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

Statistical methods and scientific inference (3rd edition), by R. A. Fisher. Pp viii, 182. £4·95. 1973. SBN 0 02 844740 9 (Collier-Macmillan)

An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.

Meixner-Pollaczek polynomials and the Heisenberg algebra

Sodicity is a major soil constraint in many arid and semi-arid regions worldwide, including Australia, which adversely affects the ability of crops to take up water and nutrients from the soil, reducing yield Reliable methods and tools are required for appropriate selection of traits, may provide a better understanding of crop responses to multiple stresses, especially in sodic soil A novel strategy was developed using unmanned aerial vehicle (UAV)-thermal imaging and agglomerative hierarchical clustering-based techniques to evaluate and rank the physiological performance of 18 contrasting wheat genotypes grown on a moderately sodic and a highly sodic soil in north-eastern Australia We obtained UAV-thermal imaging data at different times of the day (9:30, 12:00, and 15:00 hrs) close to flowering stage Crop biophysical parameters (Leaf potassium concentration, normalized difference vegetation index, crop water uptake, stomatal conductance, plant moisture content, and aboveground biomass) were measured at close to flowering by destructive plant sampling and ground-based proximal sensing and yield was machine harvested at maturity Canopy temperatures derived from thermal imagery between 289 and 354 degrees C were observed at the moderately sodic site, and between 362 and 410 degrees C at the highly sodic site from 9:30 to 15:00 hrs Canopy temperature was consistently higher than corresponding ambient air temperatures indicating plant water stress at both sites While the air temperature was not significantly different (p > 005) between the two sites, canopy temperature was significantly higher (p < 001) on highly sodic soil compared to moderately sodic soil, indicating greater water stress at the highly sodic site This difference was most likely due to the adverse impacts of sodic soil constraints and not primarily due to environmental variations Hence, our study revealed that sodic soil constraints can intensify plant water stress Statistical analysis between canopy temperature (9:30, 12:00, and 15:00 hrs) and crop biophysical parameters showed close negative correlations at both moderately sodic (R-2 = 054 to 083) and highly sodic (R-2 = 030 to 089) sites A closer correlation was observed at 15:00 hrs for both sites Thus, high-resolution UAV-thermal imaging has potential to detect water-stressed plants on sodic soil Agglomerative hierarchical clustering was used as an unsupervised machine learning tool for ranking of physiological performance of wheat genotypes Results suggest that UAV-thermal imaging and AHC techniques can discriminate cultivars tolerant to sodicity The study improves our understanding of crop physiological behaviour and can assist farmers in selection of water stress tolerant genotypes to sustain food security in sodic soil under water-limited environments

UAV-Thermal imaging and agglomerative hierarchical clustering techniques to evaluate and rank physiological performance of wheat genotypes on sodic soil

A b st r a c t : This article presents an analysis of the socio-econ omic development of the 16 federal states of Germany as compared to the whole country. The main goals of the analysis are to measure the developmen t with the use of selected taxonomic methods, to examine the similarities and diff erences between the states inasmuch as that development is concerned, as well as to illustrate the distance existing between the new eastern states (Brandenburg, Me cklenburg-Vorpommern, Saxony, Saxony-Anhalt, and Thuringia) and the remai ning states of Germany. The analysis is preceded by an illustration of the present socio-economic situation of the German states. Germany is characterized by internal diversity as regards the socio-economic development, and the polic y of supporting the East German economy has failed to reach its goals. An unfav ourable demographic situation is a factor that effectively inhibits the developme nt of the new states. A falling birth rate, an increasing population beyond retirement ag e, as well as great numbers of

The Federal States of Germany - Analysis and Measurement of Development

Research background: The labour market situation is considered to be the most widely discussed part of economic development. However, it should be noted that the unemployment situation of young people (aged 15?24 years) in Poland in general terms seems to be problematic. Overall, the unemployment rate among young people in Poland is significantly higher than the overall unemployment rate in the EU.  Moreover, the situation varies greatly across the regions.
Purpose of the article: Using multivariate techniques as a theoretical framework, the main goal of the paper is to identify groups of Polish regions that share similar patterns regarding unemployment among young people. To reach this goal, first a set of labour market indicators were selected. Next, the authors compared the labour market situation of young people between the Polish regions in 2005 and in 2014. Finally, the conclusions regarding the conducted analysis are explored.
Methods: The initial calculation is based on the concept of the taxonomic measure developed by Hellwig. The final method used to create clusters of objects (across 16 voivodeships of Poland) is cluster analysis. A segmentation of the voivodeships is observed for the years 2005 and 2014, based on selected indicators to determine the labour market situation. The data was gathered from the databases of the Central Statistical Office of Poland and Eurostat.
Findings & Value added: Through the exploration of the advantages of multivariate methods, the nature of youth unemployment is revealed in more detail. Indeed, dendrogram analysis divided the voivodeships into five groups, which are characterized by similar features associated with the labour market. It was found that the groups which emerged in 2005 have a different composition of regions than in 2014; this difference seems to be connected with the economic crisis.

/pdf/the-multivariate-techniques-in-evaluation-of-unemployment-vd11gpzg2b.pdf

The multivariate techniques in evaluation of unemployment analysis of Polish regions

Let $f(z) = z+a_2 z^2+\cdots$ be regular in the unit disk  and real valued if and only if $z$ is real and $|z| < 1$. Then $f$ is said to be typically real function. Rogosinski found the necessary and sufficient condition for a regular function to be typically-real. The main purpose of the presented paper is a consideration of the generalized typically-real functions defined via the generating function of the generalized Chebyshev polynomials of the second kind $$ \displaystyle \Psi_{p,q}(e^{i\theta};z)=\frac{1}{(1-pze^{i\theta})(1-qze^{-i\theta})}=\sum_{n=0}^\infty U_n(p,q;e^{i\theta})z^n, $$ where $-1\le p,q \le 1, \ \theta \in \langle 0,2\pi\rangle, \ |z|<1.$

/pdf/generalized-typically-real-functions-3ojfekiceg.pdf

Generalized Typically Real Functions

Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties of obtained orthogonal polynomials.

/pdf/an-extension-of-typically-real-functions-and-associated-1w1lqr59hm.pdf

An extension of typically-real functions and associated orthogonal polynomials

We consider the generalized Meixner-Pollaczek (GMP) polynomials P λ (x; θ , ψ )o f a variable x ∈ R and parameters λ >0 ,θ ∈ (0, π ), ψ ∈ R ,d ef inedvia the generating function

/pdf/generalized-meixner-pollaczek-polynomials-1ogn8gms4y.pdf

Anna Tatarczak

Papers

The multivariate techniques in evaluation of unemployment analysis of Polish regions

Generalized Typically Real Functions

An extension of typically-real functions and associated orthogonal polynomials

An extension of typically-real functions and associated orthogonal polynomials

Generalized Meixner-Pollaczek polynomials