Best-Response Dynamics in Tullock Contests with Convex Costs

We study the convergence of best-response dynamics in Tullock contests with convex cost functions (these games always have a unique pure-strategy Nash equilibrium). We show that best-response dynamics rapidly converges to the equilibrium for homogeneous agents. For two homogeneous agents, we show convergence to an $\epsilon$-approximate equilibrium in $\Theta(\log\log(1/\epsilon))$ steps. For $n \ge 3$ agents, the dynamics is not unique because at each step $n-1 \ge 2$ agents can make non-trivial moves. We consider the model proposed by Ghosh and Goldberg (2023), where the agent making the move is randomly selected at each time step. We show convergence to an $\epsilon$-approximate equilibrium in $O(\beta \log(n/(\epsilon\delta)))$ steps with probability $1-\delta$, where $\beta$ is a parameter of the agent selection process, e.g., $\beta = n^2 \log(n)$ if agents are selected uniformly at random at each time step. We complement this result with a lower bound of $\Omega(n + \log(1/\epsilon)/\log(n))$ applicable for any agent selection process.Comment: 43 pages. WINE '23 versio

On the Welfare of Cardinal Voting Mechanisms

A voting mechanism is a method for preference aggregation that takes as input preferences over alternatives from voters, and selects an alternative, or a distribution over alternatives. While preferences of voters are generally assumed to be cardinal utility functions that map each alternative to a real value, mechanisms typically studied assume coarser inputs, such as rankings of the alternatives (called ordinal mechanisms). We study cardinal mechanisms, that take as input the cardinal utilities of the voters, with the objective of minimizing the distortion - the worst-case ratio of the best social welfare to that obtained by the mechanism. For truthful cardinal mechanisms with m alternatives and n voters, we show bounds of Theta(mn), Omega(m), and Omega(sqrt{m}) for deterministic, unanimous, and randomized mechanisms respectively. This shows, somewhat surprisingly, that even mechanisms that allow cardinal inputs have large distortion. There exist ordinal (and hence, cardinal) mechanisms with distortion O(sqrt{m log m}), and hence our lower bound for randomized mechanisms is nearly tight. In an effort to close this gap, we give a class of truthful cardinal mechanisms that we call randomized hyperspherical mechanisms that have O(sqrt{m log m}) distortion. These are interesting because they violate two properties - localization and non-perversity - that characterize truthful ordinal mechanisms, demonstrating non-trivial mechanisms that differ significantly from ordinal mechanisms. Given the strong lower bounds for truthful mechanisms, we then consider approximately truthful mechanisms. We give a mechanism that is delta-truthful given delta in (0,1), and has distortion close to 1. Finally, we consider the simple mechanism that selects the alternative that maximizes social welfare. This mechanism is not truthful, and we study the distortion at equilibria for the voters (equivalent to the Price of Anarchy, or PoA). While in general, the PoA is unbounded, we show that for equilibria obtained from natural dynamics, the PoA is close to 1. Thus relaxing the notion of truthfulness in both cases allows us to obtain near-optimal distortion

Transradial versus transfemoral arterial access in the uterine artery embolization of fibroids

Purpose: Transradial arterial access has become more popular in body interventional procedures but has not been ubiquitously adapted. This retrospective study assesses the efficacy of this approach in uterine artery embolization. Aim of the study was to compare transradial to transfemoral arterial access in patients undergoing uterine artery embolization for the treatment of fibroids. Material and methods: A total of 172 patients underwent uterine artery embolization procedures at our institute from October 2014 to June 2020. Of these, 76 patients had their operations performed via transfemoral access while 96 underwent transradial access. The peak radiation dose, fluoroscopy time, procedure time, total contrast volume, and equipment cost for each procedure were all reviewed to evaluate for statistical differences between the 2 groups. Results: All cases were technically successful without major complications. The average peak skin dose was 2281 mGy, with no statistical difference between the transradial or transfemoral cohorts. Average fluoroscopy time was 25 minutes, also with no statistical difference between the subsets. Mean procedure time was 100 min, and mean contrast volume usage was 138 mL with no statistical differences. Similarly, the average equipment cost was $2204, with no significant differences found between transradial and transfemoral access. Conclusions: With respect to many pertinent radiation parameters, transradial access was evaluated as being an equally efficacious alternative to transfemoral access in uterine artery embolization procedures. The results of this study suggest that transradial access should be considered more often, whenever viable, as an option in the uterine artery embolization treatment of fibroids

