arXiv subjects

Stefanos Leonardos

Publications and source records attributed to Stefanos Leonardos.

At least 37 records · Page 2Linked to original sources

arXiv2021

Incentives in Ethereum's Hybrid Casper Protocol

We present an overview of hybrid Casper the Friendly Finality Gadget (FFG): a Proof-of-Stake checkpointing protocol overlaid onto Ethereum's Proof-of-Work blockchain. We describe its core functionalities and reward scheme, and explore its properties. Our findings indicate that Casper's implemented incentives mechanism ensures liveness, while providing safety guarantees that improve over standard Proof-of-Work protocols. Based on a minimal-impact implementation of the protocol as a smart contract on the blockchain, we discuss additional issues related to parametrisation, funding, throughput and network overhead and detect potential limitations.

cs.CR↗

arXiv2021

Oceanic Games: Centralization Risks and Incentives in Blockchain Mining

To participate in the distributed consensus of permissionless blockchains, prospective nodes -- or miners -- provide proof of designated, costly resources. However, in contrast to the intended decentralization, current data on blockchain mining unveils increased concentration of these resources in a few major entities, typically mining pools. To study strategic considerations in this setting, we employ the concept of Oceanic Games, Milnor and Shapley (1978). Oceanic Games have been used to analyze decision making in corporate settings with small numbers of dominant players (shareholders) and large numbers of individually insignificant players, the ocean. Unlike standard equilibrium models, they focus on measuring the value (or power) per entity and per unit of resource} in a given distribution of resources. These values are viewed as strategic components in coalition formations, mergers and resource acquisitions. Considering such issues relevant to blockchain governance and long-term sustainability, we adapt oceanic games to blockchain mining and illustrate the defined concepts via examples. The application of existing results reveals incentives for individual miners to merge in order to increase the value of their resources. This offers an alternative perspective to the observed centralization and concentration of mining power. Beyond numerical simulations, we use the model to identify issues relevant to the design of future cryptocurrencies and formulate prospective research questions.

cs.GT↗

arXiv2021

PREStO: A Systematic Framework for Blockchain Consensus Protocols

The rapid evolution of blockchain technology has brought together stakeholders from fundamentally different backgrounds. The result is a diverse ecosystem, as exemplified by the development of a wide range of different blockchain protocols. This raises questions for decision and policy makers: How do different protocols compare? What are their trade-offs? Existing efforts to survey the area reveal a fragmented terminology and the lack of a unified framework to reason about the properties of blockchain protocols. In this paper, we work towards bridging this gap. We present a five-dimensional design space with a modular structure in which protocols can be compared and understood. Based on these five axes -- Optimality, Stability, Efficiency, Robustness and Persistence -- we organize the properties of existing protocols in subcategories of increasing granularity. The result is a dynamic scheme -- termed the PREStO framework -- which aids the interaction between stakeholders of different backgrounds, including managers and investors, and which enables systematic reasoning about blockchain protocols. We illustrate its value by comparing existing protocols and identifying research challenges, hence making a first step towards understanding the blockchain ecosystem through a more comprehensive lens.

cs.CR↗

arXiv2021

A Class of Distributions for Linear Demand Markets

In this paper, we study distributions that describe markets with linear stochastic demand. We express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRD function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exists and are unique. In particular, markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual demand (DGMRD) and finite second moment. DGMRD distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. In real life economic applications, they arise naturally as mixtures of (possibly) IGFR distributions over disjoint intervals. We further elaborate on the relationship of the two classes and link their limiting behavior at infinity. We examine moment and closure properties of the DGMRD distributions that are important in economic applications and illustrate our results with examples.

math.PR↗

arXiv2021

Comparative Statics via Stochastic Orderings in a Two-Echelon Market with Upstream Demand Uncertainty

We revisit the classic Cournot model and extend it to a two-echelon supply chain with an upstream supplier who operates under demand uncertainty and multiple downstream retailers who compete over quantity. The supplier's belief about retail demand is modeled via a continuous probability distribution function F. If F has the decreasing generalized mean residual life (DGMRL) property, then the supplier's optimal pricing policy exists and is the unique fixed point of the mean residual life (MRL) function. This closed form representation of the supplier's equilibrium strategy facilitates a transparent comparative statics and sensitivity analysis. We utilize the theory of stochastic orderings to study the response of the equilibrium fundamentals - wholesale price, retail price and quantity - to different demand distribution parameters. We examine supply chain performance, in terms of the distribution of profits, supply chain efficiency, in terms of the Price of Anarchy, and complement our findings with numerical results.

