Game Theory: Multiplayer Games
So far this week I have, conveniently, only covered games with two players. That is in part because it’s easier to understand Game Theory concepts with simpler games, and in part because I’m lazy. Still, I shall rise to the occasion today so we can cover multiplayer games!
Of course, in the real world, most game models will have many players. Even the simple examples I have used this week, changing the price for a product, include at least three players: the seller, the buyer and the competition. How do you choose a strategy when there are so many players?
The good news is that all of the strategies we discussed work for games of any size. There is nothing in any of the techniques that changes with more than two players, other than the complexity of modeling and analysis. It can be harder to understand the payoffs with three players, since instead of 4 possible outcomes now you will have 8 (since each player’s decisions affect the others). Still, with practice this can become just as easy.
Identifying dominant strategies becomes more important with more players since it is an easy shortcut in the analysis process. If there are no dominant strategies, you can still find the Nash Equilibrium, which is the point where all players are choosing the best possible strategies and will not change them even if every other player has chosen their own best strategy. This is a form of steady-state in games which dictates how many parties might fall into a predictable behavior. I don’t have time to go into how to determine the Nash Equilibrium for your game, but I suggest reading up on it if you are interested.
In Review: Game Theory is a powerful set of tools for understanding and deciding between different options where the decisions of many people interact. These tools make it a lot easier to cut through the complexity and make a data driven decision, and apply to a surprisingly wide variety of problems ranging from product changes to hiring decisions. I hope you have found our brief introduction useful!
Next Week: We’ve spent a lot of time on the process of making decisions, let’s get back to using your data. Customer Personas are a great way to better understand your customers and answer the age old question: Who are they? We’ll cover how to find personas in your data and the wealth of benefits they yield for you when you do.
Quote of the Day: “Games lubricate the body and mind.” ― Benjamin Franklin