"Dominance, Sharing, and Assessment in an Iterated Hawk–Dove Game"

A new paper of mine — mercifully — came out in final form today after a nightmarish experience with the typesetting.

(I write this even though they pulled the trigger without showing us the final version — despite our explicit request — and a couple of minor glitches with the references reflect this. Following instructions was consistently very difficult for these typesetters.)

Anyway, I really like this paper, and I think there are some very cool avenues to pursue with it as a starting point. Our public code will hopefully help encourage such efforts. Here are some details.

Title: Dominance, Sharing, and Assessment in an Iterated Hawk–Dove Game

Authors: Cameron L. Hall, Mason A. Porter, and Marian S. Dawkins

Abstract: Animals use a wide variety of strategies to reduce or avoid aggression in conflicts over resources. These strategies range from sharing resources without outward signs of conflict to the development of dominance hierarchies, in which initial fighting is followed by the submission of subordinates. Although models have been developed to analyse specific strategies for resolving conflicts over resources, little work has focused on trying to understand why particular strategies are more likely to arise in certain situations. In this paper, we use a model based on an iterated Hawk–Dove game to analyse how resource holding potentials (RHPs) and other factors affect whether sharing, dominance relationships, or other behaviours are evolutionarily stable. We find through extensive numerical simulations that sharing is stable only when the cost of fighting is low and the animals in a contest have similar RHPs, whereas dominance relationships are stable in most other situations. We also explore what happens when animals are unable to assess each other’s RHPs without fighting, and we compare a range of strategies for contestants using simulations. We find (1) that the most successful strategies involve a limited period of assessment followed by a stable relationship in which fights are avoided and (2) that the duration of assessment depends both on the costliness of fighting and on the difference between the animals’ RHPs. Along with our direct work on modelling and simulations, we develop extensive software to facilitate further testing. It is available at https://bitbucket.org/CameronLHall/dominancesharingassessmentmatlab/.

Tales from the ArXiv: Modeling Stupid People

I am intrigued by this paper, which is called Cipolla’ s game: playing under the laws of human stupidity.

Here is a screenshot to whet your appetite.

RIP John Nash (1928–2015)

Mathematician John Nash and his wife were killed yesterday in a taxi accident.

Nash won the 1994 Nobel Memorial Prize in Economics for the work in his 27-page PhD thesis that invented the theory of non-cooperative games. Not bad. (As Joe Jewell pointed out, Nash's thesis also only has 2 references.)

Nash had recently accepted his Abel Prize (the mathematics equivalent of a Nobel Prize) for entirely different work.

Sylvia Nasar's 1994 article about John Nash, which is based on her book, is a fascinating read. Nasar's book formed the basis for the movie A Beautiful Mind.

Nash is also one of the people who invented the game Hex.

If you want to read more about Nash, go to FAQ maintained by Princeton University.

(Tip of the cap to numerous people, and thanks to Carlos Castillo Chávez for posting the article by Sylvia Nasar.)

Update (5/26/15): As I suspected, this was the final leg of their journey home after Nash was in Norway to receive his Abel Prize.

Update (5/29/15): Here is an article in the popular press about Nash's work on isometric embeddings.

Flipping the Test

A very cool test was given in a Behavioral Ecology class at UCLA. It sounds like it was a great learning experience for the students, and of course this story makes me think of a certain exam I once took in Philosophy of Probability. In both situations, the lessons from the course itself played center stage in the exam-taking strategy.

(Tip of the cap to Jasvir Grewal.)