Martin’s Maximum++ implies Woodin’s axiom (∗)
Asperó and Schindler have just published a foundational paper, Martin’s Maximum++ implies Woodin’s axiom (∗), Annals of Mathematics, 193(3), 793-835. It is a fascinating result in mathematical logic with implications to reconcile two approaches to the continuum hypothesis.
So invigorating to be taken back to topics in math that I first studied with wide-eyed wonder under the guidance of the brilliant Dr. Marina Ratner. Thankful for the knowledge gained.
Control and spread of contagion in networks
Pleased to release new research on “Control and spread of contagion in networks,” studying an important and increasingly central topic in current society. This is joint work with John Higgins. An article on this research by KU news is here.
We study proliferation of an action in a network of connected individuals. Proliferation occurs due to person-to-person spread based on network connectivity and due to viral effects based on similar activity by others in different parts of the network.
We extend the model of a network coordination game in Morris (2000) and Jackson (2008) to include a new, flexible, and tractable formulation of aggregated virality. The case of no virality is naturally subsumed in the extended model.
The model and analysis are flexible to apply to many additional situations, as described in the paper. I hope this research is valuable to other researchers within and outside economics.
Interdisciplinary application of game theory to COVID-19 vaccination decisions
Monotone games: A unified approach to games with strategic complements and substitutes
I am delighted to announce the worldwide release of my new book “Monotone games: A unified approach to games with strategic complements and substitutes,” Palgrave Macmillan/Springer.
Games with strategic complements, games with strategic substitutes, and their combinations form the basis of numerous societal interactions governed by monotone interdependent incentives.
Environments in which decisions are governed by incentives to move in the same direction as others are classified as those with strategic complements. Canonical examples are coordinating on a bank run or technology adoption, or making a run on groceries in a pandemic.
Environments in which incentives are to move in a direction opposite to others are classified as strategic substitutes. Canonical examples are competing for market share or competing for a common good, or congestion games, or taking actions with a particular externality.
Environments in which some participants have one type of incentive and others have the other type also arise frequently. For example, penalty shooter and goal keeper in soccer, or law enforcement and law-breaking activity.
The theory of strategic complements is well-established and extensive. Indeed, some of the insights of auction theory celebrated in this year’s Nobel prize are based on the general theory of strategic complements.
The theories of strategic substitutes and of combinations of the two are newer and evolving. I am fortunate to contribute in central ways to the foundations of the newer theories. There are some similarities between the new and the old and some sharp differences as well.
The book develops anew the foundations of all three classes of games in a unified manner under the umbrella of monotone games, providing systematic connections across different cases. New results and examples are included as well.
I believe that the core principles studied in the book arise in fundamental ways in a large body of human and socioeconomic interaction with interdependent effects. There is a compelling reason for this body of knowledge to be accessible to a broader audience.
I hope this book serves to further research and applications in these areas. So, while you wait for additional election results, grab a cup of coffee and read more about herd mentality, dove-hawk strategies, and hunter-hunted dynamics. Happy reading!
Methods matter: p-hacking and publication bias in causal analysis in economics
A very nice and thought-provoking article by Brodeur, Cook, and Heyes: “Methods Matter: p-Hacking and Publication Bias in Causal Analysis in Economics,” American Economic Review 2020, 110(11), 3634-3660.
With more empirical research in economics and greater uncertainty on the part of a broader audience about the reliability of results, this paper brings a welcome look at the distribution of significance results for causal inference in a breadth of published work.
Looking at 21,740 tests in 684 articles published in Top 25 relevant journals in economics, the authors document an increase in density of z-statistic in the range determined by standard statistical significance thresholds.
There are three analyses (Randomization tests, Caliper tests, and Excess test statistics) for each of four causal inference techniques (Instrumental Variables, IV, Difference-in-Differences, DID, Randomized Control Trials, RCT, and Regression Discontinuity Design, RDD).
The broad picture that emerges is that IV and to a lesser extent DID are particularly problematic in terms of p-hacking. RCT and RDD fare better, but all four methods exhibit some discontinuity around conventional statistical thresholds when using finer windows of analysis.
A thoughtful and informative empirical meta-analysis of methods that are used widely to support the credibility revolution in empirical economics. Very well-written and accessible to a broad audience; a nice read. Thanks!
How market design emerged from game theory
Professors Alvin Roth and Robert Wilson have published a very readable open access article on, "How market design emerged from game theory, a mutual interview," Journal of Economic Perspectives, 33(3), Summer 2019, 118-143.
It is a pleasure to read about their thoughts on the big picture history of economic theory, game theory, and their role in the notable success of market design, especially in auctions and matching.
It is refreshing to think about complementarity between cooperative and noncooperative approaches of game theory, to consider games as embedded in larger social systems, and to consider connections between the core in games and in general equilibrium exchange economies.
A good (and relatively quick) read to cap your summer reading.
August 6, 2019 | Tweet