Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. While used in a number of disciplines, game theory is most notably used as a tool within the study of economics. The economic application of game theory can be a valuable tool to aide in the fundamental analysis of industries, sectors and any strategic interaction between two or more firms. Here, we'll take an introductory look at game theory and the terms involved, and introduce you to a simple method of solving games, called backwards induction.

Definitions
Any time we have a situation with two or more players that involves known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes.
Let's start out by defining a few terms commonly used in the study of game theory:

  • Game: Any set of circumstances that has a result dependent on the actions of two of more decision makers ("players")
  • Players: A strategic decision maker within the context of the game
  • Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game
  • Payoff: The payout a player receives from arriving at a particular outcome. The payout can be in any quantifiable form, from dollars to utility.
  • Information Set: The information available at a given point in the game. The term information set is most usually applied when the game has a sequential component.
  • Equilibrium: The point in a game where both players have made their decisions and an outcome is reached.

Assumptions
As with any concept in economics, there is the assumption of rationality. There is also an assumption of maximization. It is assumed that players within the game are rational and will strive to maximize their payoffs in the game. (The question of rationality has been applied to investor behavior as well. Read Understanding Investor Behavior to learn more.)

When examining games that are already set up, it is assumed on your behalf that the payouts listed include the sum of all payoffs that are associated with that outcome. This will exclude any "what if" questions that may arise.

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

Solving Sequential Games Using Backwards Induction
Below is a simple sequential game between two players. The labels with Player 1 and two within them are the information sets for players one or two, respectively. The numbers in the parentheses at the bottom of the tree are the payoffs at each respective point, in the format (Player 1, Player 2). The game is also sequential, so Player 1 makes the first decision (left or right) and Player 2 makes its decision after Player 1 (up or down).

Figure 1

Backwards induction, like all game theory, uses the assumptions of rationality and maximization, meaning that Player 2 will maximize his payoff in any given situation. At either information set we have two choices, four in all. By eliminating the choices that Player 2 will not choose, we can narrow down our tree. In this way, we will bold the lines that maximize the player's payoff at the given information set.

Figure 2

After this reduction, Player 1 can maximize its payoffs now that Player 2's choices are made known. The result is an equilibrium found by backwards induction of Player 1 choosing "right" and Player 2 choosing "up". Below is the solution to the game with the equilibrium path bolded.

Figure 3

For example, one could easily set up a game similar to the one above using companies as the players. This game could include product release scenarios. If Company 1 wanted to release a product, what might Company 2 do in response? Will Company 2 release a similar competing product? By forecasting sales of this new product in different scenarios, we can set up a game to predict how events might unfold. Below is an alter-example of how one might model such a game.

Figure 4

Conclusion
By using simple methods of game theory, we can solve for what would be a confusing array of outcomes in a real-world situation. Using game theory as a tool for financial analysis can be very helpful in sorting out potentially messy real-world situations, from mergers to product releases.

Related Articles
  1. Term

    How Market Segments Work

    A market segment is a group of people who share similar qualities.
  2. Active Trading

    Market Efficiency Basics

    Market efficiency theory states that a stock’s price will fully reflect all available and relevant information at any given time.
  3. Fundamental Analysis

    The 3 Best Investments When Bull Markets Slow Down

    Find out why no bull market lasts forever, and why investors should shift their assets away from growth and toward dividends when stocks slow down.
  4. Economics

    Industries That Thrive On Recession

    Recessions are not equally hard on everyone. In fact, there are some industries that even flourish amid the adversity.
  5. Economics

    Economist Guide: 3 Lessons Adam Smith Teaches Us

    Learn three critical lessons about economics from 18th century philosopher Adam Smith, considered by many to be the father of economics.
  6. Fundamental Analysis

    5 Basic Financial Ratios And What They Reveal

    Understanding financial ratios can help investors pick strong stocks and build wealth. Here are five to know.
  7. Investing

    What Investors Need to Know About Returns in 2016

    Last year wasn’t a great one for investors seeking solid returns, so here are three things we believe all investors need to know about returns in 2016.
  8. Economics

    The Basics Of Business Forecasting

    Whether business forecasts pertain to finances, growth, or raw materials, it’s important to remember that a forecast is little more than an informed guess.
  9. Economics

    Forces Behind Interest Rates

    Interest is a cost for one party, and income for another. Regardless of the perspective, interest rates are always changing.
  10. Term

    Three Ways to Profit Using Call Options

    A call option gives an investor the right, but not the obligation, to buy a stock at a specific price, known as the strike price.
RELATED FAQS
  1. What is the difference between a dominant strategy solution and a Nash equilibrium ...

    Game theory is the science of strategy in situations that involve more than one actor. This can include actual games, military ... Read Full Answer >>
  2. How do modern corporations deal with agency problems?

    Agency problems – also known as principal-agent problems or asymmetric information-driven conflicts of interest – are inherent ... Read Full Answer >>
  3. What is finance?

    "Finance" is a broad term that describes two related activities: the study of how money is managed and the actual process ... Read Full Answer >>
  4. What is the difference between positive and normative economics?

    Positive economics is objective and fact based, while normative economics is subjective and value based. Positive economic ... Read Full Answer >>
  5. What's the difference between microeconomics and macroeconomics?

    Microeconomics is generally the study of individuals and business decisions, macroeconomics looks at higher up country and ... Read Full Answer >>
  6. How do you make working capital adjustments in transfer pricing?

    Transfer pricing refers to prices that a multinational company or group charges a second party operating in a different tax ... Read Full Answer >>
Hot Definitions
  1. Socially Responsible Investment - SRI

    An investment that is considered socially responsible because of the nature of the business the company conducts. Common ...
  2. Presidential Election Cycle (Theory)

    A theory developed by Yale Hirsch that states that U.S. stock markets are weakest in the year following the election of a ...
  3. Super Bowl Indicator

    An indicator based on the belief that a Super Bowl win for a team from the old AFL (AFC division) foretells a decline in ...
  4. Flight To Quality

    The action of investors moving their capital away from riskier investments to the safest possible investment vehicles. This ...
  5. Discouraged Worker

    A person who is eligible for employment and is able to work, but is currently unemployed and has not attempted to find employment ...
  6. Ponzimonium

    After Bernard Madoff's $65 billion Ponzi scheme was revealed, many new (smaller-scale) Ponzi schemers became exposed. Ponzimonium ...
Trading Center