Game theory leads to monkey business

It's great being a scientist. You can sound ever so impressive by telling everyone that you're studying "non-transitive relations". It sounds so much more erudite than "I play rock-paper-scissors for a living".

On 20 June, researchers from the University of Washington published a paper describing a game of rock-paper-scissors, played using three strains of E coli bacteria. One of the strains produces two toxins, both of which kill the second strain.

The third strain is immune to both toxins and multiplies much faster than the producer of the toxins. However, the strain that is sensitive to the toxins multiplies even faster. The result is that their coexistence follows the law of non-transitive relations: A beats B, B beats C and C beats A. Rock-paper-scissors to you and me.

What is so interesting is that these bacteria have evolved restraint. The toxin-resistant strain doesn't multiply too fast, for example, or it will overwhelm the toxin producer, which will allow the toxin-sensitive strain to take over the habitat.

Such situations may be the origin of co-operation across the evolutionary spectrum. While nature is often depicted as "red in tooth and claw", rock-paper-scissors experiments show "my enemy's enemy is my friend" has a role to play, too. Sometimes things are outside your control; when the optimal strategy depends on what someone else does, it makes sense to hold back from delivering a killer blow.

Other scientists have seen the same principle at work. In a population of Californian lizards, for example, males with an orange throat-patch use aggressive behaviour to ward off rivals. But males with a yellow patch sneak up on females, defeating this strategy. Males with a blue patch stand guard over their mates, ruining the yellow strategy. But the orange males beat up the blue males. It's rock-paper-scissors again: macho beats loyal, loyal beats sneaky, and sneaky beats macho. The game - sorry, the intransitive relation - seems to be the root of co-operation between males of the same colour, and may lead to the creation of entirely new species.

Pick a pattern

There are other lessons about the natural world to be learned from rock-paper-scissors. One is that animals are capable of emotions such as regret. When researchers at Yale University taught rhesus monkeys to play a version of the game for rewards of fruit juice, the monkeys would display a rudimentary understanding of why they lost a particular round. Often in the next round, they would play the hand that would have won the last round.

The research on the monkeys, published in May, gives a small indication of their ability to change their future behaviour
in the light of bad outcomes in the recent past.

The monkeys were playing a less-than-ideal strategy, but do not mock: human beings are not able to play perfectly, either. We are unable to make fully random choices, which is the only unbeatable strategy. Being poor at rock-paper-scissors is a small price to pay, however. We are hard-wired to act in and respond to patterns, because this enabled early human beings to find food and evade predators. Eventually that led humans to create the pattern-spotting exercise we call science and, with it, the chance to get paid for playing rock-paper-scissors with monkeys and bacteria. Result.