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In this article, we study the two membranes problem for operators given in terms of a mean value formula on a regular tree. We show existence of solutions under adequate conditions on the boundary data and the involved source terms. We also show that, when the boundary data are strictly separated, the coincidence set is separated from the boundary and thus it contains only a finite number of nodes.
What are the contexts that give rise to cooperation as opposed to conflict? When should we love thy neighbor, turn the other cheek, or escalate? Game theory is an effort to formalize this problem such that we can ask what decisions we should make when the consequences of those decisions depend on the decisions of others. By this accounting, war is a game, as is negotiation, rock-paper-scissors, and love making. The difference is in the payoffs. Being rational is about making decisions that lead to the best outcomes. The hawks and doves of political foreign policy – who advocate for more or less aggressive military intervention – are rational beings in this world, because the nature of the payoffs demands certain kinds of responses. The pragmatics of high stakes games underpin quotes like John F. Kennedy’s "We can secure peace only by preparing for war." But is Kennedy’s statement rational by the logic of the game in which it is embedded? Is it rational when games of conflict are played repeatedly in a network of global interactions? By combining game theory with network science, we can make some progress toward understanding these issues.
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The Philosophy and Methodology of Experimentation in Sociology
Davide Barrera, Università degli Studi di Torino, Italy,Klarita Gërxhani, Vrije Universiteit, Amsterdam,Bernhard Kittel, Universität Wien, Austria,Luis Miller, Institute of Public Goods and Policies, Spanish National Research Council,Tobias Wolbring, School of Business, Economics and Society at the Friedrich-Alexander-University Erlangen-Nürnberg
The first sociological experiments have been conducted in the second and third decades of the twentieth century, accompanied by a fierce debate about the possibilities and limits of the approach, which anticipated many of the critiques currently raised against the method. The chapter traces the development of experimental research in sociology from these beginning to modern perspectives. One of the reasons for the marginal position of experimentation in sociology has been the reluctance to give up full control of potentially intervening variables (called the ex post facto method) in favor of randomization. Inspirations from social psychology and, later, economics, have finally resulted in the experimental designs that are currently used in sociology.
Background: Congenital cardiac care involves multiple stakeholders including patients and their families, surgeons, cardiologists, anaesthetists, the wider multidisciplinary team, healthcare providers, and manufacturers, all of whom are involved in the decision-making process to some degree. Game theory utilises human behaviour to address the dynamics involved in a decision and what the best payoff is depending on the decision of other players. Aim: By presenting these interactions as a strategic game, this paper aims to provide a descriptive analysis on the utility and effectiveness of game theory in optimising decision-making in congenital cardiac care. Methodology: The comprehensive literature was searched to identify papers on game theory, and its application within surgery. Results: The analysis demonstrated that by utilising game theories, decision-making can be more aligned with patient-centric approaches, potentially improving clinical outcomes. Conclusion: Game theory is a useful tool for improving decision-making and may pave the way for more efficient and improved patient-centric approaches.
Probability-based estimates of the future suicide of psychiatric patients are of little assistance in clinical practice. This article proposes strategic management of the interaction between the clinician and the patient in the assessment of potentially suicidal patients, using principles derived from game theory, to achieve a therapeutic outcome that minimises the likelihood of suicide. Further developments in the applications of large language models could allow us to quantify the basis for clinical decisions in individual patients. Documenting the basis of those decisions would help to demonstrate an adequate standard of care in every interaction.
The frequency of left-handedness in humans is ~10% worldwide and slightly higher in males than females. Twin and family studies estimate the heritability of human handedness at around 25%. The low but substantial frequency of left-handedness has been suggested to imply negative frequency-dependent selection, e.g. owing to a ‘surprise’ advantage of left-handers in combat against opponents more used to fighting right-handers. Because such game-theoretic hypotheses involve social interaction, here we perform an analysis of the evolution of handedness based on kin-selection, which is understood to play a major role in the evolution of social behaviour generally. We show that: (1) relatedness modulates the balance of right-handedness vs. left-handedness, according to whether left-handedness is marginally selfish vs. marginally altruistic; (2) sex differences in relatedness to social partners may drive sex differences in handedness; (3) differential relatedness of parents and offspring may generate parent–offspring conflict and sexual conflict leading to the evolution of maternal and paternal genetic effects in relation to handedness; and (4) differential relatedness of maternal-origin vs. paternal-origin genes may generate intragenomic conflict leading to the evolution of parent-of-origin-specific gene effects – such as ‘genomic imprinting’ – and associated maladaptation.
