Game theory: You’ve probably heard of it, but do you know what it is?
At it’s core, a “game” is any situation where there are several decision makers, and each of them wants to achieve the best results for themselves. The optimizing decision and result will depend, however, on the decisions of others.
Game theory is the process of attempting to define, and in some cases predict, these situations in mathematical terms. They try to predict what would happen if every “player” acts rationally. Economists call it game theory, while psychologists call it the “theory of social situations”. It is the study of human behavior and the attempt to build it complexly in a mathematical model.
Once you get into this all the way, people have used game theory to determine trade agreements, elections, and used it in simulation situations and real life predictive models ranging from wars to corporate takeovers.
There are two basic branches of game theory. They are cooperative and noncooperative. Perhaps in this decision, all players act rationally and cooperatively for their best interests. (i.e. all drivers driving on the same side of the road to prevent accidents). Perhaps all players reach equilibrium but the consequences are worse for all players (pollution of natural resources). Perhaps all players are trying to act as unpredictably as they can (i.e. two sides of a war where troops are trying to outsmart one another). Noncooperative game theory is what most people refer to when they speak about game theory, as it’s the branch that deals with how intelligent individuals will act and react with situations and other players in an effort or achieve their own personal goals. (This is not selfishness that is discussed. This is human nature. The only way to stay alive as a caveperson is to act selfishly.)
Every “game” has three deciding factors to the outcome. The players (decision makers), the actions (what the players can do in their “turn”), and the payoffs (what motivates each player to “win”, and how the benefit from the results of the game). Once you define these, you know how many potential outcomes you have. This is like trying different combinations to break into a five-digit lock, with five possible digits in each position, you have 5 X 5 X 5 X 5 X 5 = 55 = 3125 potential lock combinations.
So to come up with your different outcomes, you have to break each down. You need a column down the side with every action that Player 1 can take. Then you need to put the Player 2 potential actions in rows across the top. Now you have a grid, where every square in between is the potential result of each action. Then you can narrow down what happens in the results, and determine how much each player “wins” or “loses” with every result. Once you have the win loss percentages you can try to figure out which options are the best for each player, and the way each player can optimize the potential payoff for themselves. Then, when you have the big picture of all that math, you figure out what each player is more likely to do.
One of the most famous basic studies in game theory is the Prisoner’s Dilemma game. You have two “players”. Each player was arrested for the same crime and placed in police custody. Each player is a suspect in separate cells, and they are separately offered the chance to confess. If they confess, it will implicate the other, or they can keep silent.
Player 1 is the down column, and Player 2 is the across row. Here the higher numbers are better. They represent options, mobility, and utility. If neither suspect confesses, they go free, and split the proceeds of their crime which is represented here by 5 units for each suspect. However, if one prisoner confesses and the other stays silent, the prisoner who confesses testifies against the other in exchange for going free. They get the entire 10 units to themselves. Now that second prisoner who didn’t confess ends up in prison, which results in the low score of -4. If both prisoners confess, then both are given a reduced sentence as a plea bargain, but both end up convicted, which is shown here by scoring them each 1 unit: better than having the other prisoner confess and taking all the heat, but as good as going free.
In this situation, the best outcome possible is confessing, but confession also possibly leads to the worst outcome, based on how you believe the other person will act. If both confess the outcome is worse than when both keep silent. This can be broken down into both to noncooperative and cooperative branches. Do you do what’s best for the common good, or do you do what’s best for yourself? And what do you do when your outcome depends on the other player’s decision to cooperate or not cooperate?