*Remarks at **June 29 2006** at Festkolloquium dinner*

By Phelim Boyle

 

Thank you Hans for a wonderful and affectionate speech. You become wiser and wittier each year. Hans you are an extreme event. What is the probability of a someone, who is Swiss, who is not a random Swiss but a Swiss actuary being one of the funniest people I know. This is impossible you might think. Something more impossible would be for there

to exist another Swiss actuary called Hans who was equally funny.

 

I am reminded of my favourite part of one of my favourite books: The Lord of the Rings. You may recall Bilbo Baggins birthday speech. My dear Bagginses and Boffins, Tooks and Brandybucks, Grubbs, Chubbs, Hornblowers, Bolgers, Bracegirdles, and Proudfoots.. Today is my 65-th birthday. Alas 65 years is far too short a time to live among such

excellent and admirable hobbits.

 

Today is a very happy and unique occasion for me. I would like to thank all of you for coming. You have made it this evening and this conference very special. Many of you have come here from far beyond the boundaries of the Shire.

 

Let me start with a hypothetical problem. Suppose you want to plan your ideal conference. What would you do. You would pick the topics you were most interested in. Then you would select speakers that you admire and respect and who had inspired you. You would invite your colleagues, your coauthors and your students and former students to the event. However there are additional degrees of perfection that I for one could not have imagined until recently. What if a committee of your closest colleagues conceived the idea on their own and planned a conference in your honour. What if they made decisions better than the ones you could have made on your own. What if the conference was perfectly organized. This seems like a dream. But dreams can come true.

 

My heartfelt thanks to all who made this dream a reality. I thank the Scientific Committee: Peter Forsyth, Sheldon Lin, Harry Panjer, Ranjini Sivakumar, Ken Seng Tan, Ken Vetzal, Gord Willmot and Tony Wirjanto for the great job they have done. I thank Amy Aldous or the peerless job she did in organizing the conference and I thank Mary Flatt for all her help. I would like to thank my wife Mary. Mary makes me a better person. In addition she helps me decide what to wear and even more important

what not to wear.

 

In our research we are always using the work and ideas of other people. I owe a great debt to my coauthors and students from whom I have learned so much. I am very honoured that so many of them have come to this conference.

 

It is a real pleasure to welcome Eduardo Schwartz from UCLA to Waterloo. When Eduardo was a doctoral student at UBC I can still recall his infectious enthusiasm for research. I remember that Eduardo and Michael Brennan were so excited about their work that they would run along the corridors of the Henry Angus building carrying packages of codes of punched cards to run fortan programs. It was because of Eduardo I wrote a my paper on the Monte Carlo method to check the numbers he got from his PDE code. I enjoyed many discussions with Eduardo on his thesis and learned some useful tips from him. Eduardo once told me when gets a revise and resubmit from a journal he does revise and resubmit as soon possible.

 

I met many of my international colleagues at conferences and seminars in various exotic places like Louvain in Belgium, Maratea in Italy. Both Philippe Artzner and David Wilkie are survivors from Maratea. It is great to see them both here tonight. Philippe must know I cannot never write a joint paper with you since Artzner comes just too high in the alphabet. Philippe I done want to be down among the et al. David’s knowledge is so broad it is hard to believe he is an actuary. Still on an Italian theme it is really good to see Lorenzo Garlappi. I first met Lorenzo in that magical summer school in Perugia. I fondly recall the wonderful dinners we had and being thoroughly outclassed in our football games.

 

I spent a sabbatical at Heriot Watt University in Edinburgh in 1979. Herriot Watt is a powerhouse of actuarial science. I am delighted to welcome Howard Waters who has thankfully has not told us some of the bizarre stories about me playing football there. I welcome Dave Dickson a good Glasgow man who came all the way from Melbourne Australia. Welcome also to Enrique de Alba who was such a great host when I visited Mexico city. Enrique I just want to tell you I was cheering for Mexico when they played Argentina.

 

In between the late 80’s and the early 90’s I visited the University of Illinois at Champaign Urbana and had great fun working with Inmoo Lee and Ren Raw Chen among the cornfields of the Midwest. I was lucky to spend some time at Berkeley a place everyone is above average and no one is dull. Not surprisingly that was where I first met Eric Reiner. Eric^Òs first finance conference was here at Waterloo and it is a great pleasure to welcome you back again.

