The autonomous car is driving along a path full of stones. And he’s tripping over a lot of them. Beyond the difficulties that he must overcome to obtain the approval of the regulatory authorities, which is undoubtedly one of the great challenges that he will have to overcome, in the short term he has a much more pressing challenge: adapting to the circulation in an extremely aggressive space in which an infinite number of unforeseeable circumstances can unexpectedly occur.
Fortunately, techies looking to solve this challenge have several powerful tools at their disposal, but one stands out above all others: mathematics. But not any area of this discipline. There is one in particular that is exceptionally valuable in dealing with the threats facing autonomous driving: game theory. And, curiously, one of the mathematicians who helped to strengthen his postulates was John Nash, the scientist played by Russell Crowe in ‘A Beautiful Mind’.
This dilemma has taken no less than 60 years to be resolved
Nash’s leading role during the formalization of game theory in the late 1940s is beyond doubt (in fact, it earned him the Nobel Prize in Economics in 1994), but he was not the only researcher to make contributions. decisive in this area of applied mathematics. John von Neumann and Oskar Morgenstern are some of the scientists who also contributed to the development of this highly appreciated set of mathematical tools in economics, sociology, computing, biology or psychology, among other areas of knowledge.
The technicians who are working on the development of the technologies necessary to bring the fully autonomous car to fruition regularly resort to game theory. And they do so with the purpose of identifying the strategies used by the rational agents with whom they are going to interact during displacements, such as other vehicles or pedestrians, in a competition in which all of them make the decisions they believe appropriate to fulfill their objectives. goals. Predicting the behavior of a dynamic system in which so many variables of such complexity are involved is very difficult, but differential games fit like a glove in this situation.
Predicting the behavior of a dynamic system as complex as the one that the autonomous car has to deal with is very difficult.
This branch of game theory is very useful for understanding the behavior of complex systems in which several moving players compete with each other in order to win. defend their own interests. This description allows us to intuit that autonomous cars act as one of the moving players within a much more complex system in which they are forced to interact with other players.
In fact, differential games bring together problems that raise conflicts between players who often have opposing interests. One of these problems proposes a chase game in which a fast player has to catch a slower player who can only move in a limited space. This premise was put forward by mathematicians working on game theory nearly 60 years ago, and no scientist has come up with a fully satisfactory solution. Until now.
Dejan Milutinovic, a Ph.D. in computer science and electrical engineering who teaches at the University of California at Santa Cruz, leads a research team that has been trying to solve a dilemma posed by the chasing game since its inception for several years. Until now no one had found an optimal solution based on some specific positions that can be occupied by players, but these researchers have published a scientific article in IEEE Xplore in which have managed to disassemble this mathematical dilemma.
Autonomous cars have to be able to develop optimal strategies that allow them to always make the right decisions
Milutinovic and his collaborators have shown that this dilemma does not really exist, and they have done so by devising a new method of analysis that proves that there is a deterministic solution to this tag game. This simply means that it doesn’t matter what positions the players occupy; finally one of them will reach his goal and win the game. There will never be a draw. This result is important because it is likely to help mathematicians investigating game theory to find solutions to other differential games.
Once we have reached this point we can ask ourselves what all this has to do with the autonomous car. And, actually, it has a lot to do with it. A few lines above we have seen that game theory is very useful for mathematicians because it helps them understand the behavior of some complex systems in which several agents or players compete with each other. Autonomous cars are precisely part of a complex system, so it is crucial that they are capable of develop optimal strategies that allow them to always make the right decisions to fulfill their purpose, which ultimately is to reach their destination.
It would be a very serious problem if in certain circumstances one of these vehicles gets stuck because it is unable to adopt the best strategy to move forward. In fact, John Nash proposed a concept known as a ‘Nash equilibrium’ in which all players participating in the game achieve their goal and maximize their profits.
If we transfer this idea to the autonomous car, we will have vehicles capable of always adopting the optimal strategy and reaching their goal without interfering with the purpose of others. Sounds good, although the challenge facing mathematicians now is identify what other dilemmas of game theory can be solved by applying the strategy that Milutinovic and his collaborators have proposed.
Cover image: Roberto Nickson
More information: IEEE Xplore | Phys.org
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