This chapter introduces game theory as a framework for understanding strategic interaction in biological, social, and economic systems. Beginning with the foundations of zero-sum games and the minimax theorem, it explains how rational behavior can be analyzed when outcomes depend on the actions of others. The chapter then turns to John Nash’s generalization to non-zero-sum games, introducing Nash equilibrium as a stable outcome in which no player can benefit by unilaterally changing strategy. Classic examples such as the prisoner’s dilemma illustrate the tension between individual rationality and collective welfare. Moving beyond one-shot games, the chapter explores repeated interactions and shows how cooperation can emerge over time, even among self-interested agents. Strategies such as tit-for-tat demonstrate how reciprocity, punishment, and forgiveness can stabilize cooperative behavior. The discussion then extends to evolutionary game theory, where strategies spread or disappear based on reproductive success rather than conscious choice. Concepts such as evolutionarily stable strategies explain how population-level patterns arise in biology and behavior. Together, these ideas reveal game theory as a unifying logic underlying evolution, cooperation, conflict, and decision-making across living systems.

This chapter gives motivating examples of the types of applications that the techniques of the book can be used for. This includes poker AI, wildlife protection, and fair course seat allocation.

This chapter begins our study of Nash equilibrium by giving the basic definitions, Nash’s existence result, and briefly touching on computability issues. Then we will make a few observations specifically about zero-sum games, which have much more structure to exploit.

Online Dispute Resolution (“ODR”) emerged from the convergence of Alternative Dispute Resolution practices and digital platforms, addressing the need for more accessible dispute resolution mechanisms. ODR platforms reduce logistical burdens by eliminating travel requirements and enabling asynchronous communication, while helping to level the playing field between represented and unrepresented parties.

This chapter examines how AI enhances ODR through automated settlement calculations using game theory, negotiation analysis through discourse monitoring, and sentiment analysis to detect contentious exchanges. AI systems can also assist facilitators by analyzing negotiation patterns and suggesting when interventions may be needed.

Despite significant potential benefits, ODR faces challenges, including the digital divide, algorithmic bias, and jurisdictional enforceability. Well-implemented ODR platforms, supported by transparent standards and ethical AI principles, may significantly contribute to making dispute resolution more equitable and responsive to modern societal needs, while requiring careful attention to user-centered design and robust data protection measures.

Chapter 8 addresses the implementation stage, where policy decisions and intentions are translated into concrete actions and outcomes. It analyzes the complex interplay among bureaucrats, central agencies, ministries, departments, nongovernmental actors, and street-level bureaucrats. The chapter traces the evolution of implementation studies from top-down and bottom-up perspectives to more nuanced models incorporating organization theory, game theory, and principal–agent theory. It outlines the key administrative tasks (planning, organizing, staffing, directing, coordinating, reporting, budgeting), and discusses the importance of operational capacity, coordination, and accountability mechanisms. The chapter also examines the challenges of securing compliance among target groups and dealing with environmental turbulence, uncertainty, and limited policy capacity. Emphasizing the political as well as technical nature of implementation, it highlights how organizational structures, actor motivations, and institutional context fundamentally affect policy outcomes.

Integrating insights from chapters 2 and 3, I study the strategic problems at the origins of great power rivalries under the assumption that state motives are tied to principles. I find that great power rivalries rationally unfold in one of two ways: delayed (rather than immediate) competition if emerging threats hold expansive aims, and delayed peace otherwise. While the top-line result is simple, my qualitative signaling mechanism explains four of the most puzzling aspects of how great powers forge rationalist threat perceptions and how these perceptions influence patterns of competition, hedging, and peace. Specifically, I explain: (1) why status quo powers are reassured by a rival’s early diplomatic promises of limited motives; (2) why status quo powers are willing to make repeated concessions even as a rival makes violent demands, takes territory, rapidly militarizes, or seeks to undermine the status quo in other ways; (3) punctuated (rather than gradual) changes in status quo powers’ beliefs about a rival’s strategic motives; and (4) why some cases end in competition following a specific demand, while others end in stable peace.

Researchers expect that the origins of great power rivalries are especially conflict-prone because emerging threats must militarize to pursue their core interests, and status quo powers are uncertain about their rivals’ strategic intentions. These researchers are puzzled because historical great powers often avoided conflict entirely (e.g., Anglo–American relations circa 1900), or for years, even as one state rapidly militarized and took territory (Anglo–German relations circa 1940). I review the strategic challenges emphasized in the two main theoretical approaches used to study this setting, and the remaining puzzles each approach reckons with: the trust problem studied by realists and the commitment problem studied by power transition scholars. I argue that important insights are gained by studying the interaction of these two strategic problems. I develop a new formal model that produces the interactive trust and commitment problems commonly observed in historical cases of great power rivalry, affording a structured way for future scholars to study them.

