsf{APX}$ unless $\textsf{P}=\textsf{NP}$. We propose a single-level mathematical programming reformulation which calls for the maximisation of a nonconcave quadratic function over an unbounded nonconvex feasible region defined by linear and quadratic constraints. Since, due to admitting a supremum but not a maximum, only a restricted version of this formulation can be solved to optimality with state-of-the-art methods, we propose an exact \textit{ad hoc} algorithm, which we also embed within a branch-and-bound scheme, capable of computing the supremum of the problem.

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