Chapter 10 examines a different type of long-run consequence. Various counties spent different amounts of time “on the frontier” and had different levels of absolute and relative homesteading.

This chapter introduces the three contributions that constitute Part III, “Population Dynamics, Learning, and Biology.” These contributions discuss biology and population dynamics in game theory. The chapters concern models of strategy adaptation: process models. Such models have refined our understanding of Nash and other equilibrium concepts, and the evolution of population shares through time is itself an object of interest from the perspectives of biological reproduction and of learning human (and artificial) agents.

It is argued that homesteading density is a good measure of defining “the frontier,” and it contrasts with measures based only on low population density, which are likely better measures of “isolation.”

This chapter tells how von Neumann and Morgenstern were brought together to write the “Theory of Games and Economic Behavior.” It discusses von Neumann’s early involvement in games before his emigration, Morgenstern’s curious career in interwar Vienna, their unlikely collaboration as exiles at Princeton during World War II, and the effect of war and the Cold War on the reception of their research.

This chapter gives an extensive overview of techniques and algorithms for representing and solving large imperfect-information extensive-form games and reports on recent breakthroughs that have been achieved for the game of poker. These breakthroughs were made possible by advances in three key areas: (1) game abstraction (i.e., the systematic construction of significantly smaller extensive-form games that are strategically similar to the original game), (2) equilibrium-finding algorithms, and (3) solving subgames during game play in much finer abstractions than would be possible in advance. A new proposal put forward is to reason about games whose rules are modeled via a programming language.

This chapter builds on the basic arguments of the two previous chapters. Money is an inherently imperfect and shifting measure of value; it is endogenous to capitalism but this is not equivalent to seeing it as ‘non-state’, because the state itself needs to be conceived as within, not without, the capitalist system as a whole. Institutional forms change how money works, and the actions of these institutions, particularly of states, matter in the sense of making a real difference not only to monetary forms but to accumulation. The first section comments generally on debates around exogeneity, endogeneity, and the role of the state and other institutions in managing money. The second section illustrates this, drawing on important historical examples of the essential role of states and other financial institutions in monetary affairs and hence in capital accumulation. It is impossible to tell the history of money within the scope of a single short chapter, but six important examples emphasise the conceptual points. This section develops the earlier discussions about money and interest, particularly about the non-neutrality of money and the need to take this seriously in terms of its impacts on capital accumulation and to move from relatively abstract accounts to concrete depictions of institutional relations.

The competing forces of ownership costs and regulatory costs explain the sectoral distribution and historical development of state-owned enterprises (SOEs) in China. While SOEs are generally believed to incur higher ownership costs and have thus been reformed in many sectors, they continue to play a significant role in others. This chapter focuses on several sectors where a trend of "advance of the state, retreat of the private sector" has been observed. In the water utilities sector, empirical evidence suggests that in prefectures where the government fails to frequently adjust water tariffs according to the law to reflect changes in production costs, SOEs are more prevalent, indicating that challenges in tariff regulation likely deter private investment. In the steel and coal mining sectors, frequent changes in state policy have also likely negatively affected private investment. Additionally, in the commercial banking sector, the state maintains SOEs probably due to concerns that regulatory failures could lead to a financial crisis. These examples illustrate how regulatory costs influence the development of SOEs in regulated sectors in China.

This chapter points to a fundamental difficulty associated with the formal study of dynamic adjustment processes toward a Nash equilibrium in the context of social and economic problems (i.e., for human players). This difficulty has created an unfortunate dichotomy of researchers and has hindered progress in this area of research. It suggests, with a couple of examples, that a promising way to overcome this problem is to strengthen the empirical side of research on adjustment dynamics.

This chapter introduces the six contributions in Part IV, “Computer Science.” The main focus is on topics in algorithmic game theory, algorithmic mechanism design, and computational social choice.

On a cold and snowy day in March, I met Isaac Levi (1930–2018) in his New York City home. Their friendly dog welcomed me exstatically when I entered their Upper West Side apartment near Columbia University. While he had long passed his eightieth birthday, Levi was still attending talks and seminars at the philosophy department when we met and was known as an active and provocative discussant with strong opinions. I met Levi a few months before his eighty-fourth birthday. He accompanied me into the living room, offered coffee, and then we started talking. Levi was extremely sharp and critical but also very funny and witty; three hours passed so quickly, I had not even noticed that the batteries of my recording had given up. Our conversation confirmed that he has been one of the most important formal epistemologists and decision theorists in philosophy in the second half of the twentieth century. Notably, Levi had turned slightly cynical, however, obviously affected by the fact that decision theorists might not have given his contributions the attention that he had sought for throughout his career.