Three players A, B, C play the following game. First, A picks a real number between 0 and 1 (both inclusive), then B picks a number in the same range (different from A’s choice) and finally C picks a number, also in the same range, (different from the two chosen numbers). We then pick a number in the range uniformly randomly. Whoever’s number is closest to this random number wins the game. Assume that A, B and C all play optimally and their sole goal is to maximise their chances of winning. Also assume that if one of them has several optimal choices, then that player will randomly pick one of the optimal choices.
a. If A chooses 0, then what is the best choice for B?
b. What is the best choice for A?
c. Can you write a program to figure out the best choice for the first player when the game is played among four players?
Did you like this puzzle? Are you looking for bigger challenges? Do you want to use your analytical skills to solve real world problems and see the results right away? Do you enjoy writing computer programs? Then the Quantitative Researcher position might be a great opportunity for you!
As a Quantitative Researcher you will work in a team with Traders and Researchers, right on the trading floor. You will spend your first weeks at Optiver in a structured training program to learn about options, market making and delta 1. You will then immediately start your first project, with the support of a Senior Researcher. We expect you to be versatile, flexible and very creative to think of new innovative solutions. In return we give you the freedom to pursue your ideas and implement them right into our production systems. Within a few months, you will play a key role in developing automated analysis programs and trading algorithms.
Alongside this you will get great secondary benefits such as 25 paid vacation days, fully paid first-class commuting expenses, training opportunities, discounts on health insurance, breakfast and lunch facilities, sports and leisure activities, Friday afternoon drinks and even weekly in-house chair massages. Being highly international, we are accustomed to guiding expats through their relocation, offering competitive relocation packages and providing visa sponsorship where necessary.
Are you interested in starting your career on one of the most dynamic and exciting trading floors in Europe?
Apply directly via our website for the position of Quantitative Researcher. Please provide us with a CV, a solution to part (a) of the puzzle highlighting in bold your final answer in seconds and a letter of motivation in English. Solving part b and c of the puzzle is optional. Applications without an answer to the puzzle and a letter of motivation will not be reviewed. If you have any questions feel free to contact the recruitment team on email@example.com or on +31 (0)20 708 70 00.