Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle. In this paper, we give a rigorous stochastic analysis of an attack where the goal of the adversary is to double-spend while mining selfishly. To do so, we first combine stubborn and selfish mining attacks, \textit{i.e.}, construct a strategy where the attacker acts stubborn until its private branch reaches a certain length and then switches to act selfish. We provide the optimal stubbornness for each parameter regime. Next, we provide the maximum stubbornness that is still more profitable than honest mining and argue a connection between the level of stubbornness and the $k$-confirmation rule. We show that, at each attack cycle, if the level of stubbornness is higher than $k$, the adversary gets a free shot at double-spending. At each cycle, for a given stubbornness level, we rigorously formulate how great the probability of double-spending is. We further modify the attack in the stubborn regime in order to conceal the attack and increase the doub
This paper investigates the relationship between public education spending and income inequality across U.S. counties from 2010 to 2022 using quantile regression methods. The analysis shows that total per pupil education spending is consistently associated with a small increase in income inequality, with stronger effects in high inequality counties. In contrast, the composition of education spending plays a substantially more important role. Reallocating budgets toward instructional, support service, and other current expenditures significantly reduces income inequality, particularly at the upper quantiles of the Gini distribution. Capital outlays and interest payments exhibit weaker and mixed effects. Economic and demographic factors, especially poverty, median income, and educational attainment, remain dominant drivers of inequality. Overall, the results demonstrate that how education funds are allocated matters more than how much is spent, underscoring the importance of budget composition in using public education policy to promote equity.
We show that the amount of foreign exchange reserves (FER) in the world in a given currency is highly correlated with the GDP and military spending of that country for a set of western economies during the last 20 years. Taking into account multicollinearity, Ridge and Lasso regressions reveal that the Foreign Exchange Reserve is better explained by military spending than GDP for seven western currencies. For each year shown, military spending is statistically significant more than the monetary instrument M2. Comparing the currency of the second world economy, the Chinese renminbi, is well beyond the western FER equilibrium, but yearly analysis shows that there is a steady trend towards a new FER balance. Next, we define a complex geopolitical network model in which the probability of switching to an alternative FER currency depends both on economic and political factors. Military spending is introduced into the model as an average share of GDP observed within the data. As the GDP of a particular country grows, so does the military power of a country. The nature of the creation of new currency networks initially depends only on geopolitical allegiance. As the volume of trade with a
We study online decision making problems under resource constraints, where both reward and cost functions are drawn from distributions that may change adversarially over time. We focus on two canonical settings: $(i)$ online resource allocation where rewards and costs are observed before action selection, and $(ii)$ online learning with resource constraints where they are observed after action selection, under full feedback or bandit feedback. It is well known that achieving sublinear regret in these settings is impossible when reward and cost distributions may change arbitrarily over time. To address this challenge, we analyze a framework in which the learner is guided by a spending plan--a sequence prescribing expected resource usage across rounds. We design general (primal-)dual methods that achieve sublinear regret with respect to baselines that follow the spending plan. Crucially, the performance of our algorithms improves when the spending plan ensures a well-balanced distribution of the budget across rounds. We additionally provide a robust variant of our methods to handle worst-case scenarios where the spending plan is highly imbalanced. To conclude, we study the regret of
The Oregon Health Insurance Experiment (OHIE) offers a unique opportunity to examine the causal relationship between Medicaid coverage and happiness among low-income adults, using an experimental design. This study leverages data from comprehensive surveys conducted at 0 and 12 months post-treatment. Previous studies based on OHIE have shown that individuals receiving Medicaid exhibited a significant improvement in mental health compared to those who did not receive coverage. The primary objective is to explore how Medicaid coverage impacts happiness, specifically analyzing in which direction variations in healthcare spending significantly improve mental health: higher spending or lower spending after Medicaid. Utilizing instrumental variable (IV) regression, I conducted six separate regressions across subgroups categorized by expenditure levels and happiness ratings, and the results reveal distinct patterns. Enrolling in OHP has significantly decreased the probability of experiencing unhappiness, regardless of whether individuals had high or low medical spending. Additionally, it decreased the probability of being pretty happy and having high medical expenses, while increasing the
