Game theory was coined in 1944 to describe a mathematical theory defining the strategy of game participants, and the recognition that actions impact all game participants, for better or worse.

In economics, game theory is used to make precise decisions based on logic and reasoning, measuring certain aspects – for instance, how much money you stand to lose or gain in a particular financial endeavour.

An oil cartel engaging in price-fixing and competitive espionage exemplifies how economists employ game theory. By predicting the cartel’s possible moves, companies or countries can formulate multiple strategies based on scenarios, and make proactive decisions to reduce negative impact or even completely reverse the outcome in their favour.

By applying game theory skills and analysis to business decisions and the economy, corporations can obtain a financial advantage. It can also apply to personal financial planning and be used for managing your cash flow or improving your investment practices.

What is game theory, exactly?

Game theory can be used to effectively predict social situations among competing players. Simply put, it’s the science of strategy.

The most well-known example of game theory is The Prisoner’s Dilemma. Consider the case of two crooks who have been apprehended. Prosecutors are unable to press charges on either due to a lack of hard evidence.

Investigators isolate them into different rooms and question them individually in the hope of obtaining a confession. With neither inmate able to speak with the other, investigators offer four deals:

• If they both confess, they will receive five years in prison.
• If crook 1 confesses but crook 2 does not, crook 1 will receive three years and crook 2 will receive nine.
• If crook 2 confesses but crook 1 does not, crook 1 will receive 10 years and crook 2 will receive two.
• If neither confesses, they will each be sentenced to only two years in prison.

The best tactic is for both to avoid confessing. However, neither party is aware of the other’s decision, and without a guarantee that the other will not confess, both are likely to own up and serve a five-year term.

“Nash equilibrium” is a concept within game theory where each player has nothing to gain if they change strategies based on the decisions of the other player. In a prisoner’s dilemma, the Nash equilibrium predicts both parties will choose the decision that is best for them individually but worst for them collectively.

Classifications in game theory

1. Cooperative/non-cooperative

In cooperative games, players can create legally binding agreements where decisions are determined by a coalition – for instance, how payment should be dispersed among players.

In non-cooperative games, players are unable to create legally binding agreements. To find a Nash equilibrium, non-cooperative game theory examines the various tactics and payoffs of individual players.

2. Symmetric/asymmetric

A symmetrical game is one in which the payoff is mostly determined by each player’s own strategy, rather than by the choices of other players.

The payoff in an asymmetric game, on the other hand, differs depending on who is playing. As a result, even if all players use the same strategy, the payoff for each person can and will vary.

3. Zero-sum/non-zero-sum

In a zero-sum game, the gains or losses of one player are balanced by those of the other participants. Conversely, in non-zero-sum games, the gains or losses of one player do not result in those of other players.

Put another way, a non-zero-sum game can lead to a win-win outcome.

4. Simultaneous/sequential

In a simultaneous game, all players make their decisions at the same time, usually without knowing what the others are doing.

In a sequential game, players take turns making decisions or receiving information about other players’ decisions.

5. Perfect information/imperfect information

In a perfect information game, all participants have access to the same data with which to make judgments; whereas in an imperfect information game, the knowledge is available to one or more players but not necessarily to everyone.

Applying game theory to money management

1. Make money in the markets

Risk or merger arbitrage is the simultaneous purchase of shares in a company that has declared it will be acquired, as well as the sale of the company that has announced the acquisition.

Using risk arbitrage to generate profit is one technique that takes advantage of game theory in the markets.

Assume that company A (the “acquirer”) proposes to exchange one of its shares for