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

Logic for coalitions with bounded resources

Recent work on Alternating-Time Temporal Logic and Coalition Logic has allowed the expression of many interesting properties of coalitions and strategies. However, there is no natural way of expressing resource requirements in these logics. In this article, we present a Resource-Bounded Coalition Logic (RBCL) that has explicit representation of resource bounds in the language. We give a complete and sound axiomatization of RBCL, a procedure for deciding satisfiability of RBCL formulas, and a model-checking algorithm. © 2010 The Author

Logics for strategic reasoning and collective decision-making

Strategic decision-making is ubiquitous in everyday life. The analysis of game strategies has been a research theme in game theory for several decades since von Neumann and Morgenstern. Sophisticated models and analysis tools have been developed with wide applications in Economics, Management Science, Social Science and Computer Science, especially in the field of Artificial Intelligence. However, \much of game theory is about the question whether strategic equilibria exist", as Johan van Benthem, a world-leading logician and game-theorist, points out, \but there are hardly any explicit languages for defining, comparing, or combining strategies". Without such a facility it is challenging for computer scientists to build intelligent agents that are capable of strategic decision-making. In the last twenty years, logical approaches have been proposed to tackle this problem. Pioneering work includes Game Logics, Coalition Logic and Alternating-time Temporal Logic (ATL). These logics either provide facilities for expressing and combining games or offer mechanisms for reasoning about strategic abilities of players. But none of them can solve the problem. The intrinsic difficulty in establishing such a logic is that reasoning about strategies requires combinations of temporal reasoning, counterfactual reasoning, reasoning about actions, preferences and knowledge, as well as reasoning about multi-agent interactions and coalitional abilities. More recently, a few new logical formalisms have been proposed by extending ATL with strategy variables in order to express strategies explicitly. However, most of these logics tend to have high computational complexity, because ATL introduces quantifications over strategies (functions), which leaves little hope of building any tractable inference system based on such a logic. This thesis takes up the challenge by using a bottom-up approach in order to create a balance between expressive power and computational efficiency. Instead of starting with a highly complicated logic, we propose a set of logical frameworks based on a simple and practical logical language, called Game Description Language (GDL), which has been used as an official language for General Game Playing (GGP) since 2005. To represent game strategies, we extend GDL with two binary prioritized connectives for combining actions in terms of their priorities specified by these connectives, and provide it with a semantics based on the standard state transition model. To reason about the strategic abilities of players, we further extend the framework with coalition operators from ATL for specifying the strategic abilities of players. More importantly, a unified semantics is provided for both GDL- and ATL- formulas, which allows us to verify and reason about game strategies. Interestingly, the framework can be used to formalize the fundamental game-playing principles and formally derive two well-known results on two-player games: Weak Determinacy and Zermelo's Theorem. We also show that the model-checking problem of the logic is not worse than that of ATL*, an extension of ATL. To deal with imperfect information games, we extend GDL with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. The language allows us to specify an imperfect information game and formalize its epistemic properties. Meanwhile, the framework allows us to reason about players' own as well as other players' knowledge during game playing. Most importantly, the logic has a moderate computational complexity, which makes it significantly different from similar existing frameworks. To investigate the interplay between knowledge shared by a group of players and its coalitional abilities, we provide a variant of semantics for ATL with imperfect information. The relation between knowledge sharing and coalitional abilities is investigated through the interplay of epistemic and coalition modalities. Moreover, this semantics is able to preserve the desirable properties of coalitional abilities. To deal with collective decision-making, we apply the approach of combining actions via their priorities for collective choice. We extend propositional logic with the prioritized connective for modelling reason-based individual and collective choices. Not only individual preferences but also aggregation rules can be expressed within this logic. A model-checking algorithm for this logic is thus developed to automatically generate individual and collective choices. In many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. We design an aggregation rule based on the priorities of individuals so as to investigate how the judgment from each individual affects group judgment in a hierarchical environment. We also show that this rule satisfies a set of plausible conditions and has a tractable computational complexity