Animal behavior is subject to the action of natural selection, favoring individuals that behave in ways that maximize their fitness by promoting individual survival and reproductive success. Cultural evolution plays an important role, with behavioral traits of surprising complexity spreading rapidly through a population. Behavioral ecologists measure the costs and benefits of alternative types of behavior to gain an understanding of basic behavioral processes such as territory defense, foraging, and mating. This cost–benefit approach allows quantitative predictions of behavior tightly tied to fitness, such as how long to guard a mate, or how long to forage at a particular location before moving on. Both physiological factors, such as the need to keep eggs warm, and ecological factors, such as the spatial distribution of resources, can influence the evolution of mating systems. In many species, individuals cooperate with each other in procuring food or defending against predators. Hamilton’s model of indirect selection is one possible explanation for the evolution of behavior favoring relatives, including the astounding degree of cooperation in eusocial animals. But in some species, cooperation is common even among unrelated individuals; in these cases game theory models may help explain the evolution of cooperation.
In this chapter, we depart from the observation that a strong motivation for large firms to invest substantial amounts into R&D for an AGI is due to the winner-takes-all effects it may bestow on them. This feature, while important to incentivize AI investment, has the downside that it implies that AI arms races may take place. And the danger of an AI arms race is that it may result in an inferior AGI from a human safety perspective. In this chapter, we model such an AI arms race as an innovation contest and show how a government can steer such an arms race so as to obtain a better outcome in terms of the quality of the AGI. A crucial insight from our modeling is that the intention (or goals) of teams competing in an AGI race, as well as the possibility of an intermediate outcome (“second prize”), may be important.
This chapter deals with how public policy can steer AI, by taking how it can impact the use of big data, one of the key inputs required for AI. Essentially, public policy can steer AI through putting conditions and limitations on data. But data itself can help improve public policy – also in the area of economic policymaking. Hence, this chapter touches on the future potential of economic policy improvements through AI. More specifically, we discuss under what conditions the availability of large data sets can support and enhance public policy effectiveness – including in the use of AI – along two main directions. We analyze how big data can help existing policy measures to improve their effectiveness and, second, we discuss how the availability of big data can suggest new, not yet implemented, policy solutions that can improve upon existing ones. The key message of this chapter is that the desirability of big data and AI to enhance policymaking depends on the goal of public authorities, and on aspects such as the cost of data collection and storage and the complexity and importance of the policy issue.
Linguistic pragmatics is one of the fastest growing fields in contemporary theoretical linguistics. It grew from the influential work of philosophers such as Grice, Austin, Stalnaker, Lewis, and others on context and communicative inferences. It engages directly with general rationality, theory of mind, and systems of intention. One of the major debates in pragmatics has been where to precisely draw the line between semantic phenomena and pragmatic phenomena. In this chapter, three classical and influential ideas on the nature of pragmatics, courtesy of Grice (1975), Stalnaker (1978), and Lewis (1979), are discussed. This discussion leads to three further general philosophical frameworks for separating semantic from pragmatic processes and analyses that have roots in the aforementioned triumvirate: (P1) the indexical conception, (P2) the cognitivist conception, and (P3) social-inferential conception. Each option offers a different demarcation. Finally, three linguistic theories of pragmatics are selected as candidate representations of the contemporary state of the art: (L1) optimality-theoretic pragmatics, (L2) game-theoretic pragmatics, and (L3) Bayesian pragmatics. It’s shown that each of these prominent frameworks exploit the philosophical demarcations (P1–P3) presented to different degrees.
Under closed-list proportional representation, a party's electoral list determines the order in which legislative seats are allocated to candidates. When candidates differ in their ability, parties face a trade-off between competence and incentives. Ranking candidates in decreasing order of competence ensures that elected politicians are most competent. Yet, party lists create incentives for candidates that may lead parties not to place their best candidates at the top of the list. We examine this trade-off in a game-theoretical model in which parties rank their candidates on a list, candidates choose their campaign effort, and the election is a team contest for multiple prizes. We analyze how the candidates’ objectives, voters’ attention and media coverage, incumbency, the number of parties competing in the election, and the electoral environment influence how parties rank candidates.
