We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

A Treatise on the Family. G. S. Becker. Cambridge, MA: Harvard University Press. 1981. Gary Becker is one of the most famous and influential economists of the second half of the 20th century, a fervent contributor to and expounder of the University of Chicago free-market philosophy, and winner of the 1992 Nobel Prize in economics. Although any book with the word "treatise" in its title is clearly intended to have an impact, one coming from someone as brilliant and controversial as Becker certainly had such a lofty goal. It has received many article-length reviews in several disciplines (Ben-Porath, 1982; Bergmann, 1995; Foster, 1993; Hannan, 1982), which is one measure of its scholarly importance, and yet its impact is, I think, less than it may have initially appeared, especially for scholars with substantive interests in the family. This book is, its title notwithstanding, more about economics and the economic approach to behavior than about the family. In the first sentence of the preface, Becker writes "In this book, I develop an economic or rational choice approach to the family." Lest anyone accuse him of focusing on traditional (i.e., material) economics topics, such as family income, poverty, and labor supply, he immediately emphasizes that those topics are not his focus. "My intent is more ambitious: to analyze marriage, births, divorce, division of labor in households, prestige, and other non-material behavior with the tools and framework developed for material behavior." Indeed, the book includes chapters on many of these issues. One chapter examines the principles of the efficient division of labor in households, three analyze marriage and divorce, three analyze various child-related issues (fertility and intergenerational mobility), and others focus on broader family issues, such as intrafamily resource allocation. His analysis is not, he believes, constrained by time or place. His intention is "to present a comprehensive analysis that is applicable, at least in part, to families in the past as well as the present, in primitive as well as modern societies, and in Eastern as well as Western cultures." His tone is profoundly conservative and utterly skeptical of any constructive role for government programs. There is a clear sense of how much better things were in the old days of a genderbased division of labor and low market-work rates for married women. Indeed, Becker is ready and able to show in Chapter 2 that such a state of affairs was efficient and induced not by market or societal discrimination (although he allows that it might exist) but by small underlying household productivity differences that arise primarily from what he refers to as "complementarities" between caring for young children while carrying another to term. Most family scholars would probably find that an unconvincingly simple explanation for a profound and complex phenomenon. What, then, is the salient contribution of Treatise on the Family? It is not literally the idea that economics could be applied to the nonmarket sector and to family life because Becker had already established that with considerable success and influence. At its core, microeconomics is simple, characterized by a belief in the importance of prices and markets, the role of self-interested or rational behavior, and, somewhat less centrally, the stability of preferences. It was Becker's singular and invaluable contribution to appreciate that the behaviors potentially amenable to the economic approach were not limited to phenomenon with explicit monetary prices and formal markets. Indeed, during the late 1950s and throughout the 1960s, he did undeniably important and pioneering work extending the domain of economics to such topics as labor market discrimination, fertility, crime, human capital, household production, and the allocation of time. Nor is Becker's contribution the detailed analyses themselves. Many of them are, frankly, odd, idiosyncratic, and off-putting. …

A Treatise on the Family

Trust: The Social Virtues and the Creation of Prosperity

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

The four Visegrad states — Poland, the Czech Republic, Slovakia (until 1993 Czechoslovakia) and Hungary — form a compact area between Germany and Austria in the west and the states of the former USSR in the east. They are bounded by the Baltic in the north and the Danube river in the south. They are cut by the Sudeten and Carpathian mountain ranges, which divide Poland off from the other states. Poland is an extension of the North European plain and like the latter is drained by rivers that flow from south to north west — the Oder, the Vlatava and the Elbe, the Vistula and the Bug. The Danube is the great exception, flowing from its source eastward, turning through two 90-degree turns to end up in the Black Sea, forming the barrier and often the political frontier between central Europe and the Balkans. Hungary to the east of the Danube is also an open plain. The region is historically and culturally part of western Europe, but its eastern Marches now represents a vital strategic zone between Germany and the core of the European Union to the west and the Russian zone to the east.

