Following on from Geoff Riley’s blog post (see below) on the Tutor2u site here are the games that he was alluding to.
In this blog I am reprising an article produced by our good friend Mark Johnston from New Zealand in an early edition of the now discontinued Latte Magazine(2007). I am doing so because I know that many colleagues are interested in trying some experimental games with their students for example when teaching game theory, behavioural economics and the provision of public goods.
Click the link for the games in pdf format from the Latte Magazine
Here is another that I have used recently on Oligopolies.
With the disapointment of the 2008 Champions League Final behind them, Chelsea can finally claim to be the best team in Europe. As in 2008 it was decided by another penalty shoot but this time Chelsea were the victors. As always I am particularly interested in the peanlty shoot out and the strategies, if any, that are implemented by both the penalty taker and the goalkeeper.
The situation that kickers face in a penalty kick is a simultaneous-move game where they have three alternative strategies: shooting right, left, or centre. Similarly the goalkeeper also has three alternative strategies: dive to the right, dive to the left or remaining in the centre of the goal. In defining the sides of the goal researchers use the “natural side” of the kicker (which is the goalkeeper’s right, if the kicker is right-footed, and the goalkeeper’s left, if the kicker is left-footed) and the “opposite side”. Labeled like that, the strategies of both kicker and goalkeeper will be to choose the natural side of the kicker (NS), the centre (C) or the opposite side (OS).
From data compiled by Spanish economist Ignacio Palacios-Huerta he calculated the proportion of successful penalty kicks. Below is a table that shows the success rate of penalty takers when they went to their natural side and opposite side when the goalkeeper went his natural side and opposite side. Notice that when the kicker went NS and goalkeeper OS the success rates was 95% – the remaining 5% missed the target. Similarly when the kicker went OS and goalkeeper went NS – 8% missed the target.
Here is data on the peanlty kicks from last Sunday’s Champions League final
Notice that Chelsea keeper Petr Cech went the correct way for all penalties (including the one taken during normal time) – seemingly on the plane over he studied all Bayern penalties since 2007. He said it took nearly 2 hours – did he have a strategy?
Also Chelsea penalty takers favoured the natural side whilst Bayern the opposite side. Below is the shoot out once again.
I got this clip from a tweet by Mo Tanweer of Oundle School in the UK. For those studying market structures it is a mistake to believe that ALL oligopolists face a KINKED DEMAND CURVE. Oligopolists may either:
a) COMPETE VIGOROUSLY or
b) COLLUDE (e.g. in cartels) or
c) PLAY SAFE (as in Kinked Demand Curve Theory)
In recent years game theory has become a popular way of examining the strategies that oligopolists may adopt in a market. Game theory involves studying the alternative strategies oligopolists may choose to adopt depending on their assumptions about their rivals’ behaviour. This clip is game theory in its rawest form. Very entertaining and a worth a look.
Just covering market structures at present with my A2 class and came across this video clip on the Business Insider website.
Bruce Bueno de Mesquita, a political scientist and professor at NYU, who explains how to purchase a car using game theory.
He says that you should first establish a radius for however far you are willing to go to purchase the car. You then call a car dealer and make this statement. “My name is (your name here), I plan to buy (whatever car it is) at 5:00pm. I am going to buy it from the dealer who gives me the best price. What is your best price.”
The dealer will commonly respond with “You can’t buy a car on the telephone.”
Bruce then elaborates that the response to this is “I know I can buy a car this way, because I know that many cars have been purchased this way. If you do not quote a price for me, I understand that you are telling me that you know you don’t have the best price, I appreciate you saving my time.”
Bruce then says that the dealer will worry that you are just going to take his price and use it in negotiations with another dealer, essentially using him to lower your price.
You then explain that you will buy from whoever gives you the lowest price. You will not discuss the price when you get there and you will show up to the dealership with the check in your hand. If the dealer reneges, you will move on to the second best price as you have that check in your pocket as well. You then end by asking for the dealer’s best price.
It may sound silly, but apparently it actually works.
Last week saw Chinese officials indicating that Chinese airlines will not buy European airplanes as long as the EU insists on including foreign airlines in its emission trading system. Orders of 35 Airbus A330 planes have been cancelled and another 10 A380’s were in danger of being cancelled because of the ETS. The Chinese argument is that it is not reasonable to charge Chinese airlines taxes at the same time that the plane is made in Europe. China currently buys more than 1 in 5 Airbus planes being produced and the total of Chinese orders amounts to US$9bn. Therefore one could say that the future of Airbus hinges on the ETS. This raises the question of climate change and what are the options that countries face.
Climate Change as Prisoner’s Dilemma
The initial impression from the discussions over climate change is that of a typical Prisoner’s Dilemma and some of the data provided in the Stern Review (2006) can be used to populate the payoff table.
–The cost of tackling climate change is approximately 1% of annual per capita GDP. However, if nothing is done about the issue the cost is estimated to be between 5% to 20% of GDP. So that defines what happens at the extreme of cooperative or non-cooperative behaviour. From the table above, a country that refuses to act, whilst the other cooperates, will experience a free-rider benefit – enjoying the advantage of limited climate change without the cost. On the flip side, any country that imposes limits, when its competitors do not, incurs not just the cost of limiting its own emissions, but also a further cost in terms of reduced competitiveness – estimated here at an additional 3.0%. From the table it seems predictable that countries should prefer to be self-interested: the best national policy, if others reduce emissions, is to defect; likewise, if other countries are not taking action, then it is pointless to be the only sucker to take action, and one should again defect.
