Heterogeneous Facility Location without Money

The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-life scenarios. Specifically, we propose and analyze heterogeneous facility location without money, a novel model wherein: (i) we have multiple heterogeneous (i.e., serving different purposes) facilities, (ii) agents' locations are disclosed to the mechanism and (iii) agents bid for the set of facilities they are interested in (as opposed to bidding for their position on the network). We study the heterogeneous facility location problem under two different objective functions, namely: social cost (i.e., sum of all agents' costs) and maximum cost. For either objective function, we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line. For the social cost objective function, we devise an (n-1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm. As regards the maximum cost objective function, we propose a 3-approximate deterministic strategyproof algorithm, and prove a 3/2 approximation lower bound for deterministic strategyproof mechanisms. Furthermore, we propose a 3/2-approximate randomized strategyproof algorithm and prove a 4/3 approximation lower bound for randomized strategyproof algorithms

Metastability of the Logit Dynamics for Asymptotically Well-Behaved Potential Games

Convergence rate and stability of a solution concept are classically measured in terms of “even- tually” and “forever”, respectively. In the wake of recent computational criticisms to this approach, we study whether these time frames can be updated to have states computed “quickly” and stable for “long enough”. Logit dynamics allows irrationality in players’ behavior, and may take time exponential in the number of players n to converge to a stable state (i.e., a certain distribution over pure strategy pro- files). We prove that every potential game, for which the behavior of the logit dynamics is not chaotic as n increases, admits distributions stable for a super-polynomial number of steps in n no matter the players’ irrationality, and the starting profile of the dynamics. The convergence rate to these metastable distributions is polynomial in n when the players are not too rational. Our proofs build upon the new concept of partitioned Markov chains, that might be of indepen- dent interest, and a number of involved technical contributions

Two-way Greedy: Algorithms for Imperfect Rationality

The realization that selfish interests need to be accounted for in the design of algorithms has produced many contributions in computer science under the umbrella of algorithmic mechanism design. Novel algorithmic properties and paradigms have been identified and studied. Our work stems from the observation that selfishness is different from rationality; agents will attempt to strategize whenever they perceive it to be convenient according to their imperfect rationality. Recent work has focused on a particular notion of imperfect rationality, namely absence of contingent reasoning skills, and defined obvious strategyproofness (OSP) as a way to deal with the selfishness of these agents. Essentially, this definition states that to care for the incentives of these agents, we need not only pay attention about the relationship between input and output, but also about the way the algorithm is run. However, it is not clear what algorithmic approaches must be used for OSP. In this paper, we show that, for binary allocation problems, OSP is fully captured by a combination of two well-known algorithmic techniques: forward and reverse greedy. We call two-way greedy this algorithmic design paradigm. Our main technical contribution establishes the connection between OSP and two-way greedy. We build upon the recently introduced cycle monotonicity technique for OSP. By means of novel structural properties of cycles and queries of OSP mechanisms, we fully characterize these mechanisms in terms of extremal implementations. These are protocols that ask each agent to consistently separate one extreme of their domain at the current history from the rest. Through the connection with the greedy paradigm, we are able to import a host of approximation bounds to OSP and strengthen the strategic properties of this family of algorithms. Finally, we begin exploring the power of two-way greedy for set systems

Mechanisms for Multi-unit Combinatorial Auctions with a Few Distinct Goods

We design and analyze deterministic truthful approximation mechanisms for multi-unit Combinatorial Auctions involving only a constant number of distinct goods, each in arbitrary limited supply. Prospective buyers (bidders) have preferences over multisets of items, i.e., for more than one unit per distinct good. Our objective is to determine allocations of multisets that maximize the Social Welfare. Our main results are for multi-minded and submodular bidders. In the first setting each bidder has a positive value for being allocated one multiset from a prespecified demand set of alternatives. In the second setting each bidder is associated to a submodular valuation function that defines his value for the multiset he is allocated. For multi-minded bidders, we design a truthful Fptas that fully optimizes the Social Welfare, while violating the supply constraints on goods within factor (1 + ), for any fixed > 0 (i.e., the approximation applies to the constraints and not to the Social Welfare). This result is best possible, in that full optimization is impossible without violating the supply constraints. For submodular bidders, we obtain a Ptas that approximates the optimum Social Welfare within factor (1 + ), for any fixed > 0, without violating the supply constraints. This result is best possible as well. Our allocation algorithms are Maximal-in-Range and yield truthful mechanisms, when paired with Vickrey-Clarke-Groves payments

