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.

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.

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.

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.

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

Although traditional game theory has a tendency to study games in isolation, strategic interaction in human society involves people engaged in numerous interrelated constellations over time. This chapter studies the role of sanctions and enforcement, and strategies not just to play the game that society presents us with but to change the game itself.

A pervasive assumption in game theory is that players’ utilities are concave, or at least quasiconcave, with respect to their own strategies. While mathematically instrumental, enabling the existence of many kinds of equilibria in many kinds of settings, (quasi)concavity of payoffs is too restrictive an assumption. For the same reasons that (quasi)concave utilities can only go so far in capturing single-agent optimization problems, they can only go so far in modeling the considerations of an agent in a strategic interaction. Besides, the study of games with nonconcave utilities is increasingly coming to the fore as deep learning ventures into multiagent learning applications. This chapter studies whcih types of equilibria exist in such games, and whether they are computationally tractable, proposing paths for game theory and multiagent learning in the next 100 years.

This chapter argues that to understand cooperation and conflict in large-scale societies we need to blend these ideas with a systematic study of within-society conflict and the institutions and norms that structure these relations.

This chapter describes the successful application of advances in practical truthful mechanisms design to a large-scale computationally hard problem: The FCC’s 2016–2017 incentive auction, which reallocated tens of billions of dollars of radio spectrum resources from use in television broadcasting to higher-value uses in mobile broadband. The mechanism used was an impressive combination of advances in efficiently solving NP-hard resource allocation problems (in most cases) and in new mechanism design that is simple to implement and that adapts well to limited computation capacity. The auction resulted in repurposing 84 megahertz of spectrum and yielded $19.8 billion in revenue.