Understanding the mechanics behind many of the complex financial systems that exist can be a challenging journey. Learning how these mechanisms fit together can be even more of a challenge. However, when it comes to game theory, simple examples can help us wrap our heads around concepts that have incredible impact in financial applications.
Game theory is the study of mathematical models of strategic interaction among rational decision-makers. This area of study provides a framework for many potential applications by relying on true information and possible outcomes between players.
Tick Tack Toe
A simple game that many people learn in their childhood provides us a perfect example that illustrates the most basic aspects game theory. As each turn occurs, players block one another's movements, inhibiting them from creating a line of 3 values (X or O). A large majority of the people familiar with the game will know that the chances of a draw are high when playing against someone else who has experience with the game. It's only when you are able to notice the mistake of the other player are you able to win the game. By continually blocking your opponent using the same strategy you will never lost nor win the game.
When it comes to a multi-factor game such as rock, paper scissors, a winning strategy becomes more complex. A draw is not as easily attained and sticking to one strategy doesn't provide a predetermined outcome. In fact, choosing rock, paper, or scissors repetitively will ensure a loss as well as ensuring your opponent would catch onto your strategy.
Nash's Equilibrium
In its simplest form, Nash's equilibrium is a solution to any game that involves two or more players who desire the best outcome for themselves but have to take into consideration the actions of others involved in the same game.
This equilibrium is achieved when the players can't improve their reward by changing their own strategy independently from others assuming other players won't change their strategy.
Take for instance there are 3 pieces of pie available in 3 flavors. How do you ensure you get the flavor you want when there are 2 other orders for the slices of pie. Do you attempt to get your order in first, claiming your favorite flavor right away? Or do you hesitate, missing the chance to claim your favorite flavor? Or do you put in your order for whatever is left?
Considerations
By looking at a scenario and considering all of its possible outcomes we can get a glimpse into the mechanics of how financial systems can capitalize on the movements of strategies of the "players" within its system. When individuals have a common goal and set ways of achieving that goal, additional factors that can effect outcome as well as the ecosystem in which they take place can be realized.
