# Probability Theory $\Rightarrow$ Game Theory?

It is a very simple question.

I would like to learn Game Theory but I am not that good at Probability Theory.

I would like to know it is necessary to be good at probability theory in order to learn game theory? If yes, how they are related to each others? What is the best strategy for someone to be good in Game Theory?

Please give a good reference to start learning both.

• I assume the best strategy would be a mixed strategy (SCNR) Apr 21, 2014 at 19:54
• Ok. You do not define the strategy yet. (ISBYTTS)
– Jika
Apr 21, 2014 at 20:02

Because we call it a "game" does not it make a game in the sense that is studied by Game Theory. Roulette, slot machines, and other games of chance are not strategic games.

Game Theory studies games where what is the best for you (usually) depends on what the other players are doing are doing.

For Game Theory, you will need basic probability: Bayes rule, discrete and continuous random variables, and computing expectations are the basic tools of the trade but advanced probability is not required.

Osborne: An Introduction to Game Theory is the textbook I use (undergrad level), it has a section on the Appendix on probability with everything you may need. I'm not sure if I'd recommend it for self study but the section on the appendix will show you that you need very little of probability.

Some years ago I had this kind of situation. I took a class with the name "Probability" I thought that was ok, I am fine with general probability, nothing more than that. Turned out this course was going to be more with game theory "a la Las Vegas" style then just conventional probability. And so I passed with a B. The reason for missing my A was because I did not fully comprehend the nature of the games, like card games, roulette, bridge, black jack, things like that. I never really played those games and so compared to my fellow students, I was at a disadvantage. So if you want to be good at game theory, learn how to play the games first and foremost before even going into probability. Once you know the "tricks" of the game, for the most part you do not need to know heavy probability at all. The major probability distributions even taught in a college credit high school course will suffice.

Probability only comes into play directly when you are dealing with models that have imperfect information (such as typical card games where cards are hidden,) some form of stochasticity (any type of random number generation such as shuffling or dice rolling,) or incomplete information (such as Dilemmas, where the competing agent's decision-making process is unknown, although incomplete information is something of a blanket term often applied to any form of inaccessible information.)

Game theory, via minimax, can be applied to models without these conditions, such as non-chance, perfect information games, without requiring probabilities. The major caveat here is that if the model is intractable, and the search space (gametree or, ideally a graph) cannot be exhausted, probability analysis becomes critical--all of the cutting-edge Artificial Intelligence methods rely heavily on statistics.

Logic is important, but it's probably a good idea to at least have some grounding in probability and statistics. The above links should provide pointers to general game theory references.

For probability, I might recommend starting with Bayes. Russell and Norvig's Artificial Intelligence: A Modern Approach is highly regarded [See: Part IV Uncertain Knowledge and Reasoning]. (Here is a link to a pdf of the second edition if you want to check it out, although the 3rd edition is the most current.)

Game theory and probability are interdependent when one talk about stochastic games. On the other hand learning basics of game theory doesn't need understanding of probability theory. Working with dominant strategies and reaching equilibrium using minimax learning is all fine without probability.
Game Theory by Drew Fedenburg is a good book for learning game theory.

I personally love game theory and probability theory. I have always played different card games like craps, roulette, and poker but never knew that it was included in game theory. I completely overlooked game theory, and did not realize how much it went with probability theory. There is a probability every time that you lay a card down that you will not win for that round. Once you understand the game, you realize that the probability gets lower as you get higher in your risk. I would suggest learning probability before you try to learn game theory. Once you learn probability, your odds are higher for success in game theory.