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $μ(x)$ and $σ^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip $[a+bt-(1/2)\varepsilon,a+bt+(1/2)\varepsilon]$.The limit $V$ as $\varepsilon\rightarrow0$ is the full halfline version of the local time of $X(t)-a-bt$ at zero, and can be thought of as the time $X$ spends along the straight line $x=a+bt$. We prove that $V$ is either infinite with probability 1 or distributed as a mixture of an exponential and a unit point mass at zero, and we give formulae for the parameters of this distribution in terms of $μ(\cdot)$, $σ(\cdot)$, $a$, $b$, and the starting point $X(0)$. The special case ofa Brownian motion is studied in more detail, leading in particular to a full process $V(b)$ with continuous sample paths and exponentially distributed marginals. This construction leads to new families of bivariate and multivariate exponential distributions. Truncated versions of such `total relative time' variables are also studied. A relation is pointed out to a second order asymptotics problem in statistical estimation theory, recently investigated in Hjort and F
Scholars and policymakers have vigorously debated what the impact of government spending on economic growth is. Some current research and theoretical models suggest that the reaction of economic growth to the extension of government spending can be either positive or negative. This article intends to investigate the inverted-U shaped relationship between output growth and government spending (i.e., government fixed capital formation [GFCF] and government final consumption expenditure [GFCE]). Ordinary least squares (OLS) is employed as an approach to annual data for Cambodia obtained from 1971 to 2015. The result reveals that GFCF and GFCE have an inverted-U shaped relation with economic growth and that 5.40% and 7.23% are the optimal values of GFCF and GFCE, respectively. The labour growth rate and export growth rate contribute positively to the growth rate of output. This study indicates that the increasing level of government expenditure reduces the efficacy of government spending, and also helps Cambodia's policymakers to control fiscal policy more efficiently.
Dream11 is a fantasy sports platform that allows users to create their own virtual teams for real-life sports events. We host multiple sports and matches for our 200M+ user base. In this RMG (real money gaming) setting, users pay an entry amount to participate in various contest products that we provide to users. In our current work, we discuss the problem of predicting the user's propensity to spend in a gaming round, so it can be utilized for various downstream applications. e.g. Upselling users by incentivizing them marginally as per their spending propensity, or personalizing the product listing based on the user's propensity to spend. We aim to model the spending propensity of each user based on past transaction data. In this paper, we benchmark tree-based and deep-learning models that show good results on structured data, and we propose a new architecture change that is specifically designed to capture the rich interactions among the input features. We show that our proposed architecture outperforms the existing models on the task of predicting the user's propensity to spend in a gaming round. Our new transformer model surpasses the state-of-the-art FT-Transformer, improving
This paper investigates the heterogeneous effects of military spending news shocks on household income and wealth inequality for a large, panel of advanced and emerging economies. Confirming prior literature, we find that military spending news shocks lead to persistent increases in aggregate output and Total Factor Productivity. Our primary contribution is documenting contrasting distributional impacts. We find that expansionary military spending is associated with a mitigation of income inequality, as income gains are disproportionately larger at the left tail of the distribution, primarily driven by a rise in labour income and employment in industry. Conversely, the shock is found to increase wealth inequality, particularly in high-income countries, by raising the wealth share of the top decile via effects on business asset holdings.
This study investigates the impact of a fiscal policy spending shock on the economy of the Visegrad 4 countries. The impact is estimated with an SVAR model, and the calculations are based on 84 quarterly observations (1999Q1-2019Q4). The results suggest that fiscal expansion has a larger than usual impact in the V4 countries (except for Slovakia): the estimated long-term (5-year) cumulative spending multipliers are 0.81 for Czechia, 1.14 for Hungary, and 1.76 for Poland (the Slovakian multiplier has a value of -0.18, but it is not significant). The discussion section also connects higher spending multipliers with a higher share of VAT revenues, a higher debt ratio, higher foreign debt, and lower openness.
