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16 February, 2012 in General, Images, People | Tags: Altruism, Bounded Rationality, Cooperation, Game Theory, John Forbes Nash Jr, John Nash, Mathematics, Nash equilibrium, Prisoner's Dilemma, Social cooperation, Social Dilemmas, Social Norms | Leave a comment
[…] Nash: See if I derive an equilibrium (link) where prevalence is a non-singular event where nobody loses, can you imagine the effect that would have on conflict scenarios, arm negotiations… (…) currency exchange? […], in Memorable quotes for “A Beautiful Mind” (2001), movie directed by Ron Howard, starring Russell Crowe, along with Ed Harris.
9 May, 2010 in General, Images, Research | Tags: Co-Cognition, Co-Evolution, Collective Decision Support Systems, Collective Intelligence, Collective Perception, Complex Systems, Cooperation, David Hume, Game Theory, Jean Jacques Rousseau, John Nash, Nash equilibrium, Prisoner's Dilemma, Social cooperation | Leave a comment
“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…