In game theory, a coordination game is a game where there is more than one Nash equilibrium. If the game is non-repeated (played just once), then it is difficult for the players to coordinate their actions to ensure that the equilibrium outcome is obtained. One example of a coordination game is the game of chicken (see here or here). This difficulty in coordination can even be an issue if the game is repeated (although the players may eventually be able to learn, develop trust in each other, and coordinate).
A famous example of a coordination problem (or game) was outlined by Thomas Schelling. If you needed to meet with a stranger in New York City, and you had no way of communicating with them, when and where would you try to meet them? This seems an extraordinary question to answer, as there are literally millions of possible location and time combinations you could choose. However, if you and the stranger are both thinking about the same problem, then some locations and times are more likely than others. You'd want to choose somewhere central, which is easy to find, and which many people would think about going. Similarly, you'd want to choose a time that is a pretty common time for meeting. Schelling argued that you should choose one of these 'focal points' (which we now refer to as Schelling Points), as being the most likely equilibrium. Schelling's solution to the New York City problem was that you should go to the information booth at Grand Central Station at 12 noon.
That brings me to this article from Phys.org last month:
New research from the University of Manchester suggests using a strategy linked to cooperative game playing known as 'game theory' in order to maximize the potential of finding intelligent alien life.
If advanced alien civilisations exist in our galaxy and are trying to communicate with us, what's the best way to find them? This is the grand challenge for astronomers engaged in the Search for Extraterrestrial Intelligence (SETI). A new paper published in The Astronomical Journal by Jodrell Bank astrophysicist, Dr. Eamonn Kerins, proposes a new strategy based on game theory that could tip the odds of finding them more in our favor.
Notice that this is similar to Schelling's New York City coordination problem. We want to look for extraterrestrial intelligence, but where should we look? To quote Tommy Lee Jones' character in the movie Armageddon, "beg'n your pardon sir, but it's a big-ass sky". And if some extraterrestrial intelligence is looking to broadcast their location, where should they direct their broadcasts? And to take things a step further, with two separate civilizations on different planets, which one should be the sender of the signal, and which should be the receiver? If everyone is listening but no one is sending a signal, then that is a coordination failure too. Kerins' solution is excellent:
Dr. Kerins dubs his idea "Mutual Detectability." It states that the best places to look for signals are planets from which we would be capable of determining that Earth itself may be inhabited.
"If we have evidence of a potentially inhabited planet, and civilisations there have similar evidence about our planet, both sides should be strongly incentivised to engage in SETI towards each other because both will be aware that the evidence is mutual."...
The new theory suggests examining transiting planets, planets that are on orbits that pass directly across the face of their host star, briefly making it appear dimmer. This dimming effect has been previously used to discover planets. In fact, transiting planets make up most of the planets we currently know about. For some, astronomers can determine if they are rocky planets like Earth, or if they have atmospheres that show evidence of water vapor.
"What if these planets are located in line with the plane of the Earth's orbit? They'll be able see Earth transit the Sun and they'll be able to access the same kind of information about us. Our planets will be mutually detectable." said Dr. Kerins.
And in relation to being a sender or a receiver of a signal, there is a game theoretical solution there as well:
"It turns out that civilisations on a planet located in the Earth Transit Zone can know whether the basic evidence of their transiting planet is clearer to us or if our signal is clearer to them. We'll know this too. It makes sense that the civilisation that has the clearest view of the other's planet will be most tempted to send a signal. The other party will know this and so should observe and listen for a signal."
In the research paper Dr. Kerins shows that the vast majority of habitable planets in the Earth Transit Zone are expected to be in orbits around low-mass stars that are dimmer than the Sun. He shows that these civilisations would have a clearer view of us. Using the Mutual Detectability theory suggests that targeted SETI programs should therefore concentrate on looking for signals from potentially habitable planets around dim stars.
It appears that there is a Schelling Point in the search for extraterrestrial intelligence. Now, we have to hope that, if such intelligence exists, they have also developed an understanding of game theory. And if SETI suddenly becomes successful, it may have game theory to thank.
[HT: Marginal Revolution]
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