cs.GT↗

arXiv2021

Measuring Market Performance with Stochastic Demand: Price of Anarchy and Price of Uncertainty

Globally operating suppliers face the rising challenge of wholesale pricing under scarce data about retail demand, in contrast to better informed, locally operating retailers. At the same time, as local businesses proliferate, markets congest and retail competition increases. To capture these strategic considerations, we employ the classic Cournot model and extend it to a two-stage supply chain with an upstream supplier who operates under demand uncertainty and multiple downstream retailers who compete over quantity. The supplier's belief about retail demand is modeled via a continuous probability distribution function F. If F has the decreasing generalized mean residual life property, then the supplier's optimal pricing policy exists and is the unique fixed point of the mean residual life function. We evaluate the realized Price of Uncertainty and show that there exist demand levels for which market performs better when the supplier prices under demand uncertainty. In general, performance worsens for lower values of realized demand. We examine the effects of increasing competition on supply chain efficiency via the realized Price of Anarchy and complement our findings with numerical results.

cs.GT↗

arXiv2021

Monopoly Pricing in Vertical Markets with Demand Uncertainty

Pricing decisions are often made when market information is still poor. In turn, existing theoretical models often reason about the response of optimal prices to changing market characteristics without exploiting all available information about the demand distribution. Our aim is to develop a theory for the optimization and systematic comparison of prices between different instances of the same market under various forms of knowledge about the corresponding demand distributions. We revisit the classic problem of monopoly pricing under demand uncertainty in a vertical market with an upstream supplier and multiple forms of downstream competition between arbitrary symmetric retailers. In all cases, demand uncertainty falls to the supplier who acts first and sets a uniform price before the retailers observe the realized demand and place their orders. Our main methodological contribution is that we express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This leads to a closed form characterization of the points of unitary elasticity that maximize the supplier's profits and the derivation of a mild unimodality condition for the supplier's objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently, their elasticities. Using the above, we develop a systematic framework to compare optimal prices between different market instances via the rich theory of stochastic orders. This leads to comparative statics that challenge previously established economic insights about the effects of market size, demand transformations and demand variability on monopolistic prices.

math.OC↗

arXiv2021

Endogenizing the Cost Parameter in Cournot Oligopoly

We study the effects of endogenous cost formation in the classic Cournot oligopoly through an extended two-stage game. The competing Cournot firms produce low-cost but limited quantities of a single homogeneous product. For additional procurements, they may refer to a revenue-maximizing supplier who sets a wholesale price prior to their orders. We express this chain as a two-stage game and study its equilibrium under two different information levels: complete and incomplete information on the side of the supplier about the actual market demand. In the deterministic case, we derive the unique subgame perfect Nash equilibrium for different values of the retailers' capacity levels, supplier's cost and market demand. To study the incomplete information case, we model demand uncertainty via a continuous probability distribution. Under mild assumptions, we characterize the supplier's optimal pricing policy as a fixed point of a proper translation of his expectation about the orders that he will receive from the retailers. If this expectation is decreasing in his price, then such an optimal policy always exists and is unique. Based on this characterization, we are able to proceed with comparative statics and sensitivity analysis, both analytically and numerically. Incomplete information gives rise to market inefficiencies because the supplier may ask for a too high price. Increasing supplier's cost results in increasing wholesale prices, decreasing orders from the retailers and hence decreasing consumer surplus. Increasing retailers' production capacities results in decreasing wholesale prices and increasing consumer surplus. Finally, as the number of second-stage retailers increases, the supplier's profit may initially rise but eventually drops.

