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While physician relationships (measured through shared patients) are associated with clinical and utilization outcomes, the extent to which this is driven by local or global network characteristics is not well established. The objective of this research is to examine the association between local and global network statistics with total medical spending and utilization. Data used are the 2011 Massachusetts All Payer Claims Database. The association between network statistics and total medical spending and utilization (using standardized prices) is estimated using multivariate regression analysis controlling for patient demographics and health status. We limit the sample to continuously enrolled commercially insured patients in Massachusetts in 2011. Mean patient age was 45 years, and 56.3% of patients were female. 73.4% were covered by a health maintenance organization. Average number of visits was 5.43, with average total medical spending of $4,911 and total medical utilization of $4,252. Spending was lower for patients treated by physicians with higher degree (p<0.001), eigenvector centrality (p<0.001), clustering coefficient (p<0.001), and measures reflecting the normalized degree (p<0.001) and eigenvector centrality (p<0.001) of specialists connected to a patient's PCP. Spending was higher for patients treated by physicians with higher normalized degree, which accounts for physician specialty and patient panel size (p<0.001). Results were similar for utilization outcomes, although magnitudes differed indicating patients may see different priced physicians. Generally, higher values of network statistics reflecting local connectivity adjusted for physician characteristics are associated with increased costs and utilization, while higher values of network statistics reflecting global connectivity are associated with decreased costs and utilization. As changes in the financing and delivery system advance through policy changes and healthcare consolidation, future research should examine mechanisms through which this structure impacts outcomes and potential policy responses to determine ways to reduce costs while maintaining quality and coordination of care. It is unknown whether local and global measures of physician network connectivity associated with spending and utilization for commercially insured patients?In this social network analysis, we found generally higher values of network statistics reflecting local connectivity are associated with increased costs and utilization, while higher values of network statistics reflecting global connectivity are associated with decreased costs and utilization.Understanding how to influence local and global physician network characteristics may be important for reducing costs while maintaining quality.

We present a new algorithm for computing pure-strategy ε-Bayes-Nash equilibria (ε-BNEs) in combinatorial auctions. The main innovation of our algorithm is to separate the algorithm’s search phase (for finding the ε-BNE) from the verification phase (for computing the ε). Using this approach, we obtain an algorithm that is both very fast and provides theoretical guarantees on the ε it finds. Our main contribution is a verification method which, surprisingly, allows us to upper bound the ε across the whole continuous value space without making assumptions about the mechanism. Using our algorithm, we can now compute ε-BNEs in multi-minded domains that are significantly more complex than what was previously possible to solve. We release our code under an open-source license to enable researchers to perform algorithmic analyses of auctions, to enable bidders to analyze different strategies, and many other applications.

BACKGROUND:Access to physicians is a major concern for Medicaid programs. However, little is known about relationships between physician participation in Medicaid and the individual-level and practice-level characteristics of physicians. METHODS:We used the 2011 Massachusetts All Payer Claims Database, containing all commercial and Medicaid claims; we linked with data on physician characteristics. We measured Medicaid participation intensity (fraction of the physician’s patient panel with Medicaid) for primary care physicians (PCPs) and medical specialists. We measured influence of physicians within a patient referral network using eigenvector centrality. We used regression models to associate Medicaid intensity with physician individual-level and practice-level characteristics. FINDINGS:About 92.6% of physicians treated at least 1 Medicaid patient, but the median physician’s panel contained only 5.7% Medicaid patients. Medicaid intensity was associated with physician training and influence for PCPs and specialists. For medical specialists, a 1 percentage point increase in Medicaid intensity was associated with a lower probability of being board certified (−0.22 percentage points; 95% CI, −0.30, −0.14), lower probability of attending a domestic medical school (−0.14 percentage points; 95% CI, −0.22, −0.05), having attended a less well-ranked domestic medical school (0.23 ranks; 95% CI, 0.15, 0.30), and having slightly less influence in the referral network. PCPs displayed similar results but high Medicaid intensity physicians had substantially less influence in the referral network. CONCLUSIONS:Medicaid participation intensity shows substantial variation across physicians, indicating limits of binary participation measures. Physicians with more Medicaid patients had characteristics often perceived by patients to be of lower quality.

The standard approach of mechanism design theory insists on equilibrium behaviour by participants. This assumption is captured by imposing incentive constraints on the design space. But in bridging from theory to practice, it often becomes necessary to relax incentive constraints in order to allow tradeoffs with other desirable properties. This article surveys a number of different options that can be adopted in relaxing incentive constraints, providing a current view of the state-of-the-art.

Professional and social connections among physicians impact patient outcomes, but little is known about how characteristics of insurance plans are associated with physician patientsharing network structure. We use information from commercially insured enrollees in the 2011 Massachusetts All Payer Claims Database to construct and examine the structure of the physician patient-sharing network using standard and novel social network measures. Using regression analysis, we examine the association of physician patient-sharing network measures with an indicator of whether a patient is enrolled in a health maintenance organization (HMO) or preferred provider organization (PPO), controlling for patient and insurer characteristics and observed health status. We find patients enrolled in HMOs see physicians who are more central and densely embedded in the patient-sharing network. We find HMO patients see PCPs who refer to specialists who are less globally central, even as these specialists are more locally central. Our analysis shows there are small but significant differences in physician patient-sharing network as experienced by patients with HMO versus PPO insurance. Understanding connections between physicians is essential and, similar to previous findings, our results suggest policy choices in the insurance and delivery system that change physician connectivity may have important implications for healthcare delivery, utilization and costs.

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as \"artificial items\" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We thus provide a method for converting a CA problem that admits only non-anonymous, nonlinear bundle prices into one that admits anonymous linear prices over the augmented item space, forestalling ex-post bidder complaints about opaque and strongly discriminatory pricing. To this end, we introduce a refinement of the Walrasian equilibrium which we call a \"price-match equilibrium\" (PME) in which all prices are justified by providing an iso-revenue reallocation for the hypothetical removal of any single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature.

Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we derive iterative Vickrey auctions that maintain a single price path, eliminating the overhead and incentive problems associated with multiple price paths used solely for payment calculations. We demonstrate the versatility of our method by developing a novel iterative Vickrey auction for the multi-unit setting and an iterative variant of the Product-Mix auction. The resulting auctions combine the transparency of iterative price discovery with the efficiency and incentive properties of the VCG mechanism.

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as \"artificial items\" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. While the lack of an integer programming gap is sufficient to guarantee a Walrasian equilibrium, we show that it does not guarantee a \"price-match equilibrium\" (PME), a refinement that we introduce, in which prices are justified by an iso-revenue outcome for any hypothetical removal of a single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature.

We present the design and analysis of the first fully expressive, iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language (TBBL) that is concise and expressive for CEs. Bidders specify lower and upper bounds in TBBL on their value for different trades and refine these bounds across rounds. These bounds allow price discovery and useful preference elicitation in early rounds, and allow termination with an efficient trade despite partial information on bidder valuations. All computation in the exchange is carefully optimized to exploit the structure of the bid-trees and to avoid enumerating trades. A proxied interpretation of a revealed-preference activity rule, coupled with simple linear prices, ensures progress across rounds. The exchange is fully implemented, and we give results demonstrating several aspects of its scalability and economic properties with simulated bidding strategies.

Strategyproof mechanisms provide robust equilibria with minimal assumptions about knowledge and rationality, but can be unachievable in combination with other desirable properties, such as budget-balance, stability against deviations by coalitions, and computational tractability. We thus seek a relaxation of this solution concept, and propose several definitions for general settings with private and quasi-linear utility. We are then able to describe the ideal mechanism according to these definitions by formulating the design problem as a constrained optimization problem. Discretization and statistical sampling allow us to reify this problem as a linear program to find ideal mechanisms in simple settings. However, this constructive approach is not scalable. We thus advocate for using the quantiles of the ex post unilateral gain from deviation as a method for capturing useful information about the incentives in a mechanism. Where this also is too expensive, we propose using the KL-Divergence between the payoff distribution at truthful reports and the distribution under a strategyproof \"reference\" mechanism that solves a problem relaxation. We prove bounds that relate such quasimetrics to our definitions of approximate incentive compatibility; we demonstrate empirically in combinatorial market settings that they are informative about the eventual equilibrium, where simple regret-based metrics are not. We then design, implement, and analyze a mechanism for just such an overconstrained setting: the first fully expressive, iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language (TBBL) that is concise and expressive for CEs. Bidders specify lower and upper bounds in TBBL on their value for different, trades and refine these bounds across rounds. A proxied interpretation of a revealed-preference activity rule, coupled with simple linear prices, ensures progress across rounds. We are able to prove efficiency under truthful bidding despite using linear pricing that can only approximate competitive equilibrium. Finally, we apply several key concepts from this general mechanism in a combinatorial market for finding the right balance between power and performance in allocating computational resources in a data center.