Game Theory is not the Theory of Games

(see previous Games? In Learning? I’m Confused…)

Game Theory is a branch of applied Mathematics which looks at competitive situations where two or more people have conflicting interests – it is not the theory of using games in learning.

Game Theory has been applied in many situations and contexts through history, most notably the Cold War, Global Politics, Economics and of course games like Poker, Rock, Paper, Scissors, Nim and Liars Dice (see this post – Red Dead Redemption)

The Prisoners Dilemma is synonymous when introducing Game Theory. Summarized briefly:

Two criminals, Prisoner A & Prisoner B are put in different rooms and given a similar deal. If one implicates the other, he may go free whilst the other receives a 10 year sentance. If neither of the crimanals talk, both are given 1 year sentances, and if both implicate each other, they each receive a 5 year sentence. 

Each criminal has an optimum strategy of implicating the other, and thus in equilibrium each receives a harsh punishment, but both would be better off if each remained silent. (This is assuming that both Prisoner A & B are rational) 

There are various iterations of the Prisoners Dilemma and it has been seen in popular media in various guises over the years:

(See Golden Balls & Game Theory for a nice explanation here)

John Nash, a famous mathematician and Nobel Laureate, whose work in game theory provided insight into the forces that govern chance and events inside the complex system of daily life, was made famous by popular media in the movie, A Beautiful Mind. This excerpt from the movie looks at Nash as he begins to formulate his idea of the Nash Equilibrium – for which he would later win a Nobel prize for his contributions in Game Theory.

A Nash Equilibrium is a state in the game where no player has an incentive to deviate. Each player’s equilibrium strategy is known by the other players, and no player has anything to gain by changing only his own strategy. When all the players in this case go for the blonde, every player can increase his payoff by deviating. 

One of my favourte instances of Game Theory is the Truel. Breifly:

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

(Hint: Think from the points of view of Mr. Gray and Mr. White, not just Mr. Black.)

See a Truel in action in the Clint Eastwood Western The Good, The Bad, The Ugly.

So Game Theory is a branch of Mathematics that uses vocabulary like Nash Equilibrium, complete/incomplete information, zero sum, variable sum, optimal strategy, deviation, expected value etc. – it’s not the Theory of using Games in learning.

Next Post: Game-Based Learning