Federated learning (FL) with differential privacy (DP) provides a framework for collaborative machine learning, enabling clients to train a shared model while adhering to strict privacy constraints. The framework allows each client to have an individual privacy guarantee, e.g., by adding different amounts of noise to each client's model updates. One underlying assumption is that all clients spend their privacy budgets uniformly over time (learning rounds). However, it has been shown in the literature that learning in early rounds typically focuses on more coarse-grained features that can be learned at lower signal-to-noise ratios while later rounds learn fine-grained features that benefit from higher signal-to-noise ratios. Building on this intuition, we propose a time-adaptive DP-FL framework that expends the privacy budget non-uniformly across both time and clients. Our framework enables each client to save privacy budget in early rounds so as to be able to spend more in later rounds when additional accuracy is beneficial in learning more fine-grained features. We theoretically prove utility improvements in the case that clients with stricter privacy budgets spend budgets unevenl
This article expands Milton Friedman's spending matrix to analyse 'spending efficiency' and 'preference compatibility' across different economic systems against five key outcome criteria. By generalising Friedman's typology, it compares efficiency and freedom as systems shift from laissez-faire capitalism to communism, illustrating a gradual deterioration in their key outcomes. While government intervention is sometimes necessary to address market failures, its role should always be carefully limited to avoid inefficiency and misalignment with individual preferences. The insights may provide guidance for policymakers in designing economic systems and policies that promote both economic prosperity and personal liberty.
Fintech lending has become a central mechanism through which digital platforms stimulate consumption, offering dynamic, personalized credit limits that directly shape the purchasing power of consumers. Although prior research shows that higher limits increase average spending, scalar-based outcomes obscure the heterogeneous distributional nature of consumer responses. This paper addresses this gap by proposing a new causal inference framework that estimates how continuous changes in the credit limit affect the entire distribution of consumer spending. We formalize distributional causal effects within the Wasserstein space and introduce a robust Distributional Double Machine Learning estimator, supported by asymptotic theory to ensure consistency and validity. To implement this estimator, we design a deep learning architecture comprising two components: a Neural Functional Regression Net to capture complex, nonlinear relationships between treatments, covariates, and distributional outcomes, and a Conditional Normalizing Flow Net to estimate generalized propensity scores under continuous treatment. Numerical experiments demonstrate that the proposed estimator accurately recovers dist
Theoretical guarantees for double spending probabilities for the Nakamoto consensus under the $k$-deep confirmation rule have been extensively studied for zero/bounded network delays and fixed mining rates. In this paper, we introduce a ruin-theoretical model of double spending for Nakamoto consensus under the $k$-deep confirmation rule when the honest mining rate is allowed to be an arbitrary function of time including the block delivery periods, i.e., time periods during which mined blocks are being delivered to all other participants of the network. Time-varying mining rates are considered to capture the intrinsic characteristics of the peer to peer network delays as well as dynamic participation of miners such as the gap game and switching between different cryptocurrencies. Ruin theory is leveraged to obtain the double spend probabilities and numerical examples are presented to validate the effectiveness of the proposed analytical method.
We consider a seller who offers services to a buyer with multi-unit demand. Prior to the realization of demand, the buyer receives a noisy signal of their future demand, and the seller can design contracts based on the reported value of this signal. Thus, the buyer can contract with the service provider for an unknown level of future consumption, such as in the market for cloud computing resources or software services. We characterize the optimal dynamic contract, extending the classic sequential screening framework to a nonlinear and multi-unit setting. The optimal mechanism gives discounts to buyers who report higher signals, but in exchange they must provide larger fixed payments. We then describe how the optimal mechanism can be implemented by two common forms of contracts observed in practice, the two-part tariff and the committed spend contract. Finally, we use extensions of our base model to shed light on policy-focused questions, such as analyzing how the optimal contract changes when the buyer faces commitment costs, or when there are liquid spot markets.
