Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not.Soccer; Football; MSNE; Mixed-strategies; Mixed-strategy Nash equilibrium; Sports; Penalty kicks

Ask not what economics can do for sports - ask what sports can do for economics

In this article we list the advantages of using sports data for economic research. We also provide a rich overview of economic literature that used sports data to test different fundamental economic theories as well as articles that presented divergences of economic decision making from neo-classical theories. Finally we present articles that were published in this special issue on behavioral economics and decision making in sports, all of which try to answer more general questions by means of sports data.publishedVersio

Action bias among elite soccer goalkeepers: The case of penalty kicks

In soccer penalty kicks, goalkeepers choose their action before they can clearly observe the kick direction. An analysis of 286 penalty kicks in top leagues and championships worldwide shows that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center. Goalkeepers, however, almost always jump right or left. We propose the following explanation for this behavior: because the norm is to jump, norm theory (Kahneman and Miller, 1986) implies that a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action. The omission bias, a bias in favor of inaction, is reversed here because the norm here is reversed - to act rather than to choose inaction. The claim that jumping is the norm is supported by a second study, a survey conducted with 32 top professional goalkeepers. The seemingly biased decision making is particularly striking since the goalkeepers have huge incentives to make correct decisions, and it is a decision they encounter frequently. Finally, we discuss several implications of the action/omission bias for economics and management.Decision Making; Uncertainty; Choice Behavior; Sport Psychology; Behavioral Economics; Action Bias; Omission Bias; Commission Bias; Action Effect; Inaction Effect; Actor Effect; Economic Psychology; Heuristics and Biases; Soccer; Goalkeepers; Penalty Kicks; Risk; Norms

Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not

Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not

Searching for Judgment Biases Among Elite Basketball Referees

An attacking basketball player initiating significant physical contact with a defender who has already established a legal and stationary position, should be called with an offensive foul. Offensive foul situations are particularly ambiguous and complex, making the referee’s task a difficult one. In such conditions of complexity and constraints of time, the referee is likely to be prone to systematic biases, as has been documented by previous research in other sport settings. We analyzed the referees’ decisions in 250 instances of collisions between an attacking player and a defender. In these collisions the defender fell, and potentially an offensive foul could be called. We found no evidence of favoritism granted to the home team, to star players, or to high-reputation teams, or of small players being tackled by significantly larger opponents. The findings suggest that these biases are not very robust, and are sensitive to the context, and that proper training of referees and enhanced awareness can help to alleviate referees’ biases

Action bias among elite soccer goalkeepers: The case of penalty kicks

In soccer penalty kicks, goalkeepers choose their action before they can clearly observe the kick direction. An analysis of 286 penalty kicks in top leagues and championships worldwide shows that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center. Goalkeepers, however, almost always jump right or left. We propose the following explanation for this behavior: because the norm is to jump, norm theory (Kahneman and Miller, 1986) implies that a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action. The omission bias, a bias in favor of inaction, is reversed here because the norm here is reversed - to act rather than to choose inaction. The claim that jumping is the norm is supported by a second study, a survey conducted with 32 top professional goalkeepers. The seemingly biased decision making is particularly striking since the goalkeepers have huge incentives to make correct decisions, and it is a decision they encounter frequently. Finally, we discuss several implications of the action/omission bias for economics and management

Visual Search Strategies of Soccer Players Executing a Power vs. Placement Penalty Kick

Introduction: When taking a soccer penalty kick, there are two distinct kicking techniques that can be adopted; a ‘power’ penalty or a ‘placement’ penalty. The current study investigated how the type of penalty kick being taken affected the kicker’s visual search strategy and where the ball hit the goal (end ball location). Method: Wearing a portable eye tracker, 12 university footballers executed 2 power and placement penalty kicks, indoors, both with and without the presence of a goalkeeper. Video cameras were used to determine initial ball velocity and end ball location. Results: When taking the power penalty, the football was kicked significantly harder and more centrally in the goal compared to the placement penalty. During the power penalty, players fixated on the football for longer and more often at the goalkeeper (and by implication the middle of the goal), whereas in the placement penalty, fixated longer at the goal, specifically the edges. Findings remained consistent irrespective of goalkeeper presence. Discussion/conclusion: Findings indicate differences in visual search strategy and end ball location as a function of type of penalty kick. When taking the placement penalty, players fixated and kicked the football to the edges of the goal in an attempt to direct the ball to an area that the goalkeeper would have difficulty reaching and saving. Fixating significantly longer on the football when taking the power compared to placement penalty indicates a greater importance of obtaining visual information from the football. This can be attributed to ensuring accurate foot-to-ball contact and subsequent generation of ball velocity. Aligning gaze and kicking the football centrally in the goal when executing the power compared to placement penalty may have been a strategy to reduce the risk of kicking wide of the goal altogether

Revisiting Egyptian Foreign Policy towards Israel under Mubarak: From Cold Peace to Strategic Peace

This article is the first academic study of Egyptian foreign policy towards Israel under Hosni Mubarak (1981–2011). It challenges a deeply entrenched conventional wisdom that Egypt pursued a cold-peace foreign policy towards Israel throughout this period. We demonstrate that Egyptian foreign policy towards Israel was dynamic – comprising cold peace (1981–91), a hybrid foreign policy of cold peace and strategic peace (1991–2003), and a pure strategic peace posture (2003–11). We also use the case of Egyptian foreign policy towards Israel as a heuristic to develop a conception of a new type of peace, strategic peace, as an intermediary analytical category between cold and stable peace

Macrophages Facilitate Resistance to Anti-VEGF Therapy by Altered VEGFR Expression

Abstract Purpose: VEGF-targeted therapies have modest efficacy in cancerpatients, butacquiredresistance iscommon. Themechanisms underlying such resistance are poorly understood. Experimental Design: To evaluate the potential role of immune cells in the development of resistance to VEGF blockade, we first established a preclinical model of adaptive resistance to anti-VEGF therapy. Additional in vitro and in vivo studies were carried out to characterize the role of macrophages in such resistance. Results: Using murine cancer models of adaptive resistance to anti-VEGF antibody (AVA), we found a previously unrecognized roleofmacrophagesinsuchresistance.Macrophageswereactively recruited to the tumor microenvironment and were responsible for the emergence of AVA resistance. Depletion of macrophages following emergence of resistance halted tumor growth and prolonged survival of tumor-bearing mice. In a macrophagedeficient mouse model, resistance to AVA failed to develop, but could be induced by injection of macrophages. Downregulation of macrophage VEGFR-1 and VEGFR-3 expression accompanied upregulation of alternative angiogenic pathways, facilitating escape from anti-VEGF therapy. Conclusions: These findings provide a new understanding of the mechanisms underlying the modest efficacy of current antiangiogenesis therapies and identify new opportunities for combinationapproachesforovarianandothercancers. ClinCancerRes; 23(22); 7034–46. �2017 AACR