Truthful and Near-Optimal Mechanisms for Welfare Maximization in Multi-Winner Elections

Mechanisms for aggregating the preferences of agents in elections need to balance many different considerations, including efficiency, information elicited from agents, and manipulability. We consider the utilitarian social welfare of mechanisms for preference aggregation, measured by the distortion. We show that for a particular input format called threshold approval voting, where each agent is presented with an independently chosen threshold, there is a mechanism with nearly optimal distortion when the number of voters is large. Threshold mechanisms are potentially manipulable, but place a low informational burden on voters. We then consider truthful mechanisms. For the widely-studied class of ordinal mechanisms which elicit the rankings of candidates from each agent, we show that truthfulness essentially imposes no additional loss of welfare. We give truthful mechanisms with distortion O(√m log m) for k-winner elections, and distortion O(√m log m) when candidates have arbitrary costs, in elections with m candidates. These nearly match known lower bounds for ordinal mechanisms that ignore the strategic behavior. We further tighten these lower bounds and show that for truthful mechanisms our first upper bound is tight. Lastly, when agents decide between two candidates, we give tight bounds on the distortion for truthful mechanisms

Complexity of Deliberative Coalition Formation

Elkind et al. (AAAI'21) introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their model: in the Euclidean model, proposals and agent locations are points in R^d and the distance is measured according to ||...||_2; and in the hypercube model, proposals and agent locations are vertices of the d-dimensional hypercube and the metric is the Hamming distance. They show that in the Euclidean model 2-compromises are guaranteed to succeed, but in the hypercube model for deliberation to succeed it may be necessary to use k-compromises with k >= d. We complement their analysis by (1) proving that in both models it is hard to find a proposal with a high degree of support, and even a 2-compromise transition may be hard to compute; (2) showing that a sequence of 2-compromise transitions may be exponentially long; (3) strengthening the lower bound on the size of the compromise for the d-hypercube model from d to 2^Ω(d)

Use of the gun-sight technique to create a parallel transjugular intrahepatic portosystemic shunt

A parallel shunt (PS) is often necessary to regain portal decompression in a dysfunctional transjugular intrahepatic portosystemic shunt (TIPS). Here, we successfully utilized the gun-sight technique to create a PS. An 81-year-old male with decompensated NASH cirrhosis and recent TIPS placement presents with recurrent ascites and pleural effusions in the setting of a persistent portosystemic gradient. Due to a lack of access to endovascular ultrasound and complex patient anatomy, a gun-site technique was approached to create a PS (left portal vein [PV] to left hepatic vein [HV]). After the right HV and existing TIPS were accessed via the right internal jugular vein access, the left HV was accessed. Following a left portal venogram, 10 mm snares were placed into the left HV and the left PV. An 18-gauge needle was then fluoroscopically placed through and through both snares. A 0.035 Glidewire was snared with the help of both snares, establishing access from the left HV via the left PV to the right PV. After serial dilation, a roadrunner wire and catheter were placed into the main PV and superior mesenteric vein, followed by stent dilation. Post-TIPS portal venogram showed prompt flow of contrast from the main PV to the right atrium without any stenosis through both TIPS stents in the left and right PVs. Initial and postprocedural TIPS gradients were 24 mm Hg and 6 mm Hg, respectively. Gun-site technique is a valuable technique in creating a parallel TIPS shunt