“We can model many situations using so-called game theory…”
Shutterstock/Ann Kosolapova
It is a dog-eat-dog world. Everyone for themselves, no matter the cost. If so, how would a behaviour like cooperation ever emerge?
From evolutionary biology to international diplomacy, we can model many situations using so-called game theory. These games have actions or strategies available to each participant, plus payoffs, which are positive or negative values that each player gains or loses from each outcome. Some games are “zero-sum”, where one player’s gain is equal to another’s loss. Some aren’t.
One famous game (not a zero-sum one) is especially revealing here. The prisoner’s dilemma, in its main form, imagines two “criminals” who have been caught and kept in separate cells with no way to communicate.
There isn’t enough evidence to convict either of the main charge, but enough to convict both of a lesser charge. The two are offered a deal simultaneously: testify that the other committed the greater crime and go free while the other gets three years in jail. But there is a catch: if they both betray each other, they each spend two years in prison. If both stay silent, each gets a year on the minor charge.
Each player’s payoffs can be shown as the number of years they serve in prison. If both stay silent, the payoff for each is -1. If player A betrays player B, A gets 0 and B gets -3. Betray each other, and A and B get -2 each. How can a player maximise the payoff?
Sometimes, each player has a strategy that is the best response to whatever the other player does. This is called a Nash equilibrium – both do what is best for themselves and both get their best outcome.
The dilemma is how the actions interact if they don’t know what the other will do. Imagine you plan on silence. If your opponent feels the same, you get a better payoff by betraying. If the opponent plans to betray, you get a better outcome by also betraying. Either way, your best action is to betray. This is true for both players, so each betrays, with a combined payoff of -4.
If both players trust each other and stay silent, the combined payoff is -2. The fact that dog-eat-dog leads to a worse outcome than cooperation, hints at how the latter might emerge.
In a famous 1980s experiment, 62 computer programs played 200 rounds of the prisoner’s dilemma. Crucially, they could make moves based on an opponent’s actions in earlier rounds. Selfish strategies tended to fare worse compared with altruistic ones. Successful strategies didn’t betray first, but would do so when an opponent had betrayed in an earlier game. They were also forgiving, returning to staying silent when an opponent ceased to betray.
So even though “pure” game theory leads to a bad outcome, a bit of kindness can overcome this. Be nice, but don’t let anyone take advantage of you. You have game theory to back you up.
These articles are posted each week at
newscientist.com/maker
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