math.OC↗

arXiv2021

On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty

We revisit the linear Cournot model with uncertain demand that is studied in Lagerlöf (2006)* and provide sufficient conditions for equilibrium uniqueness that complement the existing results. We show that if the distribution of the demand intercept has the decreasing mean residual demand (DMRD) or the increasing generalized failure rate (IGFR) property, then uniqueness of equilibrium is guaranteed. The DMRD condition implies log-concavity of the expected profits per unit of output without additional assumptions on the existence or the shape of the density of the demand intercept and, hence, answers in the affirmative the conjecture of Lagerlöf (2006)* that such conditions may not be necessary. *Johan Lagerlöf, Equilibrium uniqueness in a Cournot model with demand uncertainty. The B.E. Journal in Theoretical Economics, Vol. 6: Iss 1. (Topics), Article 19:1--6, 2006.

econ.TH↗

arXiv2021

On the Mean Residual Life of Cantor-Type Distributions: Properties and Economic Applications

In this paper, we consider the mean residual life (MRL) function of the Cantor distribution and study its properties. We show that the MRL function is continuous at all points, locally decreasing at all points outside the Cantor set and has a unique fixed point which we explicitly determine. These properties readily extend to the parametric family of p-singular, Cantor type distributions introduced by Mandelbrot (1983). The findings offer evidence that, contrary to common perceptions, Cantor-type distributions are tractable enough to be considered for practical applications. We provide such an example from the field of economics in which Cantor-type distributions can be used to model markets with recurrent bandwagon effects and show that earlier anticipated bandwagon effects lead to higher monopolistic prices. We conclude with a simple implementation of the algorithm by Chalice (1991) to plot Cantor-type distributions.

math.PR↗

arXiv2021

Exploration-Exploitation in Multi-Agent Competition: Convergence with Bounded Rationality

The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the balance between game rewards and exploration costs. We show that Q-learning always converges to the unique quantal-response equilibrium (QRE), the standard solution concept for games under bounded rationality, in weighted zero-sum polymatrix games with heterogeneous learning agents using positive exploration rates. Complementing recent results about convergence in weighted potential games, we show that fast convergence of Q-learning in competitive settings is obtained regardless of the number of agents and without any need for parameter fine-tuning. As showcased by our experiments in network zero-sum games, these theoretical results provide the necessary guarantees for an algorithmic approach to the currently open problem of equilibrium selection in competitive multi-agent settings.

cs.GT↗

arXiv2021

From Griefing to Stability in Blockchain Mining Economies

We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The proof relies on a generalization of evolutionary stability to non-homogeneous populations via griefing factors (ratios that measure network losses relative to deviator's own losses) which leads to a formal theoretical argument for the dissipation of resources, consolidation of power and high entry barriers that are currently observed in practice. A critical assumption in this type of analysis is that miners' decisions have significant influence in aggregate network outcomes (such as network hashrate). However, as networks grow larger, the miner's interaction more closely resembles a distributed production economy or Fisher market and its stability properties change. In this case, we derive a proportional response (PR) update protocol which converges to market equilibria at which griefing is irrelevant. Convergence holds for a wide range of miners risk profiles and various degrees of resource mobility between blockchains with different mining technologies. Our empirical findings in a case study with four mineable cryptocurrencies suggest that risk diversification, restricted mobility of resources (as enforced by different mining technologies) and network growth, all are contributing factors to the stability of the inherently volatile blockchain ecosystem.

cs.GT↗

arXiv2021

Dynamical Analysis of the EIP-1559 Ethereum Fee Market

Participation in permissionless blockchains results in competition over system resources, which needs to be controlled with fees. Ethereum's current fee mechanism is implemented via a first-price auction that results in unpredictable fees as well as other inefficiencies. EIP-1559 is a recent, improved proposal that introduces a number of innovative features such as a dynamically adaptive base fee that is burned, instead of being paid to the miners. Despite intense interest in understanding its properties, several basic questions such as whether and under what conditions does this protocol self-stabilize have remained elusive thus far. We perform a thorough analysis of the resulting fee market dynamic mechanism via a combination of tools from game theory and dynamical systems. We start by providing bounds on the step-size of the base fee update rule that suffice for global convergence to equilibrium via Lyapunov arguments. In the negative direction, we show that for larger step-sizes instability and even formally chaotic behavior are possible under a wide range of settings. We complement these qualitative results with quantitative bounds on the resulting range of base fees. We conclude our analysis with a thorough experimental case study that corroborates our theoretical findings.

