Game Theorists Research Articles

How to Evaluate Behavioral Models

Researchers building behavioral models, such as behavioral game theorists, use experimental data to evaluate predictive models of human behavior. However, there is little agreement about which loss function should be used in evaluations, with error rate, negative log-likelihood, cross-entropy, Brier score, and squared L2 error all being common choices. We attempt to offer a principled answer to the question of which loss functions should be used for this task, formalizing axioms that we argue loss functions should satisfy. We construct a family of loss functions, which we dub ``diagonal bounded Bregman divergences'', that satisfy all of these axioms. These rule out many loss functions used in practice, but notably include squared L2 error; we thus recommend its use for evaluating behavioral models.

Modeling Norm-Governed Communities with Conditional Games: Sociological Game-Determination and Economic Equilibria

Most social scientists agree that informal norms constrain available equilibria in most human interactions. However, they do not agree on how to model them: economists often make them derivative of individual preferences, while a broader tradition in social theory understands them as exogenous social facts. Non-cooperative game theory more naturally accommodates the economists’ approach. However, attention is increasingly attracted to recent work by economists who appreciate that the broader understanding may be important for full empirical adequacy. We focus on how game theorists might track this emerging shift. Extending Stirling’s previously developed Conditional Game Theory, we model macrostructural processes of norm evolution through social influence diffusion in a way that relies on no exotic solution concepts, which in turn allows norms as social facts and norms as expressions of preferences to be modeled as evaluable complements, by analogy to the complementarity of cooperative and non-cooperative game solutions under the Nash program. The result can be understood as a way of specifying mutual constraints between economic models in which normative attitudes are exogenous, and sociological models that represent such attitudes as endogenous under power relationships and ontologies of social roles.

Why Stop Grazing the Climate Commons?

Many have argued that climate change is the textbook example of a tragedy of the commons. Assuming that is correct, to make headway on climate change, we would expect an enforceable agreement that provides for global collective action. The tragedy of the commons assumes that those who cut back when others do not are—to use the formal language of game theorists—suckers. So, the last thing we would expect is a surge of unilateral action. Contrary to theory, for the past decade, unilateral climate action has flourished among governments, businesses, other organizations, and individuals. Is the number of climate suckers growing exponentially, or is there more going on? This Article proposes an alternative explanation. A growing and substantial part of the climate crisis is not subject to the tragedy of the commons, allowing rational actors to take climate action because of their self-interests, not despite them. While the ability to rely on unilateral action to make some climate progress unlocks exciting possibilities, effectively confronting climate change requires a better understanding of why unilateral actors act. This Article exposes the economic and political incentives that frequently drive unilateral action. Understanding the incentives of unilateral actors opens two promising inroads for climate action: strengthening unilateral action by playing to these incentives and building on unilateral action to make collective action more obtainable.

Action functional gradient descent algorithm for estimating escape paths in stochastic chemical reaction networks.

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then we use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points. The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updated toward the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution. We consider several applications of the algorithm and verify them against computationally expensive means such as the shooting method and stochastic simulation. While we employ theoretical techniques from mathematical physics, numerical optimization and chemical reaction network theory, we hope that our work finds practical applications with an inter-disciplinary audience including chemists, biologists, optimal control theorists and game theorists.

Is only one of my selves authentic? An empirical approach

In behavioral economics, intrapersonal conflict is predominantly interpreted hierarchically. A “present-biased” intrapersonal doer may spoil the goal of a rational planner. This often suggests paternalistic interventions that help the “true” or “authentic” self to overwhelm its present-biased alter ego. Game theorist Schelling proposed a reciprocal interpretation of intrapersonal conflict that interprets both selves as strategic players, which Elster contradicted by claiming that in any conflict only one self is capable of strategic behavior and therefore authentic. Previous empirical studies, however, cannot test this interpretation, because their design provides commitment devices unilaterally to only one self. In an experiment, we provided commitment devices to both selves and find similar inclinations to use this strategic tool. Given this, the symmetric view on intrapersonal conflict seems no less plausible than the hierarchical one. Our results might contribute to a richer debate on intrapersonal conflict by feeding in some skepticism about the self-evidence with which paternalists take sides.