Economy and Society

A classic thesis is that scientific achievement exhibits a “Matthew effect”: Scientists who have previously been successful are more likely to succeed again, producing increasing distinction. We investigate to what extent the Matthew effect drives the allocation of research funds. To this end, we assembled a dataset containing all review scores and funding decisions of grant proposals submitted by recent PhDs in a €2 billion granting program. Analyses of review scores reveal that early funding success introduces a growing rift, with winners just above the funding threshold accumulating more than twice as much research funding (€180,000) during the following eight years as nonwinners just below it. We find no evidence that winners’ improved funding chances in subsequent competitions are due to achievements enabled by the preceding grant, which suggests that early funding itself is an asset for acquiring later funding. Surprisingly, however, the emergent funding gap is partly created by applicants, who, after failing to win one grant, apply for another grant less often.

https://www.pnas.org/content/pnas/115/19/4887.full.pdf

The Matthew effect in science funding.

When entrepreneurs enter structural holes in networks, they can exploit the related benefits. Evidence for these benefits has steadily accumulated. The authors ask whether those who strive for such structural advantages can maintain them if others follow their example. Burt speculates that they cannot, but a formal demonstration of this speculation is lacking. Using a game theoretic model of network formation, the authors characterize the networks that emerge when everyone strives for structural holes. They find that the predominant stable networks distribute benefits evenly, confirming that no one is able to maintain a structural advantage in the long run.

/pdf/dynamics-of-networks-if-everyone-strives-for-structural-2y6rayoi9l.pdf

Dynamics of Networks If Everyone Strives for Structural Holes

Seemingly similar individuals often experience drastically different success trajectories, with some repeatedly failing and others consistently succeeding. One explanation is preexisting variability along unobserved fitness dimensions that is revealed gradually through differential achievement. Alternatively, positive feedback operating on arbitrary initial advantages may increasingly set apart winners from losers, producing runaway inequality. To identify social feedback in human reward systems, we conducted randomized experiments by intervening in live social environments across the domains of funding, status, endorsement, and reputation. In each system we consistently found that early success bestowed upon arbitrarily selected recipients produced significant improvements in subsequent rates of success compared with the control group of nonrecipients. However, success exhibited decreasing marginal returns, with larger initial advantages failing to produce much further differentiation. These findings suggest a lesser degree of vulnerability of reward systems to incidental or fabricated advantages and a more modest role for cumulative advantage in the explanation of social inequality than previously thought.

https://www.pnas.org/content/pnas/111/19/6934.full.pdf

Field experiments of success-breeds-success dynamics

http://pennshape.upenn.edu/files/Centola-Van_de_Rijt-2014-Choosing_Your_Network.pdf

Choosing your network: social preferences in an online health community.

In the early twenty-first century, women continue to receive substantially less media coverage than men, despite women’s much increased participation in public life. Media scholars argue that actors in news organizations skew news coverage in favor of men and male-related topics. However, no previous study has systematically examined whether such media bias exists beyond gender ratio imbalances in coverage that merely mirror societal-level structural and occupational gender inequalities. Using novel longitudinal data, we empirically isolate media-level factors and examine their effects on women’s coverage rates in hundreds of newspapers. We find that societal-level inequalities are the dominant determinants of continued gender differences in coverage. The media focuses nearly exclusively on the highest strata of occupational and social hierarchies, in which women’s representation has remained poor. We also find that women receive greater exposure in newspaper sections led by female editors, as well as in ...

https://journals.sagepub.com/doi/pdf/10.1177/0003122415596999

Arnout van de Rijt

Papers

The Matthew effect in science funding.

Dynamics of Networks If Everyone Strives for Structural Holes

Field experiments of success-breeds-success dynamics

Choosing your network: social preferences in an online health community.

A Paper Ceiling Explaining the Persistent Underrepresentation of Women in Printed News