LSE Department of Mathematics: CDAM: Computational, Discrete and Applicable Mathematics@LSE

On 11 August, the LSE hosted the Seventh International Workshop in Search Games and Rendezvous. Sponsored by the Operational Research Group and CDAM, the day saw the presentation of five lectures on various aspects of the field.

The morning session concentrated on ‘search’, as in ‘job-search’, in economics, where the problem faced by a player is when to stop the search and when to continue (in the hope of finding a better job). In game theoretic applications, there are two groups of players (say males and females), so in fact these are ‘mate selection’ games. David Ramsey (University of Limerick, Ireland) spoke on a model where individuals have two characteristics that affect their attractiveness to the opposite sex, namely ‘beauty and character’. Beauty is observable but character requires the cost of a ‘date’ to assess. He calculated the Nash Equilibria of these games.

A related talk was given by Ioanna Katrantzi (L.S.E.), who considered a model in which individuals have a single characteristic (integer), their age, which goes up by one each period until they are either mated or reach the maximum fertile age for their sex.

A final talk in this area was given by Shmuel Gal (Haifa, Israel), who considered a version of the well known ‘secretary problem’. In his version, two interviewers (with different selection priorities, such as one caring about IT skills and the other about typing) have to select a candidate from a string of applicants. They each are given an initial stock of ‘vetos’, which they may use to nix a candidate approved by the other. There are equilibria where they try to get the other interviewer to use up his vetos, and also equilbria where neither ever uses a veto.

The afternoon session began with a talk by Robbert Fokkink (Technical University of Delft, Netherlands) about accumulations games: A Hider has total wealth h which he disperses among n locations; the Searcher confiscates the material from r of these, and the Hider wins if what remains is enough to carry out some task (say enough nuts to survive the winter).

Then Jimmy Fan (Cambridge) spoke about solutions to some discrete symmetric rendezvous problems posed by Steve Alpern and John Howard. The classic problem is how two friends should go about meeting, when they have agreed to have lunch at the Mozart Café in Prague, but on arriving in the city find there are three such cafes. What is the minimum number of days, on average, that they will need to meet at the same one at the same time?

The workshop also hosted many useful informal discussions among the participants, after the talks and during the workshop lunch and dinner. This year, the Workshop was in honour of the retirements of two leaders in the field: Shmuel Gal and John Howard.

Steve Alpern, September 2008.