The fear of conflict leads people to systematically avoid potentially valuable zero-sum situations

From interpersonal interactions to international arms races, game theorists and social scientists have long studied decision-making in zero-sum situations. Yet, what happens when people can freely choose whether to enter zero-sum situations in the first place? Thirteen studies (including five pre-registered) consistently document evidence for zero-sum aversion—the desire to avoid situations that are (or are believed to be) zero-sum. Across different contexts (economic games, market entry decisions, performance reviews, negotiations, job applications), samples (online participant pool, MBA students, community sample), and designs (within- and between-participant, real and hypothetical decisions), people avoid zero-sum situations that inversely link their and others’ outcomes as well as refrain from putting others in such situations. Because people fear that zero-sum situations will be rife with conflict, they exhibit zero-sum aversion even when doing so is costly. Finally, we find that people require zero-sum situations to provide substantially higher payoffs (e.g., compensation) to overcome their zero-sum aversion. We conclude with a discussion of the implications for interpersonal and intergroup conflict.

Humans and the core partition: An agent-based modeling experiment.

Although strategic coalition formation is traditionally modeled using cooperative game theory, behavioral game theorists have repeatedly shown that outcomes predicted by game theory are different from those generated by actual human behavior. To further explore these differences, in a cooperative game theory context, we experiment to compare the outcomes resulting from human participants' behavior to those generated by a cooperative game theory solution mechanism called the core partition. Our experiment uses an interactive simulation of a glove game, a particular type of cooperative game, to collect the participant's decision choices and their resultant outcomes. Two different glove games are considered, and the outputs from 62 trial games are analyzed. The experiment's outcomes show that core coalitions, which are coalitions in a core partition, are found in about 42% of games. Though this number may seem low, a trial's outcome is more complex than whether the human player finds a core coalition or not. Finding the core coalition depends on factors such as the other possible feasible solutions and the payoffs available from these solutions. These factors, and the complexity they generate, are discussed in the paper.

The Game Theory of Sex

AbstractCalculated sexual games play out across contemporary American popular media, from self-help books and advice columns to dating apps and reality television. This article argues that economic game theory subtends the saturation of popular culture with lay theories of sex as a “numbers game.” Game theorists contribute to the invisible ubiquity of this phenomenon by using sexual examples to demonstrate the range of their discipline’s models while downplaying the significance of exemplification. Lydia Davis’s short fiction—by taking for granted the economization of intimate relationships without disavowing, naturalizing, or objecting to it—registers the cultural footprint and vernacular intellectual history of the game theory of sex, and elaborates its key modes of fictionality, antinarrativity, and self-fulfilling prophecy. Ultimately, the game theory of sex offers a prehistory of sexual gamification that extends beyond its most immediate digital substrate.

Team reasoning without a hive mind

The theory of team reasoning has been developed to resolve a long-lasting niggle in orthodox game theory. Despite its intuitive appeal, the theory has received little attention from mainstream game theorists and economists to date. We believe that this is so because of two theoretic issues, which the theory of team reasoning itself needs to resolve. One of these presents a worry that the theory achieves its explanatory and predictive success by abandoning ontological individualism — a fundamental precept in mainstream economics, including game theory. Here we argue that the theory of team reasoning is compatible with ontological individualism. We show that the core principles of the theory — those that give rise to the above worry — are in fact implicitly assumed in some branches of orthodox game theory itself. We also argue against the methodological approach that construes team reasoning as involving a transformation of the interacting players’ payoffs in modelled games.

Orangutan information broadcast via consonant-like and vowel-like calls breaches mathematical models of linguistic evolution.