cs.GT↗

arXiv2021

Learning in Markets: Greed Leads to Chaos but Following the Price is Right

We study learning dynamics in distributed production economies such as blockchain mining, peer-to-peer file sharing and crowdsourcing. These economies can be modelled as multi-product Cournot competitions or all-pay auctions (Tullock contests) when individual firms have market power, or as Fisher markets with quasi-linear utilities when every firm has negligible influence on market outcomes. In the former case, we provide a formal proof that Gradient Ascent (GA) can be Li-Yorke chaotic for a step size as small as $Θ(1/n)$, where $n$ is the number of firms. In stark contrast, for the Fisher market case, we derive a Proportional Response (PR) protocol that converges to market equilibrium. The positive results on the convergence of the PR dynamics are obtained in full generality, in the sense that they hold for Fisher markets with \emph{any} quasi-linear utility functions. Conversely, the chaos results for the GA dynamics are established even in the simplest possible setting of two firms and one good, and they hold for a wide range of price functions with different demand elasticities. Our findings suggest that by considering multi-agent interactions from a market rather than a game-theoretic perspective, we can formally derive natural learning protocols which are stable and converge to effective outcomes rather than being chaotic.

cs.GT↗

arXiv2020

Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory

Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.

cs.GT↗

arXiv2020

Exploring the Predictability of Cryptocurrencies via Bayesian Hidden Markov Models

In this paper, we consider a variety of multi-state Hidden Markov models for predicting and explaining the Bitcoin, Ether and Ripple returns in the presence of state (regime) dynamics. In addition, we examine the effects of several financial, economic and cryptocurrency specific predictors on the cryptocurrency return series. Our results indicate that the Non-Homogeneous Hidden Markov (NHHM) model with four states has the best one-step-ahead forecasting performance among all competing models for all three series. The dominance of the predictive densities over the single regime random walk model relies on the fact that the states capture alternating periods with distinct return characteristics. In particular, the four state NHHM model distinguishes bull, bear and calm regimes for the Bitcoin series, and periods with different profit and risk magnitudes for the Ether and Ripple series. Also, conditionally on the hidden states, it identifies predictors with different linear and non-linear effects on the cryptocurrency returns. These empirical findings provide important insight for portfolio management and policy implementation.

stat.AP↗

arXiv2020

Catastrophe by Design in Population Games: Destabilizing Wasteful Locked-in Technologies

In multi-agent environments in which coordination is desirable, the history of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies with a significant environmental footprint or high social cost persist despite the successful development of more environmentally friendly and/or socially efficient alternatives. The displacement of the status quo is hindered by entrenched economic interests and network effects. To exacerbate matters, the standard mechanism design approaches based on centralized authorities with the capacity to use preferential subsidies to effectively dictate system outcomes are not always applicable to modern decentralized economies. What other types of mechanisms are feasible? In this paper, we develop and analyze a mechanism that induces transitions from inefficient lock-ins to superior alternatives. This mechanism does not exogenously favor one option over another -- instead, the phase transition emerges endogenously via a standard evolutionary learning model, Q-learning, where agents trade-off exploration and exploitation. Exerting the same transient influence to both the efficient and inefficient technologies encourages exploration and results in irreversible phase transitions and permanent stabilization of the efficient one. On a technical level, our work is based on bifurcation and catastrophe theory, a branch of mathematics that deals with changes in the number and stability properties of equilibria. Critically, our analysis is shown to be structurally robust to significant and even adversarially chosen perturbations to the parameters of both our game and our behavioral model.

cs.GT↗

arXiv2019

Strategic customer behavior in a queueing system with alternating information structure

Strategic customer behavior is strongly influenced by the level of information that is provided to customers. Hence, to optimize the design of queueing systems, many studies consider various versions of the same service model and compare them under different information structures. In particular, two extreme versions are usually considered and compared: the observable in which customers are informed about the number of customers in the system and the unobservable in which they are only informed about the system parameters, e.g., arrival and service rates. In the present work, we study a model that bridges these two versions. More concretely, we assume that the system alternates between observable and unobservable periods. We characterize and compute customer equilibrium joining/balking strategies and show that the present model unifies and extends existing approaches of both heterogeneously observable models and models with delayed observations. More importantly, our findings indicate that an alternating information structure implies in general higher equilibrium throughput and social welfare in comparison to both the observable and unobservable cases. We complement our results with numerical experiments and provide managerial insight on the optimal control of the system parameters.

math.OC↗