The dating game theory

Fun research from Peter Sozou and Robert Seymour at UCL on the economics of dating. From the press release:

Reporting in the journal Proceedings of the Royal Society of London B they analysed the function of a courtship gift and what the characteristics of a ‘good’ gift are.
They show that gifts can act as a signal of a man’s intention. Offering an expensive gift may signal a long-term commitment but the man must be wary of being exploited by a gold-digger who intends to dump him once she gets the gift.
By modelling courtship as a sequential game, they show that an extravagant gift, which is costly to the man but worthless to the woman, may solve the problem.
A costly gift signals the man has long-term intentions but by being worthless to the woman, gold-diggers are deterred.[...]
The researchers constructed two versions of the game with different biological assumptions based on whether the male is involved with parental care.
Attractiveness is relevant to human courtship (model 1). Male condition and female receptiveness are the deciding factors in non-parental care species (model 2). In both cases these were represented as binary variables.
Factors in the game such as whether the male and female found each other attractive were given a probability and the possible outcomes of the interaction, either positive or negative for each player, were given scores to represent the consequences of their decisions.[...]
They considered the ‘fitness’ consequences based on a single courtship encounter involving a male and female. Despite the different biological assumptions, the two models had the same underlying mathematical structure, with both yielding equilibrium solutions in which males predominantly offer costly but worthless gifts as a prelude to mating.

Ref:
Journal: Proceedings of the Royal Society of London B
Date 27/07/05
Title: ‘Costly but worthless gifts facilitate courtship’
Authors: Peter Sozou, Robert Seymour
UCL’s Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, Gower Street, London, WC1E 6BT

Mind the gap

The UK government this week officially launched its Enterprise Capital Funds, the latest in a string of initiatives intended to promote venture capital investment at the levels that commercial VCs disdain - the oft-discussed 'equity gap'. This one offers up to £2million equity finance, with government match funding for commercial VCs and business angel networks.

Inevitably, this will nibble at other established schemes, such as the Regional Venture Capital Funds launched with much fanfare three years ago. I've been speaking to the managers of various RVCFs recently for an upcoming feature in 'Corporate Financier', and the feeling so far is that the government would be better relaxing the limits on existing funds rather than launching new schemes. The RVCFs are limited to investing £250,000 in a round, which really doesn't go that far. And in that range, they're competing with business angel syndicates as well as other DTI projects like the Early Growth Funds. There's also questions about how the demands of the government investor for more deals can be balanced with the demands of its private sector partners for a half-decent return and a relatively secure risk profile. Meanwhile, as the commercial boys look for ever-larger deals on the basis that it's no more work to do a big deal as a little one, that equity gap keeps growing.

For more on government-backed VC, see this feature from 2003.

The nuts game

An oldie but a goodie, mentioned by its creator, Julian Edney, in the latest PAE newsletter. It's a simple economic game, illustrating the exploitation of scarce resources:

"A small number of subjects (three or more) sit around a shallow, nonbreakable, open bowl which initially contains 10 hardware hexagonal nuts. An experimenter sits with the group and introduces the exercise as one where the player's goal is to get as many of the nuts as possible. Players can take nuts from the bowl at any time and in any quantities after the start of the trial. The experimenter also explains that the number of nuts remaining in the bowl after each 10-second interval is automatically doubled from an outside source (operated by the experimenter, who manually replenishes the nuts from a separate container next to him). This replenishment cycle continues until either an arbitrary time limit is reached or the bowl is emptied by the players. The experimenter can also set a ceiling to the number of nuts in the bowl throughout the trial (10 is convenient). Subjects can be asked not to communicate.
"To maximize their individual 'harvests' of nuts, one would expect that each subject would restrain himself to taking one or two nuts out of the bowl each 10-second period: this allows the replenishment cycles to continue for some time (a typical game runs 2 minutes) and each subject eventually would end up with a sizeable score. In pilot work I have found that approximately 65% of groups never in practice reach the first replenishment stage because they exhaust the pool by taking all the nuts out in the first few moments of the game."

More here, including some working solutions arising from discussion between the players:

"So far, results have suggested two main types of solution: (a) those involving numbers (such as the group which decides systematically to take only 'one' or 'two' nuts per person per 10-second interval; this type of solution is quite effective in preserving the pool) and (b) nonnumerical solutions. An interesting illustration of the latter was a group which decided deliberately to use a rather complicated system of harvesting. Each player had to hook each nut out of the bowl with a pencil, place it on his nose, walk over to a nearby chalkboard, and deposit the nut in the tray before returning for another nut. Harvesting was thus slowed down enough to prevent pool depletion, increasing individual scores, and incidentally making the game more entertaining to players. The evolution of both kinds of solutions can be regarded as analogs to community-generated laws and practices for direct and indirect governance and management of resources in real-world situations."