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Event Type
Research Presentation
Academic Department
Mathematics and Statistics
Location
Dana Science Building, 2nd floor
Start Date
14-4-2023 1:30 PM
End Date
14-4-2023 3:00 PM
Description
Under the direction of Dr. Molly Lynch
This study focuses on the concepts of mixed strategies in game theory within the football game setting using penalty kicks as the focal point. A penalty kick involves one kicker and one goalkeeper. The kicker must choose which direction (right, left, center) to shoot in order to score a goal, and the goalkeeper must choose which direction to dive (right, left, center) in order to catch the ball. Each makes a choice simultaneously without being aware of the other's decision. Thus, there is a unique mixed-strategy equilibrium with a well-defined strategy system. A goal is scored by the kicker or not (zero-sum structure1) because the goalkeeper makes a save or the kicker shoots high or wide. Given the availability of historical data, both the kickers and goalkeepers know about the past behaviors or preferred feet of their opponents, respectively. A number of studies have assessed the empirical validity of Nash equilibrium2 for the two-person zero-sum game in both experimental and natural settings. This project re-examines one model developed by Chiappori, Levitt, and Groseclose in 2002 which specified a general game in which each player can choose one out of three possible strategies (right, left, center), and then evaluates their proposed assumptions via the payoff matrix (scoring probabilities) using data from recent penalty shootouts in the World Cup games of 2014, 2018, and 2022. We gathered the data by collecting information from live commentators on players' strategies and outcomes. With this data, we tested a new model which specifies a general game in which each player can choose one out of two possible strategies (upper or lower) and then evaluated our proposed assumptions using the payoff matrix. We found that scoring is more likely when kickers successfully place the ball in the upper corner of the net, a tactic that is also known as the "Olympic goal"3. Our data also supports both the assumptions made by Chiappori, Levitt, and Groseclose 2002 and our new model. We conclude that the empirical results of our model could better inform kickers to be more effective especially in the World Cup, the most popular football competition in the world, where the pressure is insurmountable.
Game Theory in FIFA World Cup 2014-2022
Dana Science Building, 2nd floor
Under the direction of Dr. Molly Lynch
This study focuses on the concepts of mixed strategies in game theory within the football game setting using penalty kicks as the focal point. A penalty kick involves one kicker and one goalkeeper. The kicker must choose which direction (right, left, center) to shoot in order to score a goal, and the goalkeeper must choose which direction to dive (right, left, center) in order to catch the ball. Each makes a choice simultaneously without being aware of the other's decision. Thus, there is a unique mixed-strategy equilibrium with a well-defined strategy system. A goal is scored by the kicker or not (zero-sum structure1) because the goalkeeper makes a save or the kicker shoots high or wide. Given the availability of historical data, both the kickers and goalkeepers know about the past behaviors or preferred feet of their opponents, respectively. A number of studies have assessed the empirical validity of Nash equilibrium2 for the two-person zero-sum game in both experimental and natural settings. This project re-examines one model developed by Chiappori, Levitt, and Groseclose in 2002 which specified a general game in which each player can choose one out of three possible strategies (right, left, center), and then evaluates their proposed assumptions via the payoff matrix (scoring probabilities) using data from recent penalty shootouts in the World Cup games of 2014, 2018, and 2022. We gathered the data by collecting information from live commentators on players' strategies and outcomes. With this data, we tested a new model which specifies a general game in which each player can choose one out of two possible strategies (upper or lower) and then evaluated our proposed assumptions using the payoff matrix. We found that scoring is more likely when kickers successfully place the ball in the upper corner of the net, a tactic that is also known as the "Olympic goal"3. Our data also supports both the assumptions made by Chiappori, Levitt, and Groseclose 2002 and our new model. We conclude that the empirical results of our model could better inform kickers to be more effective especially in the World Cup, the most popular football competition in the world, where the pressure is insurmountable.