We study long-term equilibria that arise in the token monetary policy, or tokenomics, design of proof-of-stake (PoS) blockchain systems that engage utility maximizing users and validators. Validators are system maintainers who get rewarded with tokens for performing the work necessary for the system to function properly, while users compete and pay with such tokens for getting a desired portion of the system service. We study how the system service provision and suitable rewards schemes together can lead to equilibria with the following desirable characteristics (1) viability: the system keeps parties engaged, (2) decentralization and skin-in-the-game: multiple sufficiently invested validators are participating, (3) stability: the price path of the underlying token used to transact with the system does not change widely over time, and (4) feasibility: the mechanism is easy to implement as a smart contract, e.g., it does not require a fiat reserve on-chain to perform token buybacks or to perform bookkeeping of exponentially growing token holdings. Our analysis enables us to put forward a novel generic mechanism for blockchain monetary policy that we call quantitative rewarding (QR). We investigate how to implement QR in single-token and two-token proof of stake (PoS) blockchain systems. The latter are systems that utilize one token for the users to pay the transaction fees and a different token for the validators to participate in the PoS protocol and get rewarded. Our approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria. Our analysis also reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy - a distinction that is, to the best of our knowledge, highlighted for the first time.licy - a distinction that is, to the best of our knowledge, highlighted for the first time.

Launching a new blockchain system or application is frequently facilitated by a so called airdrop, where the system designer chooses a pre-existing set of potentially interested parties and allocates newly minted tokens to them with the expectation that they will participate in the system — such engagement, especially if it is of significant level — facilitates the system and raises its value and also the value of its newly minted token, hence benefiting the airdrop recipients. A number of challenging questions befuddle designers in this setting, such as how to choose the set of interested parties and how to allocate tokens to them. To address these considerations we put forward a game theoretic model for such airdrop games. Our model can be used to guide the designer’s choices based on the way the system’s value depends on participation (modeled by a “technology function” in our framework) and the costs that participations incurs. We identify both bad and good equilibria and identify the settings and the choices that can be made where the designer can influence the players towards good equilibria in an expedient manner.

In this work, we consider the problem of recovery a planted k-densest sub-hypergraph on d-uniform hypergraphs. This fundamental problem appears in different contexts, e.g., community detection, average-case complexity, and neuroscience applications as a structural variant of tensor-PCA problem. We provide tight information-theoretic upper and lower bounds for the exact recovery threshold by the maximum-likelihood estimator, as well as algorithmic bounds based on approximate message passing algorithms. The problem exhibits a typical statistical-to-computational gap observed in analogous sparse settings that widen with increasing sparsity of the problem. The bounds show that the signal structure impacts the location of the statistical and computational phase transition that the known existing bounds for the tensor-PCA model do not capture. This effect is due to the generic planted signal prior that this latter model addresses.

We study the problem of estimating a rank-1additive deformation of a Gaussian tensor according to the maximum-likelihood estimator (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an all-or-nothing (AoN) phase transition, already established for the minimum mean-square-error estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and second-moment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result. A full version of this paper is accessible at: https://arxiv.org/pdf/2101.09994.pdf

The realization that selfish interests need to be accounted for in the design of algorithms has produced many interesting and valuable contributions in computer science under the general umbrella of algorithmic mechanism design. Our work stems from the observation that selfishness is different from rationality; agents will attempt to strategize whenever they perceive it to be convenient. Recent work in economics 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. However, it is not clear to date what algorithmic approaches ought to be used for OSP. In this article, we rather surprisingly show that, for binary allocation problems, OSP is fully captured by a natural combination of two well-known and extensively studied algorithmic techniques: forward and reverse greedy. We call two-way greedy this underdeveloped algorithmic design paradigm. We are then able to import a host of known approximation bounds obtained through greedy algorithms to OSP and strengthen the strategic properties of this family of algorithms. Finally, we begin exploring the full power of two-way greedy (and, in turns, OSP) in the context of set systems.

Catering to the incentives of people with limited rationality is a challenging research direction that requires novel paradigms to design mechanisms and approximation algorithms. Obviously strategyproof (OSP) mechanisms have recently emerged as the concept of interest to this research agenda. However, the majority of the literature in the area has either highlighted the shortcomings of OSP or focused on the "right" definition rather than on the construction of these mechanisms. We here give the first set of tight results on the approximation guarantee of OSP mechanisms for scheduling related machines. By extending the well-known cycle monotonicity technique, we are able to concentrate on the algorithmic component of OSP mechanisms and provide some novel paradigms for their design.

