Optimal Deterministic Clock Auctions and Beyond

We design and analyze deterministic and randomized clock auctions for single-parameter domains with downward-closed feasibility constraints, aiming to maximize the social welfare. Clock auctions have been shown to satisfy a list of compelling incentive properties making them a very practical solution for real-world applications, partly because they require very little reasoning from the participating bidders. However, the first results regarding the worst-case performance of deterministic clock auctions from a welfare maximization perspective indicated that they face obstacles even for a seemingly very simple family of instances, leading to a logarithmic inapproximability result; this inapproximability result is information-theoretic and holds even if the auction has unbounded computational power. In this paper we propose a deterministic clock auction that achieves a logarithmic approximation for any downward-closed set system, using black box access to a solver for the underlying optimization problem. This proves that our clock auction is optimal and that the aforementioned family of instances exactly captures the information limitations of deterministic clock auctions. We then move beyond deterministic auctions and design randomized clock auctions that achieve improved approximation guarantees for a generalization of this family of instances, suggesting that the earlier indications regarding the performance of clock auctions may have been overly pessimistic

Cost-Sharing Methods for Scheduling Games under Uncertainty

We study the performance of cost-sharing protocols in a selfish scheduling setting with load-dependent cost functions. Previous work on selfish scheduling protocols has focused on two extreme models: omnipotent protocols that are aware of every machine and every job that is active at any given time, and oblivious protocols that are aware of nothing beyond the machine they control. The main focus of this paper is on a well-motivated middle-ground model of resource-aware protocols, which are aware of the set of machines that the system comprises, but unaware of what jobs are active at any given time. Apart from considering budget-balanced protocols, to which previous work was restricted, we augment the design space by also studying the extent to which overcharging can lead to improved performance. We first show that, in the omnipotent model, overcharging enables us to enforce the optimal outcome as the unique equilibrium, which largely improves over the Θ(log n)-approximation of social welfare that can be obtained by budget-balanced protocols, even in their best equilibrium. We then transition to the resource-aware model and provide price of anarchy (PoA) upper and lower bounds for different classes of cost functions. For concave cost functions, we provide a protocol with PoA of 1+ε for arbitrarily small ε0. When the cost functions can be both convex and concave we construct an overcharging protocol that yields PoA ≤ 2; a spectacular improvement over the bounds obtained for budget-balanced protocols, even in the omnipotent model. We complement our positive results with impossibility results for general increasing cost functions. We show that any resource-aware budget-balanced cost-sharing protocol has PoA of Θ(n) in this setting and, even if we use overcharging, no resource-aware protocol can achieve a PoA of o(√n)

Designing cost-sharing methods for Bayesian games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players

Constraining emissions of volatile organic compounds from western US wildfires with WE-CAN and FIREX-AQ airborne observations

The impact of biomass burning (BB) on the atmospheric burden of volatile organic compounds (VOCs) is highly uncertain. Here we apply the GEOS-Chem chemical transport model (CTM) to constrain BB emissions in the western USA at ∼ 25 km resolution. Across three BB emission inventories widely used in CTMs, the inventory–inventory comparison suggests that the totals of 14 modeled BB VOC emissions in the western USA agree with each other within 30 %–40 %. However, emissions for individual VOCs can differ by a factor of 1–5, driven by the regionally averaged emission ratios (ERs, reflecting both assigned ERs for specific biome and vegetation classifications) across the three inventories. We further evaluate GEOS-Chem simulations with aircraft observations made during WE-CAN (Western Wildfire Experiment for Cloud Chemistry, Aerosol Absorption and Nitrogen) and FIREX-AQ (Fire Influence on Regional to Global Environments and Air Quality) field campaigns. Despite being driven by different global BB inventories or applying various injection height assumptions, the model–observation comparison suggests that GEOS-Chem simulations underpredict observed vertical profiles by a factor of 3–7. The model shows small to no bias for most species in low-/no-smoke conditions. We thus attribute the negative model biases mostly to underestimated BB emissions in these inventories. Tripling BB emissions in the model reproduces observed vertical profiles for primary compounds, i.e., CO, propane, benzene, and toluene. However, it shows no to less significant improvements for oxygenated VOCs, particularly for formaldehyde, formic acid, acetic acid, and lumped ≥ C3 aldehydes, suggesting the model is missing secondary sources of these compounds in BB-impacted environments. The underestimation of primary BB emissions in inventories is likely attributable to underpredicted amounts of effective dry matter burned, rather than errors in fire detection, injection height, or ERs, as constrained by aircraft and ground measurements. We cannot rule out potential sub-grid uncertainties (i.e., not being able to fully resolve fire plumes) in the nested GEOS-Chem which could explain the negative model bias partially, though back-of-the-envelope calculation and evaluation using longer-term ground measurements help support the argument of the dry matter burned underestimation. The total ERs of the 14 BB VOCs implemented in GEOS-Chem only account for half of the total 161 measured VOCs (∼ 75 versus 150 ppb ppm−1). This reveals a significant amount of missing reactive organic carbon in widely used BB emission inventories. Considering both uncertainties in effective dry matter burned (× 3) and unmodeled VOCs (× 2), we infer that BB contributed to 10 % in 2019 and 45 % in 2018 (240 and 2040 Gg C) of the total VOC primary emission flux in the western USA during these two fire seasons, compared to only 1 %–10 % in the standard GEOS-Chem.</p