 

I am delighted to welcome Junichi Imai. When Junichi gives you numbers you can trust them to be correct. Junichi I am sorry that we do not have time to go and watch a baseball game. I would like to thank Sheldon for his fine portrayal of Hans Gerber this afternoon. I am very grateful to Hailiang Yang for coming here all the way from Hong Kong. Johnny Li who was student in HKU tells me HY is an excellent teacher in every studen’s eyes as well as a great researcher .

 

I would like to welcome Stan Pliska, Marcel Rindisbacher and Dietmar Liesen. I used to joke with Dietmar when he was visiting here that my dream job would be that of a German professor with all those assistants. I thank Dietmar arranged to stay here until the Germany Argentina game is over as his wife is Argentinian. Thanks to Mark Reesor, Weidong Tian and Don who are playing at home as it were.

 

Thanks to Tan Wang from UBC who is just a great colleague. I recall listening to myself in class once and realizing what I was saying was wrong. It had to do with pricing in incomplete markets. After class I rang Tan and after he thought about it a while we wrote a paper together on it. One of the many things I learned from Tan is the importance of writing a good introduction.

 

In the last part of my remarks I would like to talk about some recent research work by an economist at Brown University Dr Palacios-Huerta. The subject is very topical. It is about penalty kicks. The penalty kick was invented by an Irishman from County Armagh. I first learned about this research from an article by Tim Harford in Slate Magazine 3 days ago and I have used Tim’s article in preparing this summary.

 

In soccer or football as it is called penalty kicks pit the goalkeeper against a lone striker in a mentally demanding contest. Once the penalty-taker strikes the ball, it takes 0.3 seconds to hit the back of the net unless the goalkeeper can somehow get his body in the way. That is simply not enough time for the keeper to pick out the trajectory of the ball and intercept it. He must guess where the striker will shoot and move just as the ball is being struck. A keeper who does not guess correctly normally has no chance.

 

Both striker and keeper must make subtle decisions. Let’s say Hans Buhlmann is a right-footed striker and he always shoots to the right. I as the keeper will always anticipate the shot and Hans would be better off occasionally shooting to the left because even with a weaker shot it is best to shoot where the goalie isn’t even when I am the goalkeeper. In contrast, if Hans chooses a side by tossing a coin, I will always dive to the left: Since I can't guess where the ball will go, it is best to go where the shot will be weak if it does come. But then Hans should start favoring his stronger side again.

 

Game theory, applied to the problem of penalties, says that if the striker and the keeper are behaving optimally, neither will have a predictable strategy. The striker might favor his stronger side, of course, but that does not mean that there will be a pattern to the bias.

 

The penalty kick can be modeled as a beautiful application of a two person zero sum game. The game has a unique equilibrium and requires each player to use a mixed strategy. Prof Palacios -Huerta analyzed the behavior of professional soccer players. Their actual behavior was remarkably consistent with predictions of game theory. Their winning probabilities were statistically independent across strategies. The players choices were serially independent. His results provide strong support for von Neumann minimax theorem under very realistic conditions.

 

In a recent paper this year Prof Palacios -Huerta did a very clever extension of this idea. He constructed a laboratory game that is formally identical to a penalty kick. This was a two person zero sum game. Each player has two cards A and B. They each pick a card and place it face down. Then the experimenter says turn and they both show their

cards. Then a dice is tossed and the payoff depends on the cards selected and the number on the dice. The payoffs are calibrated to be similar to those in the penalty kick situation. It is a highly stylized setting. However nothing at all about football is mentioned in the instructions.

 

The experiment was conducted on two groups of subjects. The first group were professional players from the Spanish league 40 strikers and 40 goalkeepers and forty striker- keeper pairs were formed to play the game. The second group was a group of undergraduates from a university in Bilbao. The professional players even in this experimental and unfamiliar setting played the correct mixed strategies and their behaviour was entirely consistent with the equilibrium predictions. The college students did poorly from the perspective of game theory predictions. The players were much more strategic than the college students even though it was a pure laboratory experiment.

 

The author used a Latin title Experienta Docet . I think a snappier title might be David Beckham and Wayne Rooney are smarter than you think.

 

At the start I mentioned the idea of an ideal conference. There is one other desirable attribute of perfect conference. Lots of graduate students would attend and they would get inspired to work on new projects and meet some of the wise men and especially the wise women in their discipline. This dream can also come true.

 

Thank you all so much for coming.

 

*References *

 

For the papers on penalty kicks see Prof Palicios-Huerta’s website

 

http://www.econ.brown.edu/fac/ipalacios/

 

World Cup Game Theory*, *what economics tells us about penalty kicks,

Tim Harford Slate Magazine, Posted Saturday, June 24, 2006, at 8:17 AM ET