There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Evolutionary games on graphs

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.

http://www.matjazperc.com/publications/BioSystems_99_109.pdf

Coevolutionary games--a mini review.

Summary) The abstract should follow the structure of the article (relevance, degree of exploration of the problem, the goal, the main results, conclusion) and characterize the theoretical and practical significance of the study results. The abstract should not contain wording echoing the title, cumbersome grammatical structures and abbreviations. The text should be written in scientific style. The volume of abstracts (summaries) depends on the content of the article, but should not be less than 250 words. All abbreviations must be disclosed in the summary (in spite of the fact that they will be disclosed in the main text of the article), references to the numbers of publications from reference list should not be made. The sentences of the abstract should constitute an integral text, which can be made by use of the words “consequently”, “for example”, “as a result”. Avoid the use of unnecessary introductory phrases (eg, “the author of the article considers...”, “The article presents...” and so on.)

/pdf/ministry-of-education-and-science-of-the-russian-federation-7m2jn0xnm1.pdf

Ministry of Education and Science of the Russian Federation

Reversible cellular automata with memory: two-dimensional patterns from a single site seed

Plasmodium of a cellular slime mould Physarum polycephalum is a unique living substrate proved to be efficient in solving many computational problems with natural spatial parallelism. The plasmodium solves a problem represented by a configuration of source of nutrients by building an efficient foraging and intra-cellular transportation network. The transportation networks developed by the plasmodium are similar to transport networks built by social insects and simulated trails in multi-agent societies. In the paper we are attempting to answer the question “How close plasmodium of P. polycephalum approximates man-made motorway networks in Spain and Portugal, and what are the differences between existing motorway structure and plasmodium network of protoplasmic tubes?”. We cut agar plates in a shape of Iberian peninsula, place oat flakes at the sites of major urban areas and analyse the foraging network developed. We compare the plasmodium network with principle motorways and also analyse man-made and plasmodium networks in a framework of planar proximity graphs.

Rebuilding Iberian motorways with slime mould

Standard cellular automata (CA) are ahistoric (memoryless), that is, the new state of a cell depends on the neighborhood configuration of only the preceding time step This article introduces an extension to the standard framework of CA by considering automata with memory capabilities While the update rules of the CA remain unaltered, a history of all past iterations is incorporated into each cell by a weighted mean of all its past states The historic weighting is defined by a geometric series of coefficients based on a memory factor (Α) A study is made of the effect of historic memory on the spatio-temporal and difference patterns of elementary (one-dimensional, two states, nearest neighbors) CA starting with states assigned at random

Elementary Cellular Automata with Memory.

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e., the new state of a cell depends on its neighbourhood configuration only at the preceding time step. Historic memory of all past iterations can be incorporated into CA by featuring each cell by a summary of all its past states. CA with memory turn out to be a natural and interesting generalization of the CA paradigm.

Cellular Automata with Memory.

Cellular automata are regular uniform networks of locally-connected finite-state machines. They are discrete systems with non-trivial behaviour. Cellular automata are ubiquitous: they are mathematical models of computation and computer models of natural systems. The book presents results of cutting edge research in cellular-automata framework of digital physics and modelling of spatially extended non-linear systems; massive-parallel computing, language acceptance, and computability; reversibility of computation, graph-theoretic analysis and logic; chaos and undecidability; evolution, learning and cryptography. The book is unique because it brings together unequalled expertise of inter-disciplinary studies at the edge of mathematics, computer science, engineering, physics and biology.

Ramón Alonso-Sanz

Papers

Reversible cellular automata with memory: two-dimensional patterns from a single site seed

Rebuilding Iberian motorways with slime mould

Elementary Cellular Automata with Memory.

Cellular Automata with Memory.

Automata-2008: Theory and Applications of Cellular Automata