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Concept: Game theory


Zero-determinant strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner’s Dilemma irrespective of the opponent’s strategy (coercive strategies), or else to set the ratio between the player’s and their opponent’s expected payoff (extortionate strategies). Here we show that zero-determinant strategies are at most weakly dominant, are not evolutionarily stable, and will instead evolve into less coercive strategies. We show that zero-determinant strategies with an informational advantage over other players that allows them to recognize each other can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition.

Concepts: Game theory, Evolution, Probability theory, Strategy, Players, Prisoner's dilemma, Nash equilibrium, Player


In competitive situations, individuals need to adjust their behavioral strategy dynamically in response to their opponent’s behavior. In the present study, we investigated the neural basis of how individuals adjust their strategy during a simple, competitive game of matching pennies. We used entropy as a behavioral index of randomness in decision-making, because maximizing randomness is thought to be an optimal strategy in the game, according to game theory. While undergoing functional magnetic resonance imaging (fMRI), subjects played matching pennies with either a human or computer opponent in each block, although in reality they played the game with the same computer algorithm under both conditions. The winning rate of each block was also manipulated. Both the opponent (human or computer), and the winning rate, independently affected subjects' block-wise entropy during the game. The fMRI results revealed that activity in the bilateral anterior insula was positively correlated with subjects' (not opponent’s) behavioral entropy during the game, which indicates that during an interpersonal competitive game, the anterior insula tracked how uncertain subjects' behavior was, rather than how uncertain subjects felt their opponent’s behavior was. Our results suggest that intuitive or automatic processes based on somatic markers may be a key to optimally adjusting behavioral strategies in competitive situations.

Concepts: Game theory, Psychology, Magnetic resonance imaging, Decision theory, Behavior, Chess, Nash equilibrium, Matching pennies


Two large cardiovascular outcome trials of canagliflozin, the CANVAS Program, will complete in early 2017: the CANagliflozin cardioVascular Assessment Study (CANVAS) and the CANagliflozin cardioVascular Assessment Study - Renal (CANVAS-R). Accruing data for the sodium-glucose co-transporter 2 inhibitor (SGLT2i) class has identified questions and opportunities that were not apparent when the trials were designed. Accordingly, a series of modifications have been made to the planned analyses. These updates will ensure that the data from the CANVAS Program will maximise advances in scientific knowledge and patient care. The specification of the analysis strategy prior to knowledge of the trial results, their design by the independent scientific trial Steering Committee, the detailed a priori definition of the analysis plans and the external review provided by the US Food and Drug Administration, all provide for a maximally efficient and robust utilisation of the data. The CANVAS Program should significantly advance our understanding of the effects of canagliflozin, and the broader SGLT2i class, on a range of important efficacy and safety outcomes.

Concepts: Game theory, Scientific method, Thought, The Trial, Logic, A priori, A priori and a posteriori, Plan


The drinking water of more than six million Americans in numerous communities has been found to contain highly fluorinated chemicals at concentrations of concern. Certain of these chemicals, including perfluorooctanoic acid and perfluorooctane sulfonic acid, are known to be persistent, bioaccumulative, and associated with adverse health outcomes in humans and animal models. The possible health impacts of exposure to highly fluorinated chemicals are of great concern to communities whose water has been impacted. Community members want information, and are asking for biomonitoring, exposure pathway analysis, and health studies. Governmental agencies are striving to deal with these multiple concerns in the face of information and resource constraints. We propose the development of a high-level research strategy to maximize what can be learned about health effects of highly fluorinated chemicals and methods to reduce or eliminate exposure. We suggest coordinating the research across multiple communities for greater statistical power. If implemented, such a strategy could help to generate information and evidence integration to enable regulatory decision making and contribute to reducing future exposures.

Concepts: Game theory, Human, Decision making, Sample size, Water, Hydrogen, United States, Fluorocarbon


Recurrent hamstring injuries are a major problem in sports such as football. The aim of this paper was to use a clinical example to describe a treatment strategy for the management of recurrent hamstring injuries and examine the evidence for each intervention. A professional footballer sustained five hamstring injuries in a relatively short period of time. The injury was managed successfully with a seven-point programme-biomechanical assessment and correction, neurodynamics, core stability, eccentric strengthening, an overload running programme, injection therapies and stretching/relaxation. The evidence for each of these treatment options is reviewed. It is impossible to be definite about which aspects of the programme contributed to a successful outcome. Only limited evidence is available in most cases; therefore, decisions regarding the use of different treatment modalities must be made by using a combination of clinical experience and research evidence.

Concepts: Time, Game theory, Association football, American football, Chess, Football, Professional sports, Columbus, Ohio