The origin of language is one of the most significant evolutionary milestones of life on Earth, but one of the most persevering scientific unknowns. Two decades ago, game theorists and mathematicians predicted that the first words and grammar emerged as a response to transmission errors and information loss in language's precursor system, however, empirical proof is lacking. Here, we assessed information loss in proto-consonants and proto-vowels in human pre-linguistic ancestors as proxied by orangutan consonant-like and vowel-like calls that compose syllable-like combinations. We played back and re-recorded calls at increasing distances across a structurally complex habitat (i.e. adverse to sound transmission). Consonant-like and vowel-like calls degraded acoustically over distance, but no information loss was detected regarding three distinct classes of information (viz. individual ID, context and population ID). Our results refute prevailing mathematical predictions and herald a turning point in language evolution theory and heuristics. Namely, explaining how the vocal–verbal continuum was crossed in the hominid family will benefit from future mathematical and computational models that, in order to enjoy empirical validity and superior explanatory power, will be informed by great ape behaviour and repertoire.

The right to move and the right to exclude: Ilya Somin and ‘foot voting’

The right to move and the right to exclude: Ilya Somin and ‘foot voting’

Application of Game Theory in Middle-Management: A Military Historical Study of the Role of the Middle-Manager as a Correlated Equilibrium Factor in the Decision-Making Process

The role of the manager, defined by innumerable scientific publications, is only rarely seen through the prism of game theory and its notions of equilibrium allowing decision-makers to optimize situations. The role of the middle-manager, mindful of the human factor and respectful toward his mission shall lead to a virtuous balance, can be defined in game theory as a correlated equilibrium in the sense of the game theorist Robert Aumann. Indeed, this kind of equilibrium goes further than the Nash equilibrium by introducing the notion of a common game and an intermediary embedded in the decision-making process and getting the strategy from his superiors to translate it to his subordinated staff. We use two military historical illustrations to illustrate this concept: the case of the Auftragstaktik refers to Sherman's "march to the sea" while the study of Lee's defeat at Gettysburg refers to the necessity of having capable subordinated staff to maximize an outcome. Throughout this study, we show and formalize the essential role of the middle-manager in the elaboration of effective decisions and processes.

Game Theory in Practice, on the (Non) Discovery of Social Equilibria

What follows is an attempt to view (elementary) game theory through the prism of recent developments in philosophy of mathematics. In particular, if a model (in the sense of model theory)on an appropriate domain can be constructed from a formal theory and it can be established that homomorphic mappings between model structures are possible then such a maneuver undermines the Realistic case for solution concepts since it makes the denotation of such concepts problematic since the denotation ceases to be unique. This creates philosophical problems within the Philosophy of mathematics which affects communities of mathematicians working in particular mathematical areas. (Groups, Rings, Vector Spaces, Graphs and so on) However when it comes to game theory, problematic denotation affects not only Professionals (mathematicians, economists, game theorists) but also ‘ordinary’ people in the real world who interact with each other in social contexts amenable to game theoretic analysis I note briefly that Game theory has difficulties, still, with equilibrium selection and simple 2X2 games fail to predict and these problems have triggered extensive debates. I do not specify any specific causal connection between referential failure and any given issue within game theory I do however suggest that there is clearly a need to supplement the semantics of equilibrium concepts (here the minimax theorem) and I note that even simple 2X2 games typically come with labels, prisoner, husband-wife, hawk and so on. These perhaps provide hooks into more comprehensive semantics. I also briefly discuss conventions as an additional mechanism. Finally I suggest that if this analysis is on the right lines it might be extended to include more complex social equilibrium mechanisms like Nash equilibrium or general economic equilibrium in micro economics. The style is deliberately informal.

Plato as a Game Theorist towards an International Trade Policy

In the beginning of the second book of his Politeia (Republic) Plato in passage 2.358e–359a–c raises the issue of the administration of justice as a means of motivating people to behave fairly regarding their relationships and when cooperating with each other because, at the end, this is mutually beneficial for all of them. We argue that this particular passage could be seen as a part of a wider process of evolution and development of the institutions of the ancient Athenian economy during the Classical period (508–322 BCE) and could be interpreted through modern theoretical concepts, and more particularly, game theory. Plato argued that there are two players, each with two identical strategies, to treat the other justly or unjustly. In the beginning, each player chooses the “unjust” strategy, trying to cheat the other. In this context, which could be seen as a prisoner’s dilemma situation, both end with the worst possible outcome, that is, deceiving each other and this has severe financial consequences for both of them. Realizing this, in a repeated game situation, with increasing information on the outcome and on each other, they choose the “just” strategy so achieving the best outcome and transforming the game in a cooperative one. We analyze this, formulating a dynamic game which is related to international commercial transactions, after explaining how such a situation could really arise in Classical Athens. We argue that this is the optimal scenario for both parties because it minimizes the risk of deceiving each other and creates harmony while performing financial transactions.

