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If you want to be incrementally better: Be competitive. If you want to be exponentially better: Be cooperative“. ~ Anonymous

Two hunters decide to spent their week-end together. But soon, a dilemma emerges between them. They could choose for hunting a deer stag together or either -individually- hunt a rabbit on their own. Chasing a deer, as we know, is something quite demanding, requiring absolute cooperation between them. In fact, both friends need to be focused for a long time and in position, while not being distracted and tempted by some arbitrary passing rabbits. On the other hand, stag hunt is increasingly more beneficiary for both, but that benefice comes with a cost: it requires a high level of trust between them. Somehow at some point, each hunter concerns that his partner may diverts while facing a tempting jumping rabbit, thus jeopardizing the possibility of hunting together the biggest prey.

The original story comes from Jean Jacques Rousseau, French philosopher (above). While, the dilemma is known in game theory has the “Stag Hunt Game” (Stag = adult deer). The dilemma could then take different quantifiable variations, assuming different values for R (Reward for cooperation), T (Temptation to defect), S (Sucker’s payoff) and P (Punishment for defection). However, in order to be at the right strategic Stag Hunt Game scenario we should assume R>T>P>S. A possible pay-off table matrix taking in account two choices C or D (C = Cooperation; D = Defection), would be:

Choice — C ——- D ——
C (R=3, R=3) (S=0, T=2)
D (T=2, S=0) (P=1, P=1)

Depending on how fitness is calculated, stag hunt games could also be part of a real Prisoner’s dilemma, or even Ultimatum games. As clear from above, highest pay-off comes from when both hunters decide to cooperate (CC). Over this case (first column – first row), both receive a reward of 3 points, that is, they both really focused on hunting a big deer while forgetting everything else, namely rabbits. However – and here is where exactly the dilemma appears -, both CC or DD are Nash equilibrium! That is, at this strategic landscape point no player has anything to gain by changing only his own strategy unilaterally. The dilemma appears recurrently in biology, animal-animal interaction, human behaviour, social cooperation, over Co-Evolution, in society in general, and so on. Philosopher David Hume provided also a series of examples that are stag hunts, from two individuals who must row a boat together up to two neighbours who wish to drain a meadow. Other stories exist with very interesting variations and outcomes. Who does not knows them?!

The day before last school classes, two kids decided to do something “cool”, while conjuring on appearing before their friends on the last school day period, both with mad and strange haircuts. Although, despite their team purpose, a long, anguish and stressful night full of indecisiveness followed for both of them…

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Video – Awesome choice by Tim Burton. It fits him like a glove. Here is the official Tim Burton’s Alice in Wonderland teaser trailer (just uploaded yesterday). Alice in Wonderland is directed by visionary director Tim Burton, of everything from Pee-Wee’s Big Adventure to Beetlejuice to Batman to Edward Scissor hands to Mars Attacks to Sleepy Hollow to Charlie and the Chocolate Factory to Sweeney Todd most recently. This is based on Lewis Carroll’s beloved series of books that were first published in 1865. Disney is bringing Tim Burton’s Alice in Wonderland to both digital 3D and 2D theaters everywhere on March 5th, 2010 early next year (more). Finally, just one personal thought. Soon, Tim Burton’s will stand for cinema, as what Jules Verne represented in literature.

In 1973, under several ongoing works on Co-Evolution and Evolutionary theory, L. van Alen proposed a new hypothesis: the Red Queen effect [1]. According to him, several different species will migth propably undergo and submit themselves to a continuous re-adapation [2,3], being it genetic or synaptic, only to end themselves at the point they started. A kind of arms races between species [4], potentially leading to specialization, as well as evolutionary Punctuated equilibria [5,6].

Van Alen chose the name “Red Queen” in allusion to the romance “Alice in Wonderland”, from Charles Lutwidge Dodgson (better known as Lewis Carroll) published in 1865. Over this country (Wonderland) it was usual to run as quick as you could, just to end yourself at the same place. The dialogs between Alice and the Red Queen are sintomatic:

[…] ‘Now! Now!’ cried the Queen. ‘Faster! Faster!’ And they went so fast that at last they seemed to skim through the air, hardly touching the ground with their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she found herself sitting on the ground, breathless and giddy. The Queen propped her up against a tree, and said kindly, ‘You may rest a little, now. Alice looked round her in great surprise. ‘Why, I do believe we’ve been under this tree the whole time! Everything’s just as it was!’ ‘Of course it is,’ said the Queen. ‘What would you have it?’. ‘Well, in our country, said Alice, still panting a little, ‘you’d generally get to somewhere else – if you ran very fast for a long time as we’ve been doing.’ ‘A slow sort of country!’ said the Queen. ‘Now, here, I see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!‘ […]

Meanwhile, since 2007 (even much earlier!) I have taken Alice into my own arms. In fact, she is not heavy at all. If you feel you should keep running, some should, have a read on “Co-Cognition, Neural Ensembles and Self-Organization“, extended abstract for a seminar talk at ISR – Institute for Systems and Robotics, Technical Univ. of Lisbon (IST), May 31, 2007. Written at Granada University, Spain, 29 May 2007.

[1] van Alen, L. (1973), “A New Evolutionary Law“, Evolutionary Theory, 1, pp. 1-30.
[2] Cliff D., Miller G.F. (1995), “Tracking the Red Queen: Measurements of Adaptive Progress in Co-Evolutionary Simulations“, in F. Moran, A. Moreno, J.J. Merelo and P. Cachon (editors) Advances in Artificial Life: Proceedings of the Third European Conference on Artificial Life (ECAL95). Lecture Notes in Artificial Intelligence 929, Springer- Verlag, pp.200-218.
[3] Cliff D., Miller G.F. (1996), “Co-Evolution of Pursuit and Evasion II: Simulation Methods and Results“. In P. Maes et al. (Eds.), From Animals to Animats IV, Procs. of the Fourth Int. Conf. on Simulation of Adaptive Behaviour, MIT Press, pp. 506-515.
[4] Dawkins R., Krebs J.R. (1979), “Arms Races between and within Species“. In Procs. of the Royal Society of London: Biological Sciences, nº. 205, pp. 489-511.
[5] Eldredge, N., Gould, S. J., “Punctuated equilibria: an alternative to phyletic gradualism“. In: Models In Paleobiology (Ed. by T. J. M. Schopf), 1972.
[6] Gould, S. J., & Eldredge, N., “Punctuated equilibria: the tempo and mode of evolution reconsidered“. Paleobiology, 3, 115-151, 1977.

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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