![]() ![]() Alternatively pairs within a class can play against each other.Īn interesting extension is this applet, also on Game Theory, which models the evolution of 2 populations – residents and invaders. You can actually play the iterated Prisoner Dilemma game as an applet on the website Game Theory. So with the threat of punishment, a mutually co-operative strategy is superior. If someone is nasty to you on round one (ie by testifying) then you can punish them the next time. ![]() Basically whilst it is an optimum strategy to be selfish in a single round of the prisoner’s dilemma, any iterated games (ie repeated a number of times) actually tend towards a co-operative strategy. Game theory can be extended to evolutionary biology – and is covered in Richard Dawkin’s The Selfish Gene in some detail. Could the optimal maths strategy here be said to be responsible for saving the world? there is no incentive to deviate from the non strike policy. Such a game has a very strong Nash Equilibrium – ie. The above matrix uses negative infinity to represent the worst possible outcome, whilst both sides not striking leads to a positive pay off. The threat of Mutually Assured Destruction (MAD) meant that neither the Americans or the Russians had any incentive to strike, because that would inevitably lead to a retaliatory strike – with catastrophic consequences. Game theory became quite popular during the Cold War, as the matrix above represented the state of the nuclear stand-off. in this case mathematically optimum strategies are not “nice,” but selfish. So does mathematics provide an amoral framework? i.e. If only they can trust each other to be altruistic rather than selfish – and both remain silent, then they get away with only 6 months each. ![]() Part of the dilemma arises because if both men know that the optimum strategy is to testify, then they both end up with lengthy 5 year jail sentences. This situation represents a form of plea bargaining – which is more common in America than Europe. even if the prisoner and his partner are innocent they are is placed in a situation where it is in his best interest to testify against their partner – thus increasing the likelihood of an innocent man being sent to jail. This brings in an interesting moral dilemma – ie. If prisoner B remains silent, then prisoner A would have been best testifying (goes free rather than 6 months). Looking at it in reverse, if prisoner B testifies, then prisoner A would have been best testifying (gets 5 years rather than 10). So, what is the optimum strategy for prisoner A? In this version he should testify – because whichever strategy his partner chooses this gives prisoner A the best possible outcome. However, if they both testify they will both get 5 years, and if they both remain silent then they will both get 6 months in jail. During interrogation they are told that if they testify to everything (ie betray their partner) then they will go free and their partner will get 10 years. Two prisoners are taken into custody and held in separate rooms. The most well known example is that of the Prisoner’s Dilemma. Game theory is an interesting branch of mathematics with links across a large number of disciplines – from politics to economics to biology and psychology. If you are a teacher then please also visit my new site: for over 2000+ pdf pages of resources for teaching IB maths! Does it Pay to be Nice? Game Theory and Evolution ![]()
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