$$(\alpha , \beta , \gamma )$$-cut set based ranking approach to solving bi-matrix games in neutrosophic environment

Uncertainty provides an importance in decision making problems like game theory. Several types of uncertainties occur in the literature as fuzzy, soft, rough, interval, etc., and game theory is treated by these types of uncertainties and vagueness by game theorists and others in different aspects. Neutrosophic set and logic are emerged nowadays as another type of uncertainty. Single-valued triangular neutrosophic numbers liberally assume the indeterminacy in choice of elements based upon decision makers’ intuition, assumption, judgement, behaviour, evaluation and decision. Here, a new ranking approach is based on the $$(\alpha , \beta , \gamma )$$ -cut of single-valued triangular neutrosophic number and is applied on bi-matrix game theory. We compare our derived results with some previously defined score and accuracy functions and put some interesting and comparatively good results without any plausible fiasco. In this paper, our principal purpose is to validate and approve the proposed contemplations by applying it on illuminating real-life problems in neutrosophic realm through bi-matrix game theory.

The Gift of Testimony

AbstractIn this paper I argue that in Western contemporary societies testimony is structured by norms of reciprocation and thus is best understood as involving the exchange of gifts rather than, as philosophers and game theorists have tended to presume, market transactions. My argument is based on an initial analysis of the reactive attitudes that are exhibited in testimonial exchanges. I highlight the central role played by the reciprocating attitudes of gratitude and gratification respectively in the recipient and the donor of testimony. This analysis leads to an account of the speech act of telling that is the primary vehicle of testimony. Telling, I argue, is a commissive but it is not, as it is usually presumed, akin to promising. Instead, its nature is that of an offer of a gift. Finally, I develop an account of the norms of trust and trustfulness as reciprocating social norms. I show that adopting these norms provides a particularly effective solution of the problem of cooperation. The solution is particularly effective because it incentivises both the sharing of epistemic goods and the acquisition of further such goods so that one is able to share them.

Antibiotic development - economic, regulatory and societal challenges.

Antibiotic resistance is undoubtedly one of the greatest challenges to global health, and the emergence of resistance has outpaced the development of new antibiotics. However, investments by the pharmaceutical industry and biotechnology companies for research into and development of new antibiotics are diminishing. The public health implications of a drying antibiotic pipeline are recognized by policymakers, regulators and many companies. In this Viewpoint article, seven experts discuss the challenges that are contributing to the decline in antibiotic drug discovery and development, and the national and international initiatives aimed at incentivizing research and the development of new antibiotics to improve the economic feasibility of antibiotic development. In this Viewpoint article, seven experts discuss the challenges that are contributing to the decline in antibiotic drug discovery and development, and the international and national initiatives aimed at incentivizing research and the development of new antibiotics to improve the economic feasibility of antibiotic development. Christine Ardal co-leads research and innovation in the European Union Joint Action on Antimicrobial Resistance and Healthcare-Associated Infections. Previously she was the co-lead on incentives to stimulate antibacterial innovation for the European Union’s DRIVE-AB project. She is a senior adviser at the Norwegian Institute of Public Health, where her research and policy work focuses on medicine innovation, access and stewardship. Manica Balasegaram trained as a medical doctor at the University of Nottingham, United Kingdom, and from 2001 onwards worked as a doctor and researcher in several countries in sub-Saharan Africa and southern Asia with Medecins Sans Frontieres. In 2007, he joined the Drugs for Neglected Diseases initiative as Head of the Leishmaniasis Clinical Program before returning to Medecins Sans Frontieres as Executive Director of the Access Campaign. He joined the Global Antibiotic Research and Development Partnership in June 2016, and is a board member of the Medicines Patent Pool as well as FIND’s Scientific Advisory Committee. He is also the executive director of GARDP. Ramanan Laxminarayan is the founder and Director of the Center for Disease Dynamics, Economics & Policy in Washington, DC, United States, and a senior research scholar at Princeton University. He is a voting member of the US Presidential Advisory Council on Combating Antibiotic-Resistant Bacteria. David McAdams is a game theorist and professor of economics in the Fuqua School of Business and Economics Department at Duke University, United States. His current research focuses on the economic epidemiology of information, with applications from antibiotic resistance to ‘fake news’. Kevin Outterson is a professor of law and N. Neal Pike Scholar in Health and Disability Law at Boston University, United States, and Executive Director of CARB-X. He has grappled for a dozen years with issues peculiar to antibiotic research and development, especially relating to intellectual property, reimbursement and business models. He now leads the world’s largest push incentive for antibacterial research and development, CARB-X, with a 5-year budget exceeding US$500 million. The views expressed herein are personal, and do not necessarily represent the views of CARB-X or any CARB-X funder. John H. Rex is a physician and drug developer with more than 30 years of development and policy experience focused on antimicrobial agents. He is currently Chief Medical Officer of F2G Ltd (an antifungal biotechnology company), an expert-in-residence for the Wellcome Trust and an operating partner with a venture capital group (Advent Life Sciences) and was (2015–2019) a voting member of the US Presidential Advisory Council on Combating Antibiotic-Resistant Bacteria. He blogs regularly at http://amr.solutions/blog.html. Nithima Sumpradit is a pharmacist and lead coordinator for development and implementation of Thailand’s National Strategic Plan on Antimicrobial Resistance 2017–2021. She is also a programme manager of the Royal Thai Government–WHO Country Cooperation Strategy Programme on Antimicrobial Resistance.