Repeated Prisoner’s Dilemma and Cooperation
The dynamics of the prisoner’s dilemma do change if participants know that they will be playing the game more than once. In 1984 an American political scientist at the University of Michigan, Robert Axelrod, argued that if you play the game repeatedly you are likely to see emerging is cooperative rather than defective actions. He identified four elements to a successful strategy which is this case can be applied to climate negotiations:
1. Be Nice – sign up to unilateral cuts in emissions, as deep as your economy and financing capacity allows.
2. Be Retaliatory – single out countries that have not commenced action and, in collaboration, find ways of pressurising them until they do so.
3. Be Forgiving- when non-compliant countries come onboard give them generous applause; signal that good behaviour will be rewarded with even deeper cuts in your own emissions.
4. Be Clear – let everyone know in advance exactly how you are going to behave – that you will work with them if they take action on emissions, and that you will retaliate if they do not.
It is the belief of Michael Liebreich that this research by Axelrod should be put into practice by the world’s climate negotiators. As treaties on climate change are on-going and therefore become part of the game.
Having gone through the penalty shootout at 2008 UEFA Champions League Final I was informed by students that the AC Milan vs Liverpool final in 2005 was another penalty shootout worth looking at. As well as being a tremendous comeback by Liverpool it was interesting to observe how the penalty shootout progressed.
I proceeded to go through each penalty for AC Milan and Liverpool and write on the board the following:
*Kicker – shot NS C OS
*GK – dived NS OS
Like the Man Utd v Chelsea game there were some similarities regarding strategy. Worth a look.
In the recent edition of econoMAX (online magazine of Tutor2u) I wrote a piece on the game theory of penalty kicks in soccer. Below is an extract from it and an example of game theory in action from the 2008 UEFA Champions League Final between Manchester Utd and Chelsea.
As we approach the business end of the football season in Europe and with the potential impact of penalty kicks deciding matches, it might be appropriate to consider the relevance of game theory – economists hold in high regard the penalty kick as a real-life example of game theory. Technically the kicker and the goalkeeper play a zero-sum game – any gain for one player is exactly offset by the loss to the other side – plus one goal for me is minus one goal for you. The situation that kickers face in a penalty kick is a simultaneous-move game where they have three alternative strategies: shooting right, left, or centre. Similarly the goalkeeper also has three alternative strategies: dive to the right, dive to the left or remaining in the centre of the goal. In defining the sides of the goal researchers use the “natural side” of the kicker (which is the goalkeeper’s right, if the kicker is right-footed, and the goalkeeper’s left, if the kicker is left-footed) and the “opposite side”. Labeled like that, the strategies of both kicker and goalkeeper will be to choose the natural side of the kicker (NS), the centre (C) or the opposite side (OS).
From the data collected by Basque economist Ignacio Palacios-Huerta he calculated the proportion of successful penalty kicks. It shows the success rate of penalty takers when they went to their natural side and opposite side when the goalkeeper went his natural side and opposite side (see right). Notice that when the kicker went NS and goalkeeper OS the success rates was 95% – the remaining 5% missed the target. Similarly when the kicker went OS and goalkeeper went NS – 8% missed the target.
2008 UEFA Champions League final – Chelsea v Manchester Utd.
If you have read Soccernomics you will be well aware of the events that unfolded in this game. Ignacio had been recording how penalties were being taken and wrote an academic paper on strategies that players and goalkeepers employed. A mutal friend of Ignacio and Chelsea manager, Avram Grant, brought the two men together and subsequently Ignacio sent Grant some facts regarding Man Utd in particular about their goalkeeper Van der Sar. There were 4 main points:
1. Man Utd goalkeeper (Van der Sar) tended to dive to the kicker’s natural side (ie GK’s right for a right footed kicker)
2. Van der Sar tends to save penalties that are hit at mid-height
3. Man Utd midfielder Cristiano Ronaldo often stops in his run-up and if he does the ball is kicked towards the right hand side of the keeper. It was important that the Chelsea goalkeeper, Petr Cech, does not move early. When goalkeepers moved early Ronaldo always scored.
4. If you win the toss you take the first penalty. 60% of teams going first win the game.
Man Utd’s Rio Ferdinand won the toss and went first – not a good omen for Chelsea. Looking at the penalties and relating it to Ignacio’s research we see the following:
1. Ballack – OS – left. Van der Sar dives left – GOAL
2. Belletti – OS – left. Van der Sar dives right – GOAL
3. Lampard – OS – left. Van der Sar dives right – GOAL
4. Cole – NS – left. Van der Sar dives left (as advised by Ignacio ball hit hard and low) – GOAL
5. Terry – OS – left. Van der Sar dives right – NO GOAL – hit the post
6. Kalou – OS – left. Van der Sar dives right – GOAL
Up to this point all Chelsea right footed players had taken on the advice of Ignacio and hit to their opposite side – Van der Sar’s left.
3. Ronaldo – paused in his run-up. Petr Cech stayed upright for as long as possible and dives right – NO GOAL – saved.
It seemed that Chelsea’s strategy of going to Van der Sar’s left had been hatched by someone on the Utd bench. As Anelka prepared to take Chelsea’s 7th penalty Van der Sar pointed to the left corner. Now Anelka had a terrible dilemma. This was game theory in its rawest form. So Anelka knew that Van der Sar knew that Anelka knew that Van der Sar tended to dive right against right footers. Instead Anelka kicked right but it was at mid-height which Ignacio warned against. – Soccernomics Page 127
7. Anelka – NS – right. Van der Sar dives right – NO GOAL – saved
If Anelka had taken Ignacio’s advice would Chelsea have won? Below you can see the drama unfold on YouTube.