By David Butler
Game theory is a mathematical tool that allows social scientists think about strategic interactions. The benefits are that it provides a mathematical device that is designed for the social sciences and brings a formal dimension to studying choice that can strip away sometimes trivial details. At its core are arguable assumptions relating to an individual’s accurate beliefs, preference consistency and skill levels (which are mostly deemed to be comparable). With these assumptions social scientists have a general framework that holds the potential to integrate the behavioural sciences.
Since its emergence, decline and resurgence in economics game theory has provided a framework to cross the micro-macro dichotomy, offering a broad method to study how self-interested individuals, firms and governments behave strategically. It’s most famous game, the prisoner’s dilemma, has been applied to everything from international trade and taxation policy to croaking frogs, elk’s antler size and to the costs and benefits of females wearing high heels! At the heart of this symmetric game remains a simple logic; what’s good for the individual and what’s good for the group is often at odds. One has to ask, what choice should I make given that somebody else also has to make a choice – a mutual dependency exists.
Game theorists often use instances from sport to provide examples of such abstract logic that in a large part is not intended to reproduce how people actually make decisions but rather to reproduce what the end results of a person that uses cold logic would reach. Sport provides perfect examples as parties with different interests meet in relatively controlled environments where specific rules exist. The most famous being a penalty kick or a tennis rally (often thought of as mixed strategy games). All the components of games exist in the settings mentioned; strategic interdependence, objective pay-off functions, strategic sets and a defined set of players.
Game theory is a mathematical tool that allows social scientists think about strategic interactions. The benefits are that it provides a mathematical device that is designed for the social sciences and brings a formal dimension to studying choice that can strip away sometimes trivial details. At its core are arguable assumptions relating to an individual’s accurate beliefs, preference consistency and skill levels (which are mostly deemed to be comparable). With these assumptions social scientists have a general framework that holds the potential to integrate the behavioural sciences.
Since its emergence, decline and resurgence in economics game theory has provided a framework to cross the micro-macro dichotomy, offering a broad method to study how self-interested individuals, firms and governments behave strategically. It’s most famous game, the prisoner’s dilemma, has been applied to everything from international trade and taxation policy to croaking frogs, elk’s antler size and to the costs and benefits of females wearing high heels! At the heart of this symmetric game remains a simple logic; what’s good for the individual and what’s good for the group is often at odds. One has to ask, what choice should I make given that somebody else also has to make a choice – a mutual dependency exists.
Game theorists often use instances from sport to provide examples of such abstract logic that in a large part is not intended to reproduce how people actually make decisions but rather to reproduce what the end results of a person that uses cold logic would reach. Sport provides perfect examples as parties with different interests meet in relatively controlled environments where specific rules exist. The most famous being a penalty kick or a tennis rally (often thought of as mixed strategy games). All the components of games exist in the settings mentioned; strategic interdependence, objective pay-off functions, strategic sets and a defined set of players.
One wouldn’t usually associate George Hook with game theory but his words on RTE last weekend during the Six-Nations final round of games was another brilliant example of how game theory can be applied to sport. While I didn’t hear all of Hook’s argument his sentiment was clear; having different kick-off times for the England-Italy and Ireland-France ties altered the incentive structure and strategic choices of both teams.
In the language of the game theorist the players moves were not synchronised. England moved first by playing earlier in the day and then the Irish team could respond based on the outcome of the English tie. If Hook was questioning the fairness of last weekend’s rugby, I think he was definitely right. Ireland had the benefit of knowing exactly what they had to achieve to win the six nations when their tie in France began.
One of the most celebrated examples of an interaction like this is discussed in chapter twelve of Richard Dawkins the selfish gene where using Robert Axelrod’s classic book the evolution of cooperation Dawkins outlines how sports which are characteristically zero-sum games (where we have a winner and a loser) can become non-zero sum games when time is involved.
On the 18th of May 1977 in the English first division this strange instance of sport becoming a non-zero sum game occurred. Coventry City were taking on Bristol City and both teams were fighting against relegation. The bottom of the table is below. One team from three had to go down, Tottenham and Stoke were already relegated. Sunderland who were playing their last game at Everton would stay up on goal difference even if they lost providing there was a loser in the Coventry Bristol tie. As expected Coventry and Bristol played ferociously as their status in the division was at stake. Coventry went two up thanks to two Tommy Hutchinson goals but Bristol remarkably pulled it back to 2-2 with a Gary Rowell equaliser. Both teams pushed for the win.
The rub was however that due to the immense crowds that arrived at Highfield Road that day (reportedly 36,903) the Coventry and Bristol match kicked off fifteen minutes late and apparently the Coventry manager had the full time 'Everton 2-0 Sunderland’ result flashed up on the electronic scoreboard in the dying minutes of the tie. Both teams could now be safe if the score could be kept at 2-2. The game became farcical as the side in possession did not attempt to score, the players decided to consciously cooperate rather than to complete. Highlights from the match can be seen here.
The power of this instance and several others afterwards is why George Hook is right to suggest that timing is very important, not only to maintain fairness but also to keep things as competitive as possible. Alas, the T.V companies may think otherwise.
In the language of the game theorist the players moves were not synchronised. England moved first by playing earlier in the day and then the Irish team could respond based on the outcome of the English tie. If Hook was questioning the fairness of last weekend’s rugby, I think he was definitely right. Ireland had the benefit of knowing exactly what they had to achieve to win the six nations when their tie in France began.
One of the most celebrated examples of an interaction like this is discussed in chapter twelve of Richard Dawkins the selfish gene where using Robert Axelrod’s classic book the evolution of cooperation Dawkins outlines how sports which are characteristically zero-sum games (where we have a winner and a loser) can become non-zero sum games when time is involved.
On the 18th of May 1977 in the English first division this strange instance of sport becoming a non-zero sum game occurred. Coventry City were taking on Bristol City and both teams were fighting against relegation. The bottom of the table is below. One team from three had to go down, Tottenham and Stoke were already relegated. Sunderland who were playing their last game at Everton would stay up on goal difference even if they lost providing there was a loser in the Coventry Bristol tie. As expected Coventry and Bristol played ferociously as their status in the division was at stake. Coventry went two up thanks to two Tommy Hutchinson goals but Bristol remarkably pulled it back to 2-2 with a Gary Rowell equaliser. Both teams pushed for the win.
The rub was however that due to the immense crowds that arrived at Highfield Road that day (reportedly 36,903) the Coventry and Bristol match kicked off fifteen minutes late and apparently the Coventry manager had the full time 'Everton 2-0 Sunderland’ result flashed up on the electronic scoreboard in the dying minutes of the tie. Both teams could now be safe if the score could be kept at 2-2. The game became farcical as the side in possession did not attempt to score, the players decided to consciously cooperate rather than to complete. Highlights from the match can be seen here.
The power of this instance and several others afterwards is why George Hook is right to suggest that timing is very important, not only to maintain fairness but also to keep things as competitive as possible. Alas, the T.V companies may think otherwise.
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