Keynes Goes Nuclear: Thomas Schelling and the Macroeconomic Origins of Strategic Stability

Among the most important ideas in Cold War nuclear strategy and arms control was that of “stability”—the notion that by protecting weapons for use in retaliation, the superpowers would be less likely to fight a thermonuclear war. Conventional wisdom among strategists and historians of strategy has long held that stability was inherent to the logic of rational nuclear deterrence. This essay shows the conventional wisdom to be mistaken. It examines the technical practice of Thomas Schelling, who introduced the stability idea in a classic 1958 paper. Celebrated as a game theorist, Schelling was actually trained as a Keynesian macroeconomic modeler during the second half of the 1940s. In 1958, he used Keynesian techniques to frame deterrence as a stable system of dynamic adjustment, akin to the stable macroeconomic system he had modeled as a young economist. Among Schelling's fellow strategists, stability quickly became popular as a rationalization for their preferred nuclear deployment policies.

Universal modesty in signal-burying games.

Why would individuals hide positive information about themselves? Evolutionary game theorists have recently developed the signal-burying game as a simple model to shed light on this puzzle. They have shown that the game has an equilibrium where some agents are better off deliberately reducing the visibility of the signal by which they broadcast their positive traits. However, this equilibrium also features individuals who fully broadcast their positive traits. Here, we show that the signal-burying framework can also explain modesty norms that everyone adheres to: the game contains an equilibrium where all agents who send a signal voluntarily reduce its conspicuousness. Surprisingly, the stability of the two kinds of equilibria rely on very different principles. The equilibrium where some agents brag is stable because of costly signalling dynamics. By contrast, the universal modesty equilibrium exists because buried signals contain probabilistic information about a sender's type, and receivers make optimal use of this information. In the latter equilibrium, burying a signal can be understood as a handicap which makes the signal more honest, but honesty is not achieved through standard costly signalling dynamics.

Peter Vanderschraaf, Strategic Justice: Convention and Problems of Balancing Divergent Interests

For twenty years, Peter Vanderschraaf has been writing important papers about conventions. His new book, Strategic Justice, synthesises this body of work and displays his ability to write both as a scholarly philosopher and as a rigorous game theorist. As a preface to this review, I must declare an interest. I am the author of a book, The Economics of Rights, Cooperation and Welfare (1986), which deals with many of the same topics as Strategic Justice, drawing on the same classic sources. Van...