We consider the problem of sorting $n$ elements in the case of \emph{persistent} comparison errors. In this model (Braverman and Mossel, SODA'08), each comparison between two elements can be wrong with some fixed (small) probability $p$, and \emph{comparisons cannot be repeated}. Sorting perfectly in this model is impossible, and the objective is to minimize the \emph{dislocation} of each element in the output sequence, that is, the difference between its true rank and its position. Existing lower bounds for this problem show that no algorithm can guarantee, with high probability, \emph{maximum dislocation} and \emph{total dislocation} better than $Ω(\log n)$ and $Ω(n)$, respectively, regardless of its running time. In this paper, we present the first \emph{$O(n\log n)$-time} sorting algorithm that guarantees both \emph{$O(\log n)$ maximum dislocation} and \emph{$O(n)$ total dislocation} with high probability. Besides improving over the previous state-of-the art algorithms -- the best known algorithm had running time $\tilde{O}(n^{3/2})$ -- our result indicates that comparison errors do not make the problem computationally more difficult: a sequence with the best possible dislocation can be obtained in $O(n\log n)$ time and, even without comparison errors, $Ω(n\log n)$ time is necessary to guarantee such dislocation bounds. In order to achieve this optimal result, we solve two sub-problems, and the respective methods have their own merits for further application. One is how to locate a position in which to insert an element in an almost-sorted sequence having $O(\log n)$ maximum dislocation in such a way that the dislocation of the resulting sequence will still be $O(\log n)$. The other is how to simultaneously insert $m$ elements into an almost sorted sequence of $m$ different elements, such that the resulting sequence of $2m$ elements remains almost sorted.

In real world applications, important resources like energy are saved by deliberately using so-called low-cost operations that are less reliable. Some of these approaches are based on a dual mode technology where it is possible to choose between high-energy operations (always correct) and low-energy operations (prone to errors), and thus enable to trade energy for correctness. In this work we initiate the study of algorithms for solving optimization problems that in their computation are allowed to choose between two types of operations: high-energy comparisons (always correct but expensive) and low-energy comparisons (cheaper but prone to errors). For the errors in low-energy comparisons, we assume the persistent setting, which usually makes it impossible to achieve optimal solutions without high-energy comparisons. We propose to study a natural complexity measure which accounts for the number of operations of either type separately. We provide a new family of algorithms which, for a fairly large class of maximization problems, return a constant approximation using only polylogarithmic many high-energy comparisons and only O(n log n) low-energy comparisons. This result applies to the class of p-extendible system s [Mestre, 2006], which includes several NP-hard problems and matroids as a special case (p=1). These algorithmic solutions relate to some fundamental aspects studied earlier in different contexts: (i) the approximation guarantee when only ordinal information is available to the algorithm; (ii) the fact that even such ordinal information may be erroneous because of low-energy comparisons and (iii) the ability to approximately sort a sequence of elements when comparisons are subject to persistent errors. Finally, our main result is quite general and can be parametrized and adapted to other error models.

Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models called planted Random Energy Model (REM), inspired by Derrida's REM. For this model we provide the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold. As an application, we further consider the 2 non-equally sized community Weighted Stochastic Block Model (2-WSBM) on h uniform hypergraphs, that is equivalent to the P-REM on both sides of the spectrum, for high and low edge cardinality h. We provide upper and lower bounds for the exact recoverability for any h, mapping these problems to the aforementioned P-REM. To the best of our knowledge these are the first consistency results for the 2-WSBM on graphs and on hypergraphs with non-equally sized community.

Distributed tasks such as constructing a maximal independent set (MIS) in a network, or properly coloring the nodes or the edges of a network with reasonably few colors, are known to admit efficient distributed randomized algorithms. Those algorithms essentially proceed according to some simple generic rules, by letting each node choosing a temptative value at random, and checking whether this choice is consistent with the choices of the nodes in its vicinity. If this is the case, then the node outputs the chosen value, else it repeats the same process. Although such algorithms are, with high probability, running in a polylogarithmic number of rounds, they are not robust against actions performed by rational but selfish nodes. Indeed, such nodes may prefer specific individual outputs over others, e.g., because the formers suit better with some individual constraints. For instance, a node may prefer not being placed in a MIS as it is not willing to serve as a relay node. Similarly, a node may prefer not being assigned some radio frequencies (i.e., colors) as these frequencies would interfere with other devices running at that node. In this paper, we show that the probability distribution governing the choices of the output values in the generic algorithm can be tuned such that no nodes will rationally deviate from this distribution. More formally, and more generally, we prove that the large class of so-called LCL tasks, including MIS and coloring, admit simple "Luby's style" algorithms where the probability distribution governing the individual choices of the output values forms a Nash equilibrium. In fact, we establish the existence of a stronger form of equilibria, called symmetric trembling-hand perfect equilibria for those games.

We study the game-theoretic task of selecting mobile agents to deliver multiple items on a network. An instance is given by $m$ packages (physical objects) which have to be transported between specified source-target pairs in an undirected graph, and $k$ mobile heterogeneous agents, each being able to transport one package at a time. Following a recent model [Baertschi et al. 2017], each agent i has a different rate of energy consumption per unit distance traveled, i.e., its weight. We are interested in optimizing or approximating the total energy consumption over all selected agents. Unlike previous research, we assume the weights to be private values known only to the respective agents. We present three different mechanisms which select, route and pay the agents in a truthful way that guarantees voluntary participation of the agents, while approximating the optimum energy consumption by a constant factor. To this end, we analyze a previous structural result and an approximation algorithm given in [Baertschi et al. 2017]. Finally, we show that for some instances in the case of a single package, the sum of the payments can be bounded in terms of the optimum.

