# What is the difference between game theory and machine learning?

What is the difference between game theory and machine learning?

I had gone through the papers Deep Learning for Predicting Human Strategic Behavior, by Jason Hartford et al., and When Machine Learning Meets AI and Game Theory, by Anurag Agrawal et al., but I am not able to understand.

These are big areas, so here is a brief description of the differences:

Game theory is concerned with studying solutions for 'games', which are basically a set of decisions leading to certain outcomes. In game theory you look at strategies to achieve the best outcome for a given participant. One classic example (which isn't really a game in the traditional sense) is the Prisoner's Dilemma: you and your friend have been arrested, and if only one of you testifies against the other, that person gets a reduced sentence, and the other one a much longer one. If you both testify against each other, you both get a medium sentence, and if you both keep quiet, you both go free. You don't know what your partner in crime does, so do you a) testify, or b) keep quiet? If you keep quiet, you might go free if your partner also keeps quiet, but if he testifies, you are in it for a long time. So it's risky to keep quiet, even though you get the better outcome. If you testify you might avoid a longer sentence, but also will not go free. What is your best choice?

Game theory is often used in economics to model behaviour, as a rational agent would try to optimise gains.

Machine Learning, on the other hand, is a way of training a statistical classifier. You feed features into an algorithm, and the algorithm then gives you a certain output, depending on the data you have trained it with. This hasn't got anything to do with game theory per se, but I guess you could use machine learning to train an algorithm to choose moves in a game situation and then compare how that matches the optimal choices according to game theory.

As I said, this is a very brief comparison. For more details I suggest you follow the links to read up on those two fields.

UPDATE: Now that the papers are accessible — game theory is indeed used as a benchmark. In the first paper, the rational agent assumption from game theory is being modeled, but without a human expert telling the algorithm what that means. So you learn (using deep learning) what it means to be rational. In the second paper the authors attempt to learn a better algorithm than tit-for-tat, and indeed use game theory as a theoretical framework for comparison/evaluation.

The other answer gives the nice famous example of the sort of problem that game theory tackles and it partially describes what machine learning is.

However, it does not emphasize that this type of game theory problem, where you have two or more agents competing with each other, also appears in the context of machine learning. More concretely, machine learning can also be applied in the context of a multi-agent system, where you have multiple learning agents that compete with each other in an environment. Typical examples of these problems are two-player board games, like chess, go, or tic-tac-toe, which can be solved with machine learning, and, in particular, reinforcement learning (a specific type of machine learning): for instance, you can learn afterstate value functions to play tic-tac-toe.

There's a subarea of RL that tackles these problems with multiple agents, known as multi-agent reinforcement learning (MARL). One simple mathematical framework that generalises MDPs to multiple agents is the Markov games (aka stochastic games), which can be used to model games like rock-paper-scissors or tic-tac-toe. We could also model a multi-agent system as a single-agent system, where the other agents are incorporated into the environment. If you are interested in MARL, you could read, for example, the paper A comprehensive survey of multiagent reinforcement learning (2008) by Lucian Busoniu et al.

So, I think there are several connections between game theory and machine learning, and even other subareas of AI, such as game AI (e.g. the minimax algorithm is often taught in AI programs as an example of an adversarial search algorithm; read this to know more about the difference between search and learning) and evolutionary algorithms (in fact, there's also a related subfield of game theory known as evolutionary game theory).