Game theory foundation

Game theory is the process of modeling the strategic interaction between two or more participants with established rules and results. Although used in many disciplines, game theory is most notably used as a tool in economics research. The economic application of game theory can be a valuable tool to help basic analysis of any strategic interaction between industries, sectors, and two or more companies.

Here, we will introduce game theory and the terms involved, and introduce you to a simple method to solve the game, called reverse induction.

Game Theory Definition

Whenever we encounter a situation involving two or more players with known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcome.

Let us first define some commonly used terms in game theory research:

  • Game: Any situation that depends on the behavior of two or more decision makers (participants) occurs.
  • Player: The strategic decision maker in the gaming environment.
  • Strategy: Considering a series of situations that may occur in the game, the player will take a complete plan of action.
  • pay off: The payout received by the player for reaching a certain result. Expenses can be in any quantifiable form, from dollars to utility.
  • Information set: Information available at a given point in the game. When the game has sequential components, the term information set is most often used.
  • Equilibrium: The point in the game where both parties make a decision and reach an outcome.
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Assumptions in Game Theory

As with any concept in economics, there are rational assumptions. There is also a maximization assumption. Assume that the players in the game are rational and will try to maximize their profits in the game.

When checking a game that has been set up, you assume that the listed payout includes the sum of all payouts related to the result. This will rule out any “what if” questions that may arise.

The number of players in a game can theoretically be unlimited, but most games will be placed in the context of two players. One of the simplest games is a sequential game involving two players.

Use reverse induction to solve sequential games

Below is a simple sequential game between two players. The tags containing player 1 and player 2 are the information sets of player one or two respectively. The number in parentheses at the bottom of the tree is the revenue for each point. The game is also continuous, so player 1 makes the first decision (left or right), and player 2 makes the decision after player 1 (up or down).

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Like all game theories, reverse induction uses rationality and maximization assumptions, which means that player 2 will maximize his gains in any given situation. In any information set, we have two choices, for a total of four. By eliminating options that player 2 would not choose, we can shrink our tree. In this way, we thicken the line that maximizes the player’s revenue given a set of information.

After this reduction, now that player 2’s choice has been made public, player 1 can maximize its revenue. The result is a balance found by summarizing backwards that player 1 chooses “right” and player 2 chooses “up”. Below is the solution to the game with the balanced path shown in bold.

For example, you can easily use the company as a participant to set up a game similar to the above game. The game may include product release scenarios. If company 1 wants to release a product, what will company 2 do? Will Company 2 release similar competitive products?

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By predicting the sales of this new product in different scenarios, we can set up a game to predict how the event might develop. Below is an example of how to model this type of game.

Bottom line

By using simple game theory methods, we can solve a series of confusing results in the real world. Using game theory as a tool for financial analysis is very helpful in sorting out the potentially chaotic real-world situation from merger to product release.

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