We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation with high probability, or o(n) total dislocation in expectation, regardless of their running time.

In this paper we analyse the core-periphery clustering properties of collaboration networks, where the core of a network is formed by the nodes with highest degree. In particular, we first observe that, even for random graph models aiming at matching the degree-distribution and/or the clustering coefficient of real networks, these models produce synthetic graphs which have a spatial distribution of the triangles with respect to the core and to the periphery which does not match the spatial distribution of the triangles in the real networks. We therefore propose a new model, called CPCL, whose aim is to distribute the triangles in a way fitting with their real core-periphery distribution, and thus producing graphs matching the core-periphery clustering of real networks.

We present the first general bounds on the mixing time of logit dynamics for wide classes of strategic games. The logit dynamics describes the behaviour of a complex system whose individual components act "selfishly" and keep responding according to some partial ("noisy") knowledge of the system. In particular, we prove nearly tight bounds for potential games and games with dominant strategies. Our results show that, for potential games, the mixing time is upper and lower bounded by an "exponential" in the inverse of the noise and in the maximum potential difference. Instead, for games with dominant strategies, the mixing time cannot grow arbitrarily with the inverse of the noise. Finally, we refine our analysis for a subclass of potential games called "graphical" coordination games and we give evidence that the mixing time strongly depends on the structure of the underlying graph. Games in this class have been previously studied in Physics and, more recently, in Computer Science in the context of diffusion of new technologies.

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group-strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the "classical" model.

We consider general resource assignment games involvingselfish users/agentsin which users compete for resources and try to be assigned to those which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and study amechanism designapproach in which an allocation mechanism assigns users to resources and charges the users for using the resources so as to induce each user totruthfullyreport a private piece of information he/she holds (e.g., how much traffic he/she needs to transmit). This information is crucial for computing optimal (or close to optimal) allocations and an agent could misreport his/her information to induce the underlying allocation algorithm to output a solution which he/she likes more (e.g., which assigns better resources to him/her). For our resource allocation problems, we give analgorithmic characterizationof the solutions for which truth-telling is a Nash equilibrium. A natural application of these results is to a scheduling/routing problem which is the mechanism design counterpart of the selfish routing game of Koutsoupias and Papadimitriou [1999]: Each selfish user wants to route a piece of unsplittable traffic using one ofmlinks of different speeds so as to minimize his/herownlatency. Our mechanism design counterpart can be seen as the problem of schedulingselfish jobson parallel related machines and is the dual of the problem of scheduling (unselfish) jobs on parallelselfish machinesstudied by Archer and Tardos [2001]. Koutsoupias and Papadimitriou studied an “anarchic” scenario in which each user chooses his/her own link, and this may produce Nash equilibria of cost Ω(logm/log logm) times the optimum. Our mechanism design counterpart is a possible way of reducing the effect of selfish behavior via suitable incentives to the agents (i.e., taxes for using the links). We indeed show that in the resulting game, it is possible to guarantee an approximation factor of 8 for any number of links/machines (this solution also works for online settings). However, it remains impossible to guarantee arbitrarily good approximate solutions, even for 2 links/machines and even if the allocation algorithm is allowed superpolynomial time. This result shows that our scheduling problem with selfish jobs is more difficult than the scheduling problem with selfish machines by Archer and Tardos (which admits exact solutions). We also study some generalizations of this basic problem.

We study the problem of assigning unsplittable traffic to a set of m links so to minimize the maximum link congestion (i.e., the makespan). We consider the case of selfish agents owning pieces of the traffic. In particular, we introduce a variant of the model by Koutsopias and Papadimitriou [1999] in which owners of the traffic cannot directly choose which link to use; instead, the assignment is performed by a scheduler. The agents can manipulate the scheduler by reporting falseinformation regarding the size of each piece of unsplittable traffic.We provide upper and ower bounds on the approximation achievable by mechanisms that induce a Nash equilibrium when all agents report their true values.For the case of each agent owning one job, our positive results for m identical links show the effectiveness of introducing such a scheduler since, in this case, (1+ε)-approximate solutions are guaranteed in polynomial time. In contrast, the result by Koutsopias and Papadimitriou [1999] shows that, without payments and allowing selfish routing, Nash equilibria yield (in the worst case) Ω(log m over log log m)-approximate solutions, even for unitary weighted traffic. When links have different speeds we prove lower and upper bounds on the approximation achievable by a mechanism inducing a Nash equilibrium.Similar approximability results for identical machines have been achieved by Feldman et al. [2003]. However these results do not hold in our setting because their model assumes that the algorithm is provided with the correct traffic weights. For the case of agents owning more than one job, we give mechanisms that achieve constant approximation and prove lower bounds on the approximation ratio that can be achieved by a mechanism.