With the surge in mobile gaming, accurately predicting user spending on newly downloaded games has become paramount for maximizing revenue. However, the inherently unpredictable nature of user behavior poses significant challenges in this endeavor. To address this, we propose a robust model training and evaluation framework aimed at standardizing spending data to mitigate label variance and extremes, ensuring stability in the modeling process. Within this framework, we introduce a collaborative-enhanced model designed to predict user game spending without relying on user IDs, thus ensuring user privacy and enabling seamless online training. Our model adopts a unique approach by separately representing user preferences and game features before merging them as input to the spending prediction module. Through rigorous experimentation, our approach demonstrates notable improvements over production models, achieving a remarkable \textbf{17.11}\% enhancement on offline data and an impressive \textbf{50.65}\% boost in an online A/B test. In summary, our contributions underscore the importance of stable model training frameworks and the efficacy of collaborative-enhanced models in predicti
With the goal of building a decentralized and fully parallel payment system, we address the Fractional Spending Problem using (k1, k2)-quorum systems - both introduced by Bazzi and Tucci-Piergiovanni (PODC 2024). Fractional spending enables payments without immediate validation of an entire quorum, as necessary in classical approaches. Multiple spending from a same fund can occur concurrently, with final settlement involving previously contacted quorums. To tolerate a rushing-adaptive adversary, the composition of these quorums must stay hidden until settlement succeeds. We propose a new abstraction called secret quorums - of independent interest - that fulfill this property and implement it through ring verifiable random functions. We then propose a new protocol called StealthDust, where secret quorums allow to reduce payment latency from five to three communications steps and improve settlment message complexity from O(n^3) to O(n^2) compared to the original protocol.
Auto-bidding problem under a strict return-on-spend constraint (ROSC) is considered, where an algorithm has to make decisions about how much to bid for an ad slot depending on the revealed value, and the hidden allocation and payment function that describes the probability of winning the ad-slot depending on its bid. The objective of an algorithm is to maximize the expected utility (product of ad value and probability of winning the ad slot) summed across all time slots subject to the total expected payment being less than the total expected utility, called the ROSC. A (surprising) impossibility result is derived that shows that no online algorithm can achieve a sub-linear regret even when the value, allocation and payment function are drawn i.i.d. from an unknown distribution. The problem is non-trivial even when the revealed value remains constant across time slots, and an algorithm with regret guarantee that is optimal up to logarithmic factor is derived.
When a single photon traverses a cloud of 2-level atoms, the average time it spends as an atomic excitation -- as measured by weakly probing the atoms -- can be shown to be the spontaneous lifetime of the atoms multiplied by the probability of the photon being scattered into a side mode. A tempting inference from this is that an average scattered photon spends one spontaneous lifetime as an atomic excitation, while photons that are transmitted spend zero time as atomic excitations. However, recent experimental work by some of us [PRX Quantum 3, 010314 (2022)] refutes this intuition. We examine this problem using the weak-value formalism and show that the time a transmitted photon spends as an atomic excitation is equal to the group delay, which can take on positive or negative values. We also determine the corresponding time for scattered photons and find that it is equal to the time delay of the scattered photon pulse, which consists of a group delay and a time delay associated with elastic scattering, known as the Wigner time delay. This work provides new insight into the complex and surprising histories of photons travelling through absorptive media.
We study the incentives behind double-spend attacks on Nakamoto-style Proof-of-Work cryptocurrencies. In these systems, miners are allowed to choose which transactions to reference with their block, and a common strategy for selecting transactions is to simply choose those with the highest fees. This can be problematic if these transactions originate from an adversary with substantial (but less than 50\%) computational power, as high-value transactions can present an incentive for a rational adversary to attempt a double-spend attack if they expect to profit. The most common mechanism for deterring double-spend attacks is for the recipients of large transactions to wait for additional block confirmations (i.e., to increase the attack cost). We argue that this defense mechanism is not satisfactory, as the security of the system is contingent on the actions of its users. Instead, we propose that defending against double-spend attacks should be the responsibility of the miners; specifically, miners should limit the amount of transaction value they include in a block (i.e., reduce the attack reward). To this end, we model cryptocurrency mining as a mean-field game in which we augment t