Logics for strategic reasoning and collective decision-making

Cette thèse aborde le problème du raisonnement stratégique. Le raisonnement stratégique est un thème de recherches existant depuis e nombreuses années en théorie des jeux. Toutefois, celui-ci a le plus souvent pour objet de déterminer si des équilibres stratégiques existent sans détailler la définition en elle-même de ces stratégies. La construction d'agents artificiels capable de raisonner stratégiquement implique de se poser la question de la représentation de ces stratégies afin que les agents puissent les construire, combiner, comparer et enfin et surtout exécuter. Cette thèse propose un ensemble de logiques pour le raisonnement stratégique et la prise de décision collective. Elle établit dans un premier temps un cadre unifiée pour la définition de jeux, la représentation de stratégies et le raisonnement sur celles-ci dans le contexte des jeux à information parfaite. Ce cadre est ensuite étendu pour prendre en compte les jeux à information imparfaite. Les relations entre les connaissances de groupe, le pouvoir des coalitions ainsi que le partage d'informations dans une coalition sont ensuite étudiés. Dans un dernier temps, est introduit une logique modale permettant de de raisonner sur les choix collectifs, cette logique permet de généraliser les approches logiques existantes pour l'agrégation de jugements. La complexité de ces différents cadres logiques est aussi étudiée et nous montrons que ces différents cadres offre un équilibre pertinent entre efficacité computationnelle et pouvoir d'expression.This thesis proposes a set of logics for modelling strategic reasoning and collective decision-making. It first establishes a unified logical framework for game specifications, strategy representation and strategic reasoning in perfect information games. Based on that, it proposes an epistemic extension to address imperfect information games. To investigate the interplay of group knowledge and coalitional abilities, it further models knowledge sharing within coalitions. Finally it introduces a modal logic for collective choice and generalizes the logic-based approach to judgment aggregation. The complexity analysis of these logics indicates that these frameworks make a good balance between expressive power and computational efficiency

Reasoning about resource-bounded multi-agent systems

The thesis presents logic-based formalisms for modelling and reasoning about resource-bounded multi-agent systems. In the field of multi-agent system, it is well-known that temporal logics such as CTL and ATL are powerful tools for reasoning about multi-agent systems. However, there is no natural way to utilise these logics for expressing and reasoning about properties of multi-agent systems where actions of agents require resources to be able to perform. This thesis extends logics including Computational Tree Logic (CTL), Coalition Logic (CL) and Alternating-time Temporal Logic (ATL) which have been used to reasoning about multi-agent systems so that the extended ones have the power to specify and to reason about properties of resource-bounded multi-agent systems. While the extension of CTL is adapted for specifying and reasoning about properties of systems of resource-bounded reasoners where the resources are explicitly memory, communication and time, the extensions of CL and ATL are generalised so that any resource-bounded multi-agent system can be modelled, specified and reasoned about. For each of the logics, we describe the range of resource-bounded multi-agent systems they can account for and axiomatisation systems for reasoning which are proved to be sound and complete. Moreover, we also study the satisfiability problem of these logics

Reasoning about resource-bounded multi-agent systems

The thesis presents logic-based formalisms for modelling and reasoning about resource-bounded multi-agent systems. In the field of multi-agent system, it is well-known that temporal logics such as CTL and ATL are powerful tools for reasoning about multi-agent systems. However, there is no natural way to utilise these logics for expressing and reasoning about properties of multi-agent systems where actions of agents require resources to be able to perform. This thesis extends logics including Computational Tree Logic (CTL), Coalition Logic (CL) and Alternating-time Temporal Logic (ATL) which have been used to reasoning about multi-agent systems so that the extended ones have the power to specify and to reason about properties of resource-bounded multi-agent systems. While the extension of CTL is adapted for specifying and reasoning about properties of systems of resource-bounded reasoners where the resources are explicitly memory, communication and time, the extensions of CL and ATL are generalised so that any resource-bounded multi-agent system can be modelled, specified and reasoned about. For each of the logics, we describe the range of resource-bounded multi-agent systems they can account for and axiomatisation systems for reasoning which are proved to be sound and complete. Moreover, we also study the satisfiability problem of these logics

Logic for Automated Mechanism Design -- A Progress Report

Over the past half decade, we have been exploring the use of logic in the specification and analysis of computational economic mechanisms. We believe that this approach has the potential to bring the same benefits to the design and analysis of computational economic mechanisms that the use of temporal logics and model checking have brought to the specification and analysis of reactive systems. In this paper, we give a survey of our work. We first discuss the use of cooperation logics such as Alternating-time Temporal Logic (ATL) for the specification and verification of mechanisms such as social choice procedures. We motivate the approach, and then discuss the work we have done on extensions to ATL to support incomplete information, preferences, and quantification over coalitions. We then discuss is the use of ATL-like cooperation logics in the development of social laws