This chapter examines four examples of concept formation in formal modeling and draws lessons for scholars outside formal theory. Because defining concepts is often more straightforward than solving models, formalization offers valuable tools for clarifying ideas. First, it highlights how formal definitions of conceptual primitives precede and shape model construction. For example, in economics, elasticity is formalized with intuitive ideal-type values, while in political science, audience costs – defined as part of a payoff structure – have endured owing to their clarity and portability. After solving models, scholars can aggregate and disaggregate equilibrium outcomes to build typologies. The chapter illustrates this with two further concepts: state-sponsored protection (refined through a model of cartel–police interactions), and commitment problems (which benefit from formal aggregation of diverse mechanisms). These cases demonstrate how formal tools, like natural-language concept analysis, help structure concepts – offering transparency, precision, and manipulability, though sometimes at the cost of nuance. For nonformal scholars, the chapter encourages “conceptual accounting”: experimenting with mathematical representations to clarify meanings and omissions. Ultimately, the formalization of concepts is not only compatible with broader conceptual analysis – it can enrich it. A glossary is included to assist readers less familiar with formal theory.

The chapter surveys various papers in the literature that specifically analyze deterrence and preemption policies from the perspective of game theory. Emphasis is given to certain classes of models in order to highlight key aspects and characteristics of the policies studied. For example, when countries engage in deterrence against terrorist organizations, it is likely that they may simply deflect terrorist attacks to other countries. Preemptive policies on the other hand, provide positive benefits to other countries and therefore any benefits stemming from this policy, may be underprovided due to the problem of free riding.

Terrorism has instrumental value in terms of achieving political, ideological, or religious goals; and non-instrumental value, in terms of organizational and psychological motivations. I introduce canonical models of terrorism under asymmetric information that account for both types of goals. As these equilibria identify counterfactuals that would be otherwise unobservable, they illuminate the ‘known unknowns’ that matter for counterterror policy. Finally, I address the signaling value of partial government concessions when voters or terrorists are uncertain about a target government’s type.

This chapter discusses empirical evidence for a range of decision procedures underlying individuals’ choices in games. These include (1) quantal response equilibria. These are stochastic choice models where a player does not best reply to their beliefs, but instead chooses actions with a higher expected payoff with a higher probability. It also includes (2) cognitive hierarchy models where, roughly speaking, players possess different, discrete levels of cognition. A level-0 player chooses some fixed anchor strategy. And, recursively, having fixed the strategies of players of level 0,...,k-1, a level-k player best responds to a belief that all other players are of a lower level. Lastly, it includes (3) a variety of learning models.

This chapter is the introduction to Part I, “The early history of game theory from Borel”. Starting from a 1921 paper by Émile Borel, it surveys the historical development of game theory during its first few decades.

Game theory in biology emerged as a theoretical and modeling approach to the evolutionary study of behavior and other phenotypes. It was inspired by the prominence of game theory in economics. This chapter gives a perspective on this influence of economic thinking on biology. Which ideas were taken from economics and the social sciences to biology, how were they modified, which biological phenomena were they applied to, and what are the successes, challenges, and the possible future of the field? It focuses on two of the earliest applications of game theory in biology, namely sex-ratio theory and animal contests.

This chapter reviews literature on game-theoretic analysis of voting. Both cooperative and noncooperative concepts are used to answer questions, such as, How do candidates or parties propose alternatives to voters in strategic interactions? Why do voters vote? What are the implications of asymmetric information for candidates’ and voters’ incentives? Do prevoting deliberations improve information sharing? If so, through what type of rules? Sophisticated voters may act strategically, and therefore it matters whether one’s choices are pivotal. In the presence of private information, the mechanism design approach is highly appropriate, as voters’ incentives can be heavily influenced by the institutional settings that determine how votes are transformed to election outcomes. The analysis of information aggregation in large-scale elections brings important insights to our understanding of representative democracy. Due to the nonexistence of a core and the cyclical structure of pairwise comparison, there may be a fundamental difficulty in the preference aggregation by majoritarian democracy in large-scale elections. The chapter concludes with questions for future research: How does the limitation of preference/information aggregation in large-scale elections affect the stability of representative democracy? What determines the robustness of democratic norms? What is the role of the media in the presence of information asymmetry, particularly in ideological battles where information filtering can play an exacerbating role?