Conventional wisdom holds that open, collaborative, and transparent organizations are innovative. But some of the most radical innovations—satellites, lithium-iodine batteries, the internet—were conceived by small, secretive teams in national security agencies. Are these organizations more innovative because of their secrecy, or in spite of it? We study a principal–agent model of public-sector innovation. We give research teams a secret option and a public option during the initial testing and prototyping phase. Secrecy helps advance high-risk, high-reward projects through the early phase via a cost-passing mechanism. In open institutions, managers will not approve pilot research into high-risk, high-reward ideas for fear of political costs. Researchers exploit secrecy to conduct pilot research at a higher personal cost to generate evidence that their project is viable and win their manager's approval. Contrary to standard principal–agent findings, we show that researchers may exploit secrecy even if their preferences are perfectly aligned with their manager's, and that managers do not monitor researchers even if monitoring is costless and perfect. We illustrate our theory with two cases from the early Cold War: the CIA's attempt to master mind control (MKULTRA) and the origins of the reconnaissance satellite (CORONA). We contribute to the political application of principal–agent theory and studies of national security innovation, emerging technologies, democratic oversight, the Sino–American technology debate, and great power competition.
Edited by
Jeremy Koster, Max Planck Institute for Evolutionary Anthropology, Leipzig,Brooke Scelza, University of California, Los Angeles,Mary K. Shenk, Pennsylvania State University
The chapter discusses the field of cultural evolution, which emerged in the wake of sociobiology and alongside evolutionary psychology and human behavioral ecology in the 1970s. Cultural evolution theory can be divided into three parts: investigating the genetic evolution of psychological capacities underlying culture, studying how populations adapt to their environments, and exploring how genes and culture influence each other’s evolutionary dynamics. The first sections of the chapter examine how human culture differs from nonhuman culture, why and how culture evolved in humans during the Pleistocene, how our cultural capacity predisposed us to be cooperative, and how cultural group selection created the conditions for the genetic evolution of prosocial preferences. Addressing a common criticism that cultural evolution focuses too heavily on mathematical modeling, subsequent sections showcase the recent explosion of empirical research that has been inspired by cultural evolutionary theory. This research is divided into three methods: fieldwork, experiments, and phylogenetics. The chapter concludes by noting that the dividing lines between cultural evolution and human behavioral ecology are blurring, with students of each subfield increasingly borrowing from the other, suggesting that these labels may soon be obsolete.
How do leaders select their top-level foreign policy appointees? Through a formal model of the domestic and intragovernmental politics surrounding an international crisis, I investigate the trade-offs shaping leaders’ appointment strategies. In the model, a leader selects a foreign policy appointee, anticipating how the appointment will affect the advice he receives in the crisis, the electorate's evaluation of his performance, and ultimately the policies that he and his foreign counterparts pursue as a consequence. The analysis uncovers a fundamental tension in the leader's ability to use appointments to advance his core political and policy objectives of deterring foreign aggression, obtaining accurate advice, and maximizing domestic approval: any appointment that advances one of these objectives invariably comes at the cost of another, and the leader's appointment strategy must balance across these trade-offs. Analyzing cross-national appointment patterns to the offices of ministers of defense and foreign affairs, I find descriptive evidence consistent with the model's predictions: leaders from dovish parties are more than twice as likely as leaders from hawkish parties to select cross-partisan and politically independent appointees, and such appointments are less likely for leaders of either party as they approach re-election.
A core contention woven into the fabric of Sun Tzu’s thinking is that all situations faced by a strategic actor, even those that appear on their face to be losing ones, hold seeds of opportunity that, if grasped correctly, can be parlayed into strategic advantage.1 An illustrative statement starts off Passage #5.1 below.
There are two Sun Tzu verses which, by Sun Tzu’s own affirmations, may be seen as summations of the active ingredient of his way of war. One is Theme #6’s centerpiece verse III.4 (Passage #6.1).
It is argued that the natural and human vicissitudes of the Northern Hemisphere—or at least western European history between 1315 and 1648—provide a preview of the sort of consequences for humanity and its demography that will result from the serious if not catastrophic climate change that is now anticipated by the Intergovernmental Panel on Climate Change (IPCC). Game theory suggests that at least some nation-state players in the strategic problem that climate change raises will not choose Nash equilibria that mitigate the problem. The only feasible solution will be the discovery or invention of some non-greenhouse-gas-emitting energy source so cheap that its owner will be indifferent to free-riding by all other users of energy. Recent efforts to develop fusion reactors do not provide much hope for this eventuality.