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

Synchronization in large populations of limit cycle oscillators with long-range interactions

We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range reflecting the non extensive behavior of the system, but an adequate scaling removes the dependency and collapses the long-range synchronization curves with the one resulting from a system with uniform coupling. Two descriptions are considered, the Kuramoto or phase description model and a Cell Dynamical System model for phases and amplitudes. Oscillator death is observed in the second approach.Comment: 9 pages, 4 figures, presented at LAWNP 2001, to appear in Physica D Needs package elsar

The referee's challenge: a threshold process model for decision making in sport games

Judgment and decision making in sporting officials is a challenging task that involves the use of context. Although process models of decision making describe decision contexts, none of the existing models explains when sports officials use rule-driven decision making, or game management. The basic idea of our work is that referees use a subjective threshold to apply game management, which may explain this decision behavior. We propose a new dynamic threshold model that is based on concepts derived from Decision Field Theory (Busemeyer & Townsend, 1993). The model includes two thresholds of game management (high/low) and two contact situations (foul/no foul) as approaching one of these thresholds. Using the example of soccer refereeing, we argue that if the game hits a subjective threshold of aggressive play, then the referee shifts from applying the rules to managing the game. This new approach changes the scientific discussion from one focused on what referees should decide in one situation or the other, to a dynamic model that explains the basic psychological mechanism underlying the referee’s change in behavior during the game, both at the intra-individual as well as inter-individual leve

The past, present and future of research on judgment and decision making in sport

Objectives: The study of judgment and decision-making in sports is at least as old as the anniversary of FEPSAC we celebrate with this special issue. It seems therefore appropriate to look into the past, present and future of this topic. Design: For the past, a focus of the review is relating the European perspective of the co-authors into a larger frame of areas in judgment and decision making within the last 50 years and beyond. Method/Results/Conclusions: For the present, scientific current developments will be structured as judgments from the most influential perspectives such as the economical, social cognition, ecological dynamics or cognitive approaches illustrating some milestones in research on judgment and decision-making in sports of today. For the future, potentials of the field will be structured based on theory, methodology and practical applications showcasing challenges for the next decades of research ahead of us

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

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

A Large Copper Artefacts Assemblage of Fazael, Jordan Valley: New Evidence of Late Chalcolithic Copper Metallurgy in the Southern Levant

Late Chalcolithic metallurgy developed in the southern Levant simultaneously with other crafts and new social institutions, reflecting advances in social organization, cults and technology. Until recently, copper items were mostly found in the Negev and Judean Desert, while other areas, specifically the Jordan Valley, were considered poor, with limited copper finds. Recent excavations at Late Chalcolithic Fazael in the Jordan Valley yielded dozens of copper items that allow for the first time a comprehensive study of copper items from this area. The assemblage is one of the largest of any site in the Late Chalcolithic period and includes most of the known components of the Late Chalcolithic copper industry. The current paper presents the new metallurgical discoveries from the Fazael Basin and discusses their significance to our understanding of the Late Chalcolithic copper industry.Pozno halkolitska metalurgija se je razvila v južni Levanti sočasno z drugimi obrtmi in novimi družbenimi inštitucijami, kar odraža napredek v družbeni organizaciji, kultu in tehnologiji. Do nedavnega so bakrene predmete večinoma našli v Negevski in Judejski puščavi, medtem ko so druga območja, med njimi zlasti dolina reke Jordan, veljala za prostor z omejenimi najdbami iz bakra. Nedavno so izkopavanja na pozno halkolitskem najdišču Fazael v dolini reke Jordan prinesla na desetine bakrenih predmetov, ki nam prvič omogočajo celovito študijo bakrenih izdelkov s tega območja. Ta zbir je eden največjih iz kateregakoli najdišča iz časa poznega halkolitika in vključuje večino znanih sestavnih delov industrije bakra iz tega obdobja. V članku predstavljamo nove izsledke o metalurgiji bakra iz bazena Fazael in razpravljamo o pomenu teh najdb pri razumevanju te industrije v poznem halkolitiku

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