What Is Game Theory? And why is it an important decision-making tool?
I came across the concept of Game Theory when I was listening to a podcast interviewing Naval Ravikant.
Here is a screenshot of the blog post of that interview (Parrish, n.d.)
So What Is Game Theory? I’m going to give a basic rundown on game theory and provide you with all the terms you need to know.
Let’s start with its history.
In 1944, Jon von Neumann, a mathematician, teamed up with Oskar Morgenstern, an economist, and wrote a short paper called the Theory of Games and Economic Behaviour (Princeton University Press, n.d.). The two conceived a groundbreaking mathematical theory of economic and social organization based on a hypothesis strategy in games.
The Game theory came to its conception due to John von Neumann interest in poker. According to a Forbes article, he was only interested in poker because he saw it as a path toward developing the mathematics of life itself.
He wanted a general theory to apply to diplomacy, war, love, evolution or business strategy and called it The Game Theory.
But he thought that there could be no better starting point than poker: “Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do? And that is what games are about in my theory.” (Harford, 2006).
Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded — game theory — has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations (Princeton University Press, n.d.). And it is today established throughout both the social sciences and a wide range of other sciences, which I will further explain below.
A simple definition of Game Theory;
Game Theory is a theoretical framework for conceiving social situations — it is the process of forming the strategic interplay between two or more players in a circumstance bearing set rules and outcomes.
Let us take an introductory look at game theory and the terms involved extracted from Investopedia (Hayes, 2021).
- Game: Any set of circumstances that has a result dependent on the actions of two or 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
- Strategic choice: A choice based on the recognition that the actions of others will affect the outcome of the choice and that takes these possible actions into account is called a strategic choice. For example, strategic choices available to an oligopoly firm are pricing choices, marketing strategies, and product development efforts.
- Payoff: The payout a player receives from arriving at a particular outcome. The outcome of a strategic decision is called a payoff. The payoff depends partly on the strategic choice it makes and partly on the strategic choice of its rivals.
- Information set: The information set is 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 received.
Players within the game are rational and will strive to maximize their payoffs in the game, which is what is assumed. Players can be individuals like you and me or big firms like Coca-cola and Pepsi.
Prisoner’s Dilemma
The prisoners’ dilemma is known to be one of the best examples of a game analyzed in game theory. Let’s look into this furthermore.
Let’s say that Jake Peralta, a Detective from Brooklyn-nine-nine, is sure that two individuals, Jimmy and Eleanor, have committed a fraud, but he has no evidence that would be admissible to charge them for their crime.
The detective arrests the two. On being searched, a small amount of cocaine was possed by each was found. The detective now has a sure conviction on a possession of cocaine charge, but he can only charge them on the fraud only if at least one of the prisoners confesses and implicates the other.
The detective decides on a strategy to extract confessions. He separates both Jimmy and Eleanor in different interrogation rooms and lay out the consequences to each:
- If you confess and your partner does not confess, you will get the minimum sentence of one year in jail on the possession and fraud charges.
- If you both confess, your sentence will be three years in prison.
- If your partner confesses and you do not, the plea bargain is off, and you will get ten years in prison.
- If neither of you confesses, you will each get two years in prison on the drug charge.
The two convicts each confront a dilemma; both can choose to confess or not confess. Because the detainees are separated, they cannot plan a joint strategy. Each must make a strategic choice in isolation.
What would you do? Would you risk staying silent and trust your partner, who is a criminal, to do the same?
The outcomes of these strategic choices depend on the strategic choice made by the other prisoner, as seen in the payoff matrix for this game in Figure 1.
There are four possible outcomes:
Cell A: Jimmy and Eleanor both confess
Cell B: Eleanor confesses, but Jimmy does not
Cell C: Eleanor does not confess, but Jimmy does
Cell D: Neither Eleanor nor Jimmy confesses
The portion at the lower left in each cell shows Eleanor’s payoff; the shaded area at the upper right shows Jimmy’s payoff.
If Jimmy confesses, Eleanor’s best choice is to confess — she will get a three-year sentence rather than the ten-year sentence she would get if she did not disclose. If Jimmy does not admit, Eleanor’s best strategy is still to confess — she will get a one-year rather than a two-year sentence. In this game, Eleanor’s best strategy is to confess, regardless of what Johnny does, when one player’s best strategy is the same no matter the other player’s strategic choice, it is called a dominant strategy (lumenlearning, n.d.). Eleanor’s dominant strategy is to confess to the fraud.
It is the same case for Jimmy- the dominant strategy is to confess regardless of Eleanor’s strategic choice.
