Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

Studies have shown that good comments can help programmers quickly understand what a method does, aiding program comprehension and software maintenance. Unfortunately, few software projects adequately comment the code. One way to overcome the lack of human-written summary comments, and guard against obsolete comments, is to automatically generate them. In this paper, we present a novel technique to automatically generate descriptive summary comments for Java methods. Given the signature and body of a method, our automatic comment generator identifies the content for the summary and generates natural language text that summarizes the method's overall actions. According to programmers who judged our generated comments, the summaries are accurate, do not miss important content, and are reasonably concise.

Towards automatically generating summary comments for Java methods

Matching is a classic problem with a rich history and a significant impact, both on the theory of algorithms and in practice. Recently there has been a surge of interest in the online version of matching and its generalizations, due to the important new application domain of Internet advertising. The theory of online matching and allocation has played a critical role in designing algorithms for ad allocation. This monograph surveys the key problems, models and algorithms from online matchings, as well as their implication in the practice of ad allocation. The goal is to provide a classification of the problems in this area, an introduction into the techniques used, a glimpse into the practical impact, and to provide direction in terms of open questions. Matching continues to find core applications in diverse domains, and the advent of massive online and streaming data emphasizes the future applicability of the algorithms and techniques surveyed here.

/pdf/online-matching-and-ad-allocation-2bagnfnhyu.pdf

Online Matching and Ad Allocation

: This report briefly summarizes research on the following topics: game theory and energy; scheduling of large research and development programs; bimatrix games; cost/benefit analyses; measures of worth of weapons systems; hybrid primal algorithm; branch and round algorithm. A listing of papers prepared and published is included. (Author)

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA049700&Location=U2&doc=GetTRDoc.pdf

Mathematics of Operations Research.

We provide a reduction from revenue maximization to welfare maximization in multi-dimensional Bayesian auctions with arbitrary (possibly combinatorial) feasibility constraints and independent bidders with arbitrary (possibly combinatorial) demand constraints, appropriately extending Myerson's result to this setting. We also show that every feasible Bayesian auction can be implemented as a distribution over virtual VCG allocation rules. A virtual VCG allocation rule has the following simple form: Every bidder's type t_i is transformed into a virtual type f_i(t_i), via a bidder-specific function. Then, the allocation maximizing virtual welfare is chosen. Using this characterization, we show how to find and run the revenue-optimal auction given only black box access to an implementation of the VCG allocation rule. We generalize this result to arbitrarily correlated bidders, introducing the notion of a second-order VCG allocation rule. 
We obtain our reduction from revenue to welfare optimization via two algorithmic results on reduced forms in settings with arbitrary feasibility and demand constraints. First, we provide a separation oracle for determining feasibility of a reduced form. Second, we provide a geometric algorithm to decompose any feasible reduced form into a distribution over virtual VCG allocation rules. In addition, we show how to execute both algorithms given only black box access to an implementation of the VCG allocation rule. 
Our results are computationally efficient for all multi-dimensional settings where the bidders are additive. In this case, our mechanisms run in time polynomial in the total number of bidder types, but not type profiles. For generic correlated distributions, this is the natural description complexity of the problem. The runtime can be further improved to poly(#items, #bidders) in item-symmetric settings by making use of recent techniques.

Optimal Multi-Dimensional Mechanism Design: Reducing Revenue to Welfare Maximization

We provide a reduction from revenue maximization to welfare maximization in multi-dimensional Bayesian auctions with arbitrary (possibly combinatorial) feasibility constraints and independent bidders with arbitrary (possibly combinatorial) demand constraints, appropriately extending Myerson's single-dimensional result [Myerson81] to this setting. We also show that every feasible Bayesian auction (including in particular the revenue-optimal one) can be implemented as a distribution over virtual VCG allocation rules. A virtual VCG allocation rule has the following simple form: Every bidder's type t_i is transformed into a virtual type f_i(t_i), via a bidder-specific function. Then, the allocation maximizing virtual welfare is chosen. Using this characterization, we show how to find and run the revenue-optimal auction given only black-box access to an implementation of the VCG allocation rule. We generalize this result to arbitrarily correlated bidders, introducing the notion of a second-order VCG allocation rule. Our results are computationally efficient for all multi-dimensional settings where the bidders are additive, or can be efficiently mapped to be additive, albeit the feasibility and demand constraints may still remain arbitrary combinatorial. In this case, our mechanisms run in time polynomial in the number of items and the total number of bidder types, but not type profiles. This is polynomial in the number of items, the number of bidders, and the cardinality of the support of each bidder's value distribution. For generic correlated distributions, this is the natural description complexity of the problem. The runtime can be further improved to polynomial in only the number of items and the number of bidders in item-symmetric settings by making use of techniques from [15].

