Game theories have been used in some form or another for thousands of years. Naturally, these “games” were not always referred to as such a thing. They were often utilized, however, in things like war or in counsel. Even monarchies used to employ them to make decisions for their kingdom. Game theories were originally developed by someone making up a specific situation where two or more people competed. This covers A LOT of things, of course. But the idea here is that one would use mathematical models and form strategies within real-world settings. The games are also driven by the interactions and actions of “rational agents.”
Simply put, a rational agent can be anything or anyone that can make a decision. Therefore, a human could compete against a computer. While game theories used to involve only zero-sum games, they’d eventually branch out into social science through things like behavioral actions. Where one might use their knowledge on how someone might act or guesstimate their decisions. Essentially, these games always use overall logic but that can be employed in many forms The idea is to see specifically how our decision-making (human, animal, or machine) ranks among each other. On top of “why” we made those decisions.
The St. Petersberg Game
- Inventor of Game: Nicolas Bernoulli
This is likely one of the most famous game theories known today. You can potentially form this game around a few different scenarios, but the most popular is the casino setting. Here, you’re part of a game of chance where a fair coin is tossed at each point. The initial stake is that the winner will win a specific amount of money each time this coin lands on heads. Let’s just use $3 for the example. The player will win money every single time the coin lands on heads, doubling each time. But the moment it lands on tails, the game ends. One flip, landing on heads, you win $3. The second time, you win $6. The third time, you win $12, and so on. What you must now consider is: what is a fair price to pay the casino to play this game?
The game is using a fair coin, thus you know the casino isn’t rigging the game. The casino also has unlimited resources. On top of this, your money does indeed double for every period the coin lands on heads. Moreover, you are only having to buy into the game once and once the coin lands on tails, you will leave with all of the money you won. Many game theorists have come up with their own concept, but the best in our view is that you play the game at any price if it is offered to you. While simplistic, the game is not about your specific money but rather the idea of what the game offers. Many try to add a specific amount to this, but this is a game of chance with only two possible outcomes. Thus, specific pricing seems illogical.