Proving soundness of combinatorial Vickrey auctions and generating verified executable code

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable code from the formally defined auction. This removes a source of error in implementing the auction design. We intend to use formal methods to verify new auction designs. Here, our contribution is to introduce and demonstrate the use of formal methods for auction verification in the familiar setting of a well-known auction

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

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

Unit Testing in ASPIDE

Answer Set Programming (ASP) is a declarative logic programming formalism, which is employed nowadays in both academic and industrial real-world applications. Although some tools for supporting the development of ASP programs have been proposed in the last few years, the crucial task of testing ASP programs received less attention, and is an Achilles' heel of the available programming environments. In this paper we present a language for specifying and running unit tests on ASP programs. The testing language has been implemented in ASPIDE, a comprehensive IDE for ASP, which supports the entire life-cycle of ASP development with a collection of user-friendly graphical tools for program composition, testing, debugging, profiling, solver execution configuration, and output-handling.Comment: 12 pages, 4 figures, Proceedings of the 25th Workshop on Logic Programming (WLP 2011

Constraint programming for random testing of a trading system

Financial markets use complex computer trading systems whose failures can cause serious economic damage, making reliability a major concern. Automated random testing has been shown to be useful in nding defects in these systems, but its inherent test oracle problem (automatic generation of the expected system output) is a drawback that has typically prevented its application on a larger scale. Two main tasks have been carried out in this thesis as a solution to the test oracle problem. First, an independent model of a real trading system based on constraint programming, a method for solving combinatorial problems, has been created. Then, the model has been integrated as a true test oracle in automated random tests. The test oracle maintains the expected state of an order book throughout a sequence of random trade order actions, and provides the expected output of every auction triggered in the order book by generating a corresponding constraint program that is solved with the aid of a constraint programming system. Constraint programming has allowed the development of an inexpensive, yet reliable test oracle. In 500 random test cases, the test oracle has detected two system failures. These failures correspond to defects that had been present for several years without being discovered neither by less complete oracles nor by the application of more systematic testing approaches. The main contributions of this thesis are: (1) empirical evidence of both the suitability of applying constraint programming to solve the test oracle problem and the e ectiveness of true test oracles in random testing, and (2) a rst attempt, as far as the author is aware, to model a non-theoretical continuous double auction using constraint programming.Castañeda Lozano, R. (2010). Constraint programming for random testing of a trading system. http://hdl.handle.net/10251/8928.Archivo delegad