http://people.csail.mit.edu/ycai/Virtual%20VCG.pdf

Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization

We show that every feasible, Bayesian, multi-item multi-bidder mechanism for independent, additive bidders can be implemented as a mechanism that: (a) allocates every item independently of the other items; (b) for the allocation of each item it uses a strict ordering of all bidders' types; and allocates the item using a distribution over hierarchical mechanisms that iron this ordering into a non-strict ordering, and give the item uniformly at random to the bidders whose reported types dominate all other reported types according to the non-strict ordering. Combined with cyclic-monotonicity our results provide a characterization of feasible, Bayesian Incentive Compatible mechanisms in this setting. Our characterization is enabled by a new, constructive proof of Border's theorem [Border 1991], and a new generalization of this theorem to independent (but not necessarily identically distributed) bidders, improving upon the results of [Border 2007, Che-Kim-Mierendorf 2011]. For a single item and independent bidders, we show that every feasible reduced form auction can be implemented as a distribution over hierarchical mechanisms that are consistent with the same strict ordering of all bidders' types, which every mechanism in the support of the distribution irons to a non-strict ordering. We also give a polynomial-time algorithm for determining feasibility of a reduced form auction, or providing a separation hyperplane from the set of feasible reduced forms. To complete the picture, we provide polynomial-time algorithms to find and exactly sample from a distribution over hierarchical mechanisms consistent with a given feasible reduced form. All these results generalize to multi-item reduced form auctions for independent, additive bidders. Finally, for multiple items, additive bidders with hard demand constraints, and arbitrary value correlation across items or bidders, we give a proper generalization of Border's Theorem, and characterize feasible reduced form auctions as multi-commodity flows in related multi-commodity flow instances. We also show that our generalization holds for a broader class of feasibility constraints, including the intersection of any two matroids. As a corollary of our results we compute revenue-optimal, Bayesian Incentive Compatible (BIC) mechanisms in multi-item multi-bidder settings, when each bidder has arbitrarily correlated values over the items and additive valuations over bundles of items, and the bidders are independent. Our mechanisms run in time polynomial in the total number of bidder types (and {not} type profiles). This running time is polynomial in the number of bidders, but potentially exponential in the number of items. We improve the running time to polynomial in both the number of items and the number of bidders by using recent structural results on optimal BIC auctions in item-symmetric settings [Daskalakis-Weinberg 2011].

/pdf/an-algorithmic-characterization-of-multi-dimensional-1b7nblt7ue.pdf

An algorithmic characterization of multi-dimensional mechanisms

We obtain a characterization of feasible, Bayesian, multi-item multi-bidder auctions with independent, additive bidders as distributions over hierarchical mechanisms. Combined with cyclic-monotonicity our results provide a complete characterization of feasible, Bayesian Incentive Compatible (BIC) auctions for this setting. 
Our characterization is enabled by a novel, constructive proof of Border's theorem, and a new generalization of this theorem to independent (but not necessarily iid) bidders. For one item and independent bidders, we show that any feasible reduced form auction can be implemented as a distribution over hierarchical mechanisms. We also give a polytime algorithm for determining feasibility of a reduced form, or finding a separation hyperplane from feasible reduced forms. Finally, we provide polytime algorithms to find and exactly sample from a distribution over hierarchical mechanisms consistent with a given feasible reduced form. 
Our results generalize to multi-item reduced forms for independent, additive bidders. For multiple items, additive bidders with hard demand constraints, and arbitrary value correlation across items or bidders, we give a proper generalization of Border's theorem, and characterize feasible reduced forms as multicommodity flows in related multicommodity flow instances. We show that our generalization holds for a broader class of feasibility constraints, including intersections of any two matroids. 
As a corollary we obtain revenue-optimal, BIC mechanisms in multi-item multi-bidder settings, when each bidder has arbitrarily correlated values over the items and additive valuations over bundles, and bidders are independent. Their runtime is polynomial in the total number of bidder types (instead of type profiles), and is improved to poly(#items, #bidders) using recent structural results on optimal BIC auctions in item-symmetric settings.

An Algorithmic Characterization of Multi-Dimensional Mechanisms

We provide a computationally efficient black-box reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximation-preserving reduction from truthfully maximizing any objective under arbitrary feasibility constraints with arbitrary bidder types to (not necessarily truthfully) maximizing the same objective plus virtual welfare (under the same feasibility constraints). Our reduction is based on a fundamentally new approach: we describe a mechanism's behavior indirectly only in terms of the expected value it awards bidders for certain behavior, and never directly access the allocation rule at all. Applying our new approach to revenue, we exhibit settings where our reduction holds both ways. That is, we also provide an approximation-sensitive reduction from (non-truthfully) maximizing virtual welfare to (truthfully) maximizing revenue, and therefore the two problems are computationally equivalent. With this equivalence in hand, we show that both problems are NP-hard to approximate within any polynomial factor, even for a single monotone sub modular bidder. We further demonstrate the applicability of our reduction by providing a truthful mechanism maximizing fractional max-min fairness.

/pdf/understanding-incentives-mechanism-design-becomes-algorithm-4jku4ivvdt.pdf

Yang Cai

Papers

Optimal Multi-Dimensional Mechanism Design: Reducing Revenue to Welfare Maximization

Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization

An algorithmic characterization of multi-dimensional mechanisms

An Algorithmic Characterization of Multi-Dimensional Mechanisms

Understanding Incentives: Mechanism Design Becomes Algorithm Design