Background The effect of a restrictive versus liberal red-cell transfusion strategy on clinical outcomes in patients undergoing cardiac surgery remains unclear. Methods In this multicenter, open-label, noninferiority trial, we randomly assigned 5243 adults undergoing cardiac surgery who had a European System for Cardiac Operative Risk Evaluation (EuroSCORE) I of 6 or more (on a scale from 0 to 47, with higher scores indicating a higher risk of death after cardiac surgery) to a restrictive red-cell transfusion threshold (transfuse if hemoglobin level was <7.5 g per deciliter, starting from induction of anesthesia) or a liberal red-cell transfusion threshold (transfuse if hemoglobin level was <9.5 g per deciliter in the operating room or intensive care unit [ICU] or was <8.5 g per deciliter in the non-ICU ward). The primary composite outcome was death from any cause, myocardial infarction, stroke, or new-onset renal failure with dialysis by hospital discharge or by day 28, whichever came first. Secondary outcomes included red-cell transfusion and other clinical outcomes. Results The primary outcome occurred in 11.4% of the patients in the restrictive-threshold group, as compared with 12.5% of those in the liberal-threshold group (absolute risk difference, -1.11 percentage points; 95% confidence interval [CI], -2.93 to 0.72; odds ratio, 0.90; 95% CI, 0.76 to 1.07; P<0.001 for noninferiority). Mortality was 3.0% in the restrictive-threshold group and 3.6% in the liberal-threshold group (odds ratio, 0.85; 95% CI, 0.62 to 1.16). Red-cell transfusion occurred in 52.3% of the patients in the restrictive-threshold group, as compared with 72.6% of those in the liberal-threshold group (odds ratio, 0.41; 95% CI, 0.37 to 0.47). There were no significant between-group differences with regard to the other secondary outcomes. Conclusions In patients undergoing cardiac surgery who were at moderate-to-high risk for death, a restrictive strategy regarding red-cell transfusion was noninferior to a liberal strategy with respect to the composite outcome of death from any cause, myocardial infarction, stroke, or new-onset renal failure with dialysis, with less blood transfused. (Funded by the Canadian Institutes of Health Research and others; TRICS III number, NCT02042898 .).

Concepts: Game theory, Renal failure, Epidemiology, Myocardial infarction, Medical statistics, Surgery, Relative risk, Blood transfusion


How do humans learn to trust unfamiliar others? Decisions in the absence of direct knowledge rely on our ability to generalize from past experiences and are often shaped by the degree of similarity between prior experience and novel situations. Here, we leverage a stimulus generalization framework to examine how perceptual similarity between known individuals and unfamiliar strangers shapes social learning. In a behavioral study, subjects play an iterative trust game with three partners who exhibit highly trustworthy, somewhat trustworthy, or highly untrustworthy behavior. After learning who can be trusted, subjects select new partners for a second game. Unbeknownst to subjects, each potential new partner was parametrically morphed with one of the three original players. Results reveal that subjects prefer to play with strangers who implicitly resemble the original player they previously learned was trustworthy and avoid playing with strangers resembling the untrustworthy player. These decisions to trust or distrust strangers formed a generalization gradient that converged toward baseline as perceptual similarity to the original player diminished. In a second imaging experiment we replicate these behavioral gradients and leverage multivariate pattern similarity analyses to reveal that a tuning profile of activation patterns in the amygdala selectively captures increasing perceptions of untrustworthiness. We additionally observe that within the caudate adaptive choices to trust rely on neural activation patterns similar to those elicited when learning about unrelated, but perceptually familiar, individuals. Together, these findings suggest an associative learning mechanism efficiently deploys moral information encoded from past experiences to guide future choice.

Concepts: Game theory, Psychology, Learning, Knowledge, Behavior, Play, Shape, Player


Humans often cooperate with strangers, despite the costs involved. A long tradition of theoretical modeling has sought ultimate evolutionary explanations for this seemingly altruistic behavior. More recently, an entirely separate body of experimental work has begun to investigate cooperation’s proximate cognitive underpinnings using a dual-process framework: Is deliberative self-control necessary to reign in selfish impulses, or does self-interested deliberation restrain an intuitive desire to cooperate? Integrating these ultimate and proximate approaches, we introduce dual-process cognition into a formal game-theoretic model of the evolution of cooperation. Agents play prisoner’s dilemma games, some of which are one-shot and others of which involve reciprocity. They can either respond by using a generalized intuition, which is not sensitive to whether the game is one-shot or reciprocal, or pay a (stochastically varying) cost to deliberate and tailor their strategy to the type of game they are facing. We find that, depending on the level of reciprocity and assortment, selection favors one of two strategies: intuitive defectors who never deliberate, or dual-process agents who intuitively cooperate but sometimes use deliberation to defect in one-shot games. Critically, selection never favors agents who use deliberation to override selfish impulses: Deliberation only serves to undermine cooperation with strangers. Thus, by introducing a formal theoretical framework for exploring cooperation through a dual-process lens, we provide a clear answer regarding the role of deliberation in cooperation based on evolutionary modeling, help to organize a growing body of sometimes-conflicting empirical results, and shed light on the nature of human cognition and social decision making.

Concepts: Game theory, Decision making, Cognition, Evolutionary biology, The Evolution of Cooperation, Kin selection, Reciprocal altruism, Altruism


Artificial intelligence has seen several breakthroughs in recent years, with games often serving as milestones. A common feature of these games is that players have perfect information. Poker is the quintessential game of imperfect information, and a longstanding challenge problem in artificial intelligence. We introduce DeepStack, an algorithm for imperfect information settings. It combines recursive reasoning to handle information asymmetry, decomposition to focus computation on the relevant decision, and a form of intuition that is automatically learned from self-play using deep learning. In a study involving 44,000 hands of poker, DeepStack defeated with statistical significance professional poker players in heads-up no-limit Texas hold'em. The approach is theoretically sound and is shown to produce more difficult to exploit strategies than prior approaches.

Concepts: Game theory, Psychology, Machine learning, Learning, Computer, Logic, Computer science, Information theory


The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.

Concepts: Game theory, Mind, Metaphysics, The Evolution of Cooperation, Prisoner's dilemma, Nash equilibrium, Evolutionarily stable strategy, Stag hunt