Now that we have developed inifinitary languages, we study how to work with them from a computability theory perspective. The computably infinitary formulas play a key role in this book, as they provide the link between structural and complexity notions.

This chapter studies bipartite classical correlations using mutual information and common information measures.

One relatively recent development related to the growth of practical market design is the need to deal with big strategy sets that may involve parts of the economic environment beyond the boundaries of the individual marketplaces. A related matter is that in naturally occurring environments, strategies may be discovered in the course of play. Discovering new strategies is very much like inventing new technology, or new game theory: all of these things can change the game in important ways. These issues blur the borders of what historically were regarded as separate domains of game theory, namely the theories of cooperative and non-cooperative games.

This chapter explores quantifying uncertainty through prediction, introducing Tsallis and Rényi entropy alongside Shannon entropy.

This chapter is about the complexity of the isomorphism problem, that is, the problem of deciding when two ?-presentations of a structure are isomorphic.

The purpose of this chapter is to review the key contributions of game theory to the field of cultural evolution, focusing particularly on interfaces between cultural evolution and economics. Because many readers may not be familiar with the interdisciplinary field of cultural evolution, it begins with a brief orientation to this field as a scientific enterprise and then highlights the important ways that game theory has been deployed in both theoretical and empirical research within the field, noting spillovers and interactions with economics.

Chapter 7 zooms out of conceptual and empirical studies of AI governance to ask if we can build a better future with AI. The technical, corporate, and legal governance models presented in this book are necessary but insufficient to endow ordinary people with the power to push back against risks and harms, and chart a course for AI for the common good. Thinking together with philosophers and social scientists in the Critical Theory, Science and Technology Studies, and Democratic Theory traditions, I argue that most people’s experience with AI is one of fear as a result of their long-standing disempowerment and alienation from the technologies shaping their lives. Attributing disempowerment and alienation to technical aspects of AI is wrongheaded: It is the evolution of modern capitalism that has widened the gap between people and the technologies that are supposed to make their lives better. Reorienting the relationship between people and AI requires a radical-democratic politics that questions hierarchy in government and in the workplace. Technology can serve as a force for the social good only if informed citizens participate in the decisions shaping their lives in the design, development, deployment, and use of modern technology, AI included.

This chapter discusses both motivations and choice mechanisms that underly how people make strategic choices. It lists multiple areas where our understanding could benefit from closer study. About the early work by Tversky and Kahneman on framing (i.e., the dependence of human choice behavior on different presentations of what to rational agents should be irrelevant factors), it concludes that one must make a choice between normative adequacy and descriptive accuracy. Concerning recent work on reciprocity, it argues that players’ reactions to, for instance, kind acts may lead to volatile behavior in settings with noise, whereas reciprocity toward perceived kind types can be more forgiving and result in more stable reciprocal relations.

The game metatheorem was recently developed by the author to simplify various constructions in computable structure theory that involve zero-to-the-alpha priority arguments for transfinite alpha. It is a powerful tool, that allows the user to produce proves without worrying about the inctricate combinatorics of approximations to Sigma-alpha sets.

A large share of individuals deviates from self-interested behavior in many paradigmatic games, but in many other strategic situations almost all individuals behave in a self-interested manner. Models with heterogeneous social preferences provide a unifying understanding for these seemingly contradictory facts by focusing on the interaction between agents with other-regarding and selfish preferences. This focus explains why and when selfish agents behave as if they were other-regarding, as well as to why and when other-regarding agents behave as if they were selfish. This focus also helps understand (1) the importance of seemingly irrelevant institutional details, (2) the role of contractual incompleteness for the behavioral relevance of social preferences, (3) the role of social preferences for the prevalence of contractual incompleteness, and (4) why social preferences are an important component in explaining key characteristics of the employment relation. More recent evidence suggests that the empirical distribution of social preferences can be parsimoniously characterized by a small number of preference types which also have out-of-sample predictive power for important behaviors such as the demand for politically enforced redistribution.