Constraining emissions of volatile organic compounds from western US wildfires with WE-CAN and FIREX-AQ airborne observations

The impact of biomass burning (BB) on the atmospheric burden of volatile organic compounds (VOCs) is highly uncertain. Here we apply the GEOS-Chem chemical transport model (CTM) to constrain BB emissions in the western US at ~25 km resolution. Across three BB emission inventories widely used in CTMs, the total of 14 modeled BB VOC emissions in the western US agree with each other within 30&ndash;40 %. However, emissions for individual VOC differ by up to a factor of 5 (i.e., lumped &ge; C4 alkanes), driven by the regionally averaged emission ratios (ERs) among inventories. We further evaluate GEOS-Chem simulations with aircraft observations made during WE-CAN (Western Wildfire Experiment for Cloud Chemistry, Aerosol Absorption, and Nitrogen) and FIREX-AQ (Fire Influence on Regional to Global Environments and Air Quality) field campaigns. Despite being driven by different global BB inventories or applying various injection height assumptions, GEOS-Chem simulations underpredict observed vertical profiles by a factor of 3&ndash;7. The model shows small-to-no bias for most species in low/no smoke conditions. We thus attribute the negative model biases mostly to underestimated BB emissions in these inventories. Tripling BB emissions in the model reproduces observed vertical profiles for primary compounds, i.e., CO, propane, benzene, and toluene. However, it shows no-to-less significant improvements for oxygenated VOCs, particularly formaldehyde, formic acid, acetic acid, and lumped &ge; C3 aldehydes, suggesting the model is missing secondary sources of these compounds in BB-impacted environments. The underestimation of primary BB emissions in inventories is likely attributable to underpredicted amounts of effective dry matter burned, rather than errors in fire detection, injection height, or ERs. We cannot rule out potential sub-grid uncertainties (i.e., not being able to fully resolve fire plumes) in the nested GEOS-Chem which could explain the model negative bias partially, though the back-of-the-envelope calculation and evaluation using longer-term ground measurements help increase the argument of the dry matter burned underestimation. The ERs of the 14 BB VOCs implemented in GEOS-Chem account for about half of the total 161 measured VOCs (~75 versus 150 ppb ppm-1). This reveals a significant amount of missing reactive organic carbon in widely-used BB emission inventories. Considering both uncertainties in effective dry matter burned and unmodeled VOCs, we infer that BB contributed up to 10 % in 2019 and 45 % in 2018 (240 and 2040 GgC) of the total VOC primary emission flux in the western US during these two fire seasons, compared to only 1&ndash;10 % in the standard GEOS-Chem.</p

Coordination mechanisms, cost-sharing, and approximation algorithms for scheduling

We reveal a connection between coordination mechanisms for unrelated machine scheduling and cost-sharing protocols. Using this connection, we interpret three coordination mechanisms from the recent literature as Shapley-value-based cost-sharing protocols, thus providing a unifying justification regarding why these mechanisms induce potential games. More importantly, this connection provides a template for designing novel coordination mechanisms, as well as approximation algorithms for the underlying optimization problem. The designer need only decide the total cost to be suffered on each machine, and then the Shapley value can be used to induce games guaranteed to possess a potential function; these games can, in turn, be used to design algorithms. To verify the power of this approach, we design a combinatorial algorithm that achieves an approximation guarantee of 1.81 for the problem of minimizing the total weighted completion time for unrelated machines. To the best of our knowledge, this is the best approximation guarantee among combinatorial polynomial-time algorithms for this problem