Survival of dominated strategies under evolutionary dynamics

We show that any evolutionary dynamic that satisfies three mild requirements— continuity, positive correlation, and innovation—does not eliminate strictly dominated strategies in all games. Likewise, we demonstrate that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics

Universal Voting Protocol Tweaks to Make Manipulation Hard

Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. A number of recent papers study the complexity of manipulating existing protocols. This paper is the first work to take the next step of designing new protocols that are especially hard to manipulate. Rather than designing these new protocols from scratch, we instead show how to tweak existing protocols to make manipulation hard, while leaving much of the original nature of the protocol intact. The tweak studied consists of adding one elimination preround to the election. Surprisingly, this extremely simple and universal tweak makes typical protocols hard to manipulate! The protocols become NP-hard, #P-hard, or PSPACE-hard to manipulate, depending on whether the schedule of the preround is determined before the votes are collected, after the votes are collected, or the scheduling and the vote collecting are interleaved, respectively. We prove general sufficient conditions on the protocols for this tweak to introduce the hardness, and show that the most common voting protocols satisfy those conditions. These are the first results in voting settings where manipulation is in a higher complexity class than NP (presuming PSPACE $\neq$ NP)

Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Sequential Posted Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a take-it-or-leave-it offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i's, we prove that a constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be extracted.Comment: 29 pages, To appear in WINE 201

Large-scale distributions of tropospheric nitric, formic, and acetic acids over the western Pacific basin during wintertime

We report here measurements of the acidic gases nitric (HNO3), formic (HCOOH), and acetic (CH3COOH) over the western Pacific basin during the February-March 1994 Pacific Exploratory Mission-West (PEM-West B). These data were obtained aboard the NASA DC-8 research aircraft as it flew missions in the altitude range of 0.3–12.5 km over equatorial regions near Guam and then further westward encompassing the entire Pacific Rim arc. Aged marine air over the equatorial Pacific generally exhibited mixing ratios of acidic gases \u3c100 parts per trillion by volume (pptv). Near the Asian continent, discrete plumes encountered below 6 km altitude contained up to 8 parts per billion by volume (ppbv) HNO3 and 10 ppbv HCOOH and CH3COOH. Overall there was a general correlation between mixing ratios of acidic gases with those of CO, C2H2, and C2Cl4, indicative of emissions from combustion and industrial sources. The latitudinal distributions of HNO3 and CO showed that the largest mixing ratios were centered around 15°N, while HCOOH, CH3COOH, and C2Cl4 peaked at 25°N. The mixing ratios of HCOOH and CH3COOH were highly correlated (r2 = 0.87) below 6 km altitude, with a slope (0.89) characteristic of the nongrowing season at midlatitudes in the northern hemisphere. Above 6 km altitude, HCOOH and CH3COOH were marginally correlated (r2 = 0.50), and plumes well defined by CO, C2H2, and C2Cl4 were depleted in acidic gases, most likely due to scavenging during vertical transport of air masses through convective cloud systems over the Asian continent. In stratospheric air masses, HNO3 mixing ratios were several parts per billion by volume (ppbv), yielding relationships with O3 and N2O consistent with those previously reported for NOy

Influence of biomass combustion emissions on the distribution of acidic trace gases over the southern Pacific basin during austral springtime

This paper describes the large-scale distributions of HNO3, HCOOH, and CH3COOH over the central and South Pacific basins during the Pacific Exploratory Mission-Tropics (PEM-Tropics) in austral springtime. Because of the remoteness of this region from continental areas, low part per trillion by volume (pptv) mixing ratios of acidic gases were anticipated to be pervasive over the South Pacific basin. However, at altitudes of 2–12 km over the South Pacific, air parcels were encountered frequently with significantly enhanced mixing ratios (up to 1200 pptv) of acidic gases. Most of these air parcels were centered in the 3–7 km altitude range and occurred within the 15°−65°S latitudinal band. The acidic gases exhibited an overall general correlation with CH3Cl, PAN, and O3, suggestive of photochemical and biomass burning sources. There was no correlation or trend of acidic gases with common industrial tracer compounds (e.g., C2Cl4 or CH3CCl3). The combustion emissions sampled over the South Pacific basin were relatively aged exhibiting C2H2/CO ratios in the range of 0.2–2.2 pptv/ppbv. The relationships between acidic gases and this ratio were similar to what was observed in aged air parcels (i.e., \u3e3–5 days since they were over a continental area) over the western North Pacific during the Pacific Exploratory Mission-West Phases A and B (PEM-West A and B). In the South Pacific marine boundary layer a median C2H2/CO ratio of 0.6 suggested that this region was generally not influenced by direct inputs of biomass combustion emissions. Here we observed the lowest mixing ratios of acidic gases, with median values of 14 pptv for HNO3, 19 pptv for HCOOH, and 18 pptv for CH3COOH. These values were coincident with low mixing ratios of NOx(\u3c10 pptv), CO (≈50 parts per billion by volume (ppbv)), O3 (\u3c 20 ppbv), and long-lived hydrocarbons (e.g., C2H6 \u3c300 pptv). Overall, the PEM-Tropics data suggest an important influence of aged biomass combustion emissions on the distributions of acidic gases over the South Pacific basin in austral springtime