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{"Abstract":["For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3).\r\nFor domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following:\r\n1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. \r\n2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest.\r\nWe also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019]."]} 

Selfish miners selectively withhold blocks to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. [Carlsten et al., 2016] is a notable exception, observing that similar strategic behavior is profitable in a zero-block-reward regime (the endgame for Bitcoin’s quadrennial halving schedule) if miners are compensated with transaction fees alone. Neither model fully captures miner incentives today. The block reward remains 3.125 BTC, yet some blocks yield significantly higher revenue. For example, congestion during the launch of the Babylon protocol in August 2024 caused transaction fees to spike from 0.14 BTC to 9.52 BTC, a 68× increase in fees within two blocks. Our results are both practical and theoretical. Of practical interest, we study selfish mining profitability under a combined reward function that more accurately models miner incentives. This analysis enables us to make quantitative claims about protocol risk (e.g., the mining power at which a selfish strategy becomes profitable is reduced by 22% when optimizing over the combined reward function versus block rewards alone) and qualitative observations (e.g., a miner considering both block rewards and transaction fees will mine more or less aggressively respectively than if they cared about either alone). These practical results follow from our novel model and methodology, which constitute our theoretical contributions. We model general, time-accruing stochastic rewards in the Nakamoto Consensus Game, which requires explicit treatment of difficult adjustment and randomness; we characterize reward function structure through a set of properties (e.g., that rewards accrue only as a function of time since the parent block). We present a new methodology to analytically calculate expected selfish miner rewards under a broad class of stochastic reward functions and validate our method numerically by comparing it with the existing literature and simulating the combined reward sources directly. 

{"Abstract":["We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is 1/2. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio 1-O(√{(log k)/k}) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme.\r\nThe key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a 1-Lipschitz function that is not (approximately) self-bounding."]}