Error in the Euclidean Preference Model

Spatial models of preference, in the form of vector embeddings, are learned by many deep learning and multiagent systems, including recommender systems. Often these models are assumed to approximate a Euclidean structure, where an individual prefers alternatives positioned closer to their "ideal point", as measured by the Euclidean metric. However, Bogomolnaia and Laslier (2007) showed that there exist ordinal preference profiles that cannot be represented with this structure if the Euclidean space has two fewer dimensions than there are individuals or alternatives. We extend this result, showing that there are realistic situations in which almost all preference profiles cannot be represented with the Euclidean model, and derive a theoretical lower bound on the expected error when using the Euclidean model to approximate non-Euclidean preference profiles. Our results have implications for the interpretation and use of vector embeddings, because in some cases close approximation of arbitrary, true ordinal relationships can be expected only if the dimensionality of the embeddings is a substantial fraction of the number of entities represented.Comment: 11 pages, 5 figures. Accepted as an Extended Abstract to AAMAS 202

A Mechanism Design Approach to Measure Awareness

In this paper, we study protocols that allow to discern conscious and unconscious decisions of human beings; i.e., protocols that measure awareness. Consciousness is a central research theme in Neuroscience and AI, which remains, to date, an obscure phenomenon of human brains. Our starting point is a recent experiment, called Post Decision Wagering (PDW) (Persaud, McLeod, and Cowey 2007), that attempts to align experimenters' and subjects' objectives by leveraging financial incentives. We note a similarity with mechanism design, a research area which aims at the design of protocols that reconcile often divergent objectives through incentive-compatibility. We look at the issue of measuring awareness from this perspective. We abstract the setting underlying the PDW experiment and identify three factors that could make it ineffective: rationality, risk attitude and bias of subjects. Using mechanism design tools, we study the barrier between possibility and impossibility of incentive compatibility with respect to the aforementioned characteristics of subjects. We complete this study by showing how to use our mechanisms to potentially get a better understanding of consciousness

Detecting Financial Market Manipulation with Statistical Physics Tools

We take inspiration from statistical physics to develop a novel conceptual framework for the analysis of financial markets. We model the order book dynamics as a motion of particles and define the momentum measure of the system as a way to summarise and assess the state of the market. Our approach proves useful in capturing salient financial market phenomena: in particular, it helps detect the market manipulation activities called spoofing and layering. We apply our method to identify pathological order book behaviours during the flash crash of the LUNA cryptocurrency, uncovering widespread instances of spoofing and layering in the market. Furthermore, we establish that our technique outperforms the conventional Z-score-based anomaly detection method in identifying market manipulations across both LUNA and Bitcoin cryptocurrency markets

What to Verify for Optimal Truthful Mechanisms without Money

We aim at identifying a minimal set of conditions under which algorithms with good approximation guarantees are truthful without money. In line with recent literature, we wish to express such a set via verification assumptions, i.e., kind of agents' misbehavior that can be made impossible by the designer. We initiate this research endeavour for the paradigmatic problem in approximate mechanism design without money, facility location. It is known how truthfulness imposes (even severe) losses and how certain notions of verification are unhelpful in this setting; one is thus left powerless to solve this problem satisfactorily in presence of selfish agents. We here address this issue and characterize the minimal set of verification assumptions needed for the truthfulness of optimal algorithms, for both social cost and max cost objective functions. En route, we give a host of novel conceptual and technical contributions ranging from topological notions of verification to a lower bounding technique for truthful mechanisms that connects methods to test truthfulness (i.e., cycle monotonicity) with approximation guarantee