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

Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality

Designing a complex intervention for dementia case management in primary care

Background: Community-based support will become increasingly important for people with dementia, but currently services are fragmented and the quality of care is variable. Case management is a popular approach to care co-ordination, but evidence to date on its effectiveness in dementia has been equivocal. Case management interventions need to be designed to overcome obstacles to care co-ordination and maximise benefit. A successful case management methodology was adapted from the United States (US) version for use in English primary care, with a view to a definitive trial. Medical Research Council guidance on the development of complex interventions was implemented in the adaptation process, to capture the skill sets, person characteristics and learning needs of primary care based case managers. Methods: Co-design of the case manager role in a single NHS provider organisation, with external peer review by professionals and carers, in an iterative technology development process. Results: The generic skills and personal attributes were described for practice nurses taking up the case manager role in their workplaces, and for social workers seconded to general practice teams, together with a method of assessing their learning needs. A manual of information material for people with dementia and their family carers was also created using the US intervention as its source. Conclusions: Co-design produces rich products that have face validity and map onto the complexities of dementia and of health and care services. The feasibility of the case manager role, as described and defined by this process, needs evaluation in ‘real life’ settings

Second-price auctions with private entry costs

We study asymmetric second-price auctions under incomplete information. The bidders have potentially different, commonly-known, valuations for the object and private information about their entry costs. The seller, however, does not benefit from these entry costs. We calculate the equilibrium strategies of the bidders and analyze the optimal design for the seller in this environment

First E region observations of mesoscale neutral wind interaction with auroral arcs

We report the first observations of E region neutral wind fields and their interaction with auroral arcs at mesoscale spatial resolution during geomagnetically quiet conditions at Mawson, Antarctica. This was achieved by using a scanning Doppler imager, which can observe thermospheric neutral line-of-sight winds and temperatures simultaneously over a wide field of view. In two cases, the background E region wind field was perpendicular to an auroral arc, which when it appeared caused the wind direction within ∼50 km of the arc to rotate parallel along the arc, reverting to the background flow direction when the arc disappeared. This was observed under both westward and eastward plasma convection. The wind rotations occurred within 7–16 min. In one case, as an auroral arc propagated from the horizon toward the local zenith, the background E region wind field became significantly weaker but remained unaffected where the arc had not passed through. We demonstrate through modeling that these effects cannot be explained by height changes in the emission layer. The most likely explanation seems to be the greatly enhanced ion drag associated with the increased plasma density and localized ionospheric electric field associated with auroral arcs. In all cases, the F region neutral wind appeared less affected by the auroral arc, although its presence is clear in the data

Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions

Decentralized subcontractor scheduling with divisible jobs

Subcontracting allows manufacturer agents to reduce completion times of their jobs and thus obtain savings. This paper addresses the coordination of decentralized scheduling systems with a single subcontractor and several agents having divisible jobs. Assuming complete information, we design parametric pricing schemes that strongly coordinate this decentralized system, i.e., the agents’ choices of subcontracting intervals always result in efficient schedules. The subcontractor’s revenue under the pricing schemes depends on a single parameter which can be chosen to make the revenue as close to the total savings as required. Also, we give a lower bound on the subcontractor’s revenue for any coordinating pricing scheme. Allowing private information about processing times, we prove that the pivotal mechanism is coordinating, i.e., agents are better off by reporting their true processing times, and by participating in the subcontracting. We show that the subcontractor’s maximum revenue with any coordinating mechanism under private information equals the lower bound of that with coordinating pricing schemes under complete information. Finally, we address the asymmetric case where agents obtain savings at different rates per unit reduction in completion times. We show that coordinating pricing schemes do not always exist in this case