Although the ideal condition is where both choose to stay silent, Cell D, yet the most rational thing to do is confess. Because by doing so, one isn’t putting trust in a criminal who could walk away gaining the upper hand and walk free in just one year rather than three years due to the strategic choice made by the other.
The case where both decide to stay silent is called the Nash Equilibrium.
Nash equilibrium in game theory is a situation in which a player will continue with their chosen strategy, having no incentive to deviate from it, after taking into consideration the opponent’s strategy.
So if Jimmy and Eleanor knew each other’s strategies, they would choose the most rational choice that will benefit both individuals interests, thus pick Cell D. They will cooperate because each is aware of each other’s decisions, however when they are separated and aren’t aware of each other’s choices, it becomes a non-cooperative game.
Cooperative and Non-cooperative Games
Cooperative and non-cooperative game theories are the most common.
Cooperative game theory deals with how coalition in groups interact when only the payoffs are known. It is a game between collaborating players rather than between individuals, and it questions how groups form and how they allocate the payoff among players.
Non-cooperative game theory deals with how rational agents deal with each other to achieve their own goals. The above prisoner’s dilemma is a non-cooperative game. Another example of a real-world non-cooperative game is Rock-Paper-Scissors.
Tit for tat
Implementing a tit-for-tat strategy occurs when one agent cooperates with another agent in the very first interaction and then mimics their subsequent moves. This strategy works on the concepts of retaliation and altruism.
For example, if at first opponent A collaborates but opponent B cheated, opponent A will retaliate by cheating the next time.
I recommend watching this video to understand further how tit for tat works;
Importance of Game Theory
It helps explain how we interact in decision-making processes in conflicts and construct effective strategies (Hayes, 2021). The best use of game theory is to figure out the optimal solution from the best possible choices while determining costs and benefits to each participant who competes with each other. Game theory is applicable in different fields, like business, psychology, biology, sports, economics, political science, and computers (Hayes, 2021).
Some real-life examples of Game Theory are;
First-price sealed-bid auctions. In this kind of auction, bidders submit simultaneously sealed bids( bids written down and provided in sealed envelopes) to the seller, who will open them all together.
Different players try to devise a bidding strategy, irrespective of having complete information whilst taking into account each opponents behaviour.
Stock Market Decisions, using game theory, wiser decisions can be undertaken when buying and selling shares. Investors can analyze how other investors and different players will behave in the market and use appropriate strategies which maximize their profit.
Limitations of Game Theory
A limitation of game theory is that it assumes that people are rational beings that are self-interested and utility-maximizing. In real life, people are often more willing to cooperate at their own expense. We are social being who do cooperate and care about the welfare of others.
Game theory cannot account for the fact that in some situations, we may fall into a Nash equilibrium, and other times not, depending on the social context and who the players are (Hayes, 2021).
Conclusion
Game Theory is a valuable decision-making tool to know, especially when running a business and forming contracts with opponents. However, it is vital to keep its limitation in mind.
I hope you enjoyed this long read about game theory. I highly recommend going through the referenced sites to learn more about Game Theory.
References
Bat, T., 2020. GAME THEORY: The Ultimate Tool for Strategic Decision-Making. [online] Thinkingbat.substack.com. Available at: <https://thinkingbat.substack.com/p/game-theory> [Accessed 10 May 2021].
Harford, T., 2006. A Beautiful Theory. [online] Forbes.com. Available at: <https://www.forbes.com/2006/12/10/business-game-theory-tech-cx_th_games06_1212harford.html?sh=5b6268855e94> [Accessed 8 May 2021].
Hayes, A., 2021. How Game Theory Works. [online] Investopedia. Available at: <https://www.investopedia.com/terms/g/gametheory.asp> [Accessed 10 May 2021].
lumenlearning, n.d. Reading: Game Theory | Microeconomics. [online] Courses.lumenlearning.com. Available at: <https://courses.lumenlearning.com/suny-microeconomics/chapter/reading-game-theory/#:~:text=Game%20theory%20is%20an%20analytical,strategic%20choices%20can%20be%20assessed.&text=Once%20a%20firm%20implements%20a,economic%20profit%20to%20each%20firm.> [Accessed 10 May 2021].
Parrish, S., n.d. THE KNOWLEDGE PROJECT Naval Ravikant. [online] Fs.blog. Available at: <https://fs.blog/wp-content/uploads/2017/02/Naval-Ravikant-TKP.pdf> [Accessed 10 May 2021].
Princeton University Press, n.d. Theory of Games and Economic Behavior. [online] Press.princeton.edu. Available at: <https://press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior> [Accessed 8 May 2021].
