This chapter describes the early contributions of Émile Borel to the theory of games. It also discusses early reactions and controversies.

It took some thirty years before the game theoretic ideas of Émile Borel became known to a wider audience, with the publication of the seminal book by John von Neumann and Oskar Morgenstern. Similarly, it took thirty years for the evolutionary approach of Brown, von Neumann, and Nash to be taken up by a wider community. By now, a substantial set of potential updating mechanisms has been modeled and analyzed via game dynamics. Large as it is, it is yet unlikely to capture the full range of adaptive behavior used by human players. A closer relation between the dynamics of nonequilibrium play and empirical data on adaptation and learning is sorely needed. This is a topic where psychology and economics can fruitfully join hands.

This chapter introduces the three contributions that constitute Part VII, “Political Science,” about game theoretic models in political science, armed conflict, and trade policy.

This chapter summarizes three key contributions of Borel’s 1921 paper: (1) the strategic normalization of games in extensive form, (2) the introduction of randomized strategies, and (3) expected payoff maximization. It also discusses the impact Borel had on other early contributors to game theory, notably von Neumann, Nash, and Schelling.

This chapter shows how the theory of symmetric two-player zero-sum games, which was initiated by Borel in 1921, can be used for randomly selecting an alternative based on quantified pairwise comparisons between alternatives. It points out desirable properties satisfied by the equilibrium distribution and gives examples where these distributions arise as the limit of simple dynamic processes that have been studied across various disciplines, such as population biology, quantum physics, and machine learning.

The core concept of rational choice is what each undergraduate of economics is introduced to in one of the first sessions of their economics course at university. So was I. My fellow students and I sat in one of those large lecture halls in Heidelberg, enthusiastic toward that which was about to come. The teacher enters, starts the class with telling us about consumer demand, a theory grounded in the idea that people’s choices can be modeled via indifference curves. After studying the properties of those curves for several weeks, we concluded that thinking about behavior in this way had up until then been the most puzzling thing we had ever heard of. In German high school, the subject of economics is usually absent. When I began my degree program in economics at the university, I was excited to hopefully be able to critically engage one day in the public and political discourse about economics and the economy by making use of tools provided by the field. My idealistic self was convinced (and potentially still is) that one could only change the system from within, ideally using the language that a system and its proponents use themselves. Yet, I quickly felt that I might fail with economics. The technical language to model behavior in terms of consistent choices, rational preferences, and indifference curves was counterintuitive and so different from everyday discourse that I had a hard time translating. During my first semesters, I did not see any way to connect the two and almost gave up on the subject entirely. Understanding the basics in my first microeconomics class as an undergraduate has been a concern of mine ever since. This book is the result of finding one way to take this puzzlement as a starting point for making a serious attempt to better understand what economists are up to.

This chapter explores different strands of the theory of two-player zero-sum games and equilibrium concepts for general multiplayer games. The conventional viewpoint is that equilibrium is an extension of the concept of value (and its associated optimal strategies) to non-zero-sum games, and the value is just a special case of an equilibrium payoff. However, it is argued that a number of important concepts apply only to one of these concepts.

The chapter argues that while the purpose of this book is to discuss Keynes’s ideas, these make better sense in the context of his life and times. Both the life and the times were extraordinary, and despite Keynes’s individual brilliance, there is a strong case for seeing him as a product of and spokesperson for his class and nation. Keynes’s thinking was shaped during a period of remarkable social and economic upheaval. From an age of apparent stability and complacent British imperial hegemony, he lived through two world wars, the descent into the Great Depression and times of sharpened class struggles. A liberal economics based on enlightened self-interest in which, by assumption, neither states nor unemployment existed made sense neither as theory nor ideology, and Keynes became the most prominent of many economists trying to articulate a more realistic theory, a theory which would better describe capitalism but also better defend it. By the end of this period, Keynes had become both the world’s most famous economist and a leading player in the negotiations to shape the post-WWII order – now a world where the US had displaced Britain as the dominant power. The chapter’s content highlights how Keynes’s life (1883–1946) spanned this extraordinary age. It is divided chronologically into four parts, from 1883 to 1914, to 1929, to 1939 and to 1946, marking vital stages in Keynes’s intellectual and political career.

Keynes’s General Theory of Employment, Interest and Money is a notoriously difficult book, which this chapter tries to explain as simply as possible. Keynes could be a great stylist and the General Theory’s many quotable passages have enhanced its appeal. Elsewhere, however, Keynes’s prose is dense and the arguments highly technical and convoluted. In contrast to other great works of political economy like Smith’s Wealth of Nations or Marx’s Capital, the General Theory was never meant to be understood by non-specialists. The difficulties of comprehension appear to be confirmed in the way the General Theory has been subject to widely different interpretations, as a radical departure or a mild amendment of the orthodoxy he was criticising. The chapter argues for something in between. The General Theory provides a substantial critique of standard economics but it does this by engaging with the mainstream on its own terms, and this qualifies claims of Keynes’s radicalism. The chapter provides a very brief overview and commentary on the overall argument of the book and its conceptual priorities. It is then organised around sections on savings and consumption, on money and the rate of interest, and on investment and employment, introducing a general discussion of how this leads to Keynes’s vision of the prospect of ‘unemployment equilibrium’ and the possibility of state intervention to ameliorate this. A final substantive section discusses dynamic change, cycles and long-term tendencies, into which it suggests the General Theory provides important but subsidiary insights.

The chapter discusses Keynes’s philosophy. Probably more than any major economist since Marx, Keynes thought deeply about political and philosophical issues. He was a sophisticated thinker, close intellectually as well as personally to several leading philosophers of the age. He was particularly strongly influenced by Moore, and wrote one major work, the Treatise on Probability, which operates at the intersection of mathematics, logic and philosophy. There is controversy about the influence of this early work, and of Keynes’s philosophical thought in general, but there are important connections between his philosophy and his mature economics. It is argued that Keynes never develops an entirely coherent overall philosophy. This undermines grander claims for a ‘Keynesian economic system’ and for the generality of the General Theory. Keynes develops profound insights, around intuition, organic unity, time and uncertainty, which he does not always follow through, and makes philosophically provocative statements from whose implications he pulls back. An apparently individualist idealism and questions about the basis of knowledge might, if pushed to their (il)logical conclusions, appear radically incompatible with a genuinely critical political economy. More positively, however, these ambiguities enable the adoption or appropriation of Keynes’s insights in a way that a more rigorously internally consistent system might preclude. In particular, Keynes is right that individuals act in the face of real uncertainties and that this has important economic implications.

Describes Meade’s and his colleagues’ early efforts to plan for the postwar world.

This chapter introduces the three contributions in Part VI, “Individual Behavior in Strategic Interactions.” It frames the contributions in terms of two main issues that underlie models in behavioral game theory: (1) what motivates players (i.e., their goals or preferences) and (2) the mechanisms or procedures behind their choices.

Game theory has a long history in the political economy of trade policy. Beginning with work by Johnson in the 1950s, trade economists have used these tools to study strategic interactions between governments, interest groups representing industries or factors of production, political parties, and legislators representing different voting districts. Research has focused both on trade policies that have been set noncooperatively, sometimes in response to internal political pressures, and on the negotiation and features of cooperative trade agreements.

Keynes was intensely political. He was an activist, a populariser of economic ideas, an influential Treasury official and seldom for long out of touch with the British prime minister of the day. Economics was never a neutral scientific endeavour, and it makes sense to understand his economics in the light of his political views. Keynes wants to develop a more realistic theory, but even his most abstract work is oriented to providing a better guide to policy. Keynes wrote in the ‘advice to princes’ tradition, offering a better guide for rulers of the existing system. As usual with Keynes, there are ambiguities and his political stance is contested, but it is argued that although Keynes says some different things, he fairly consistently occupies a space bounded on the one hand by a conservatism drawn particularly from Edmund Burke and on the other by British liberalism. The first two sections of the chapter discuss these two influences. The third section discusses alternative claims that Keynes was a socialist, arguing that while there were radical aspects to his thought, Keynes is better understood as a pro-capitalist not a socialist thinker. As the fourth and final section continues, Keynes brings in the state, but in a quite consistently liberal way in that he still conceives the requisite level of state intervention as being minimal, albeit while raising the perceived necessary minimum. A specifically British, but also more broadly a national rather than international or global, orientation also informs and limits Keynes’s political economy.

This chapter introduces the two contributions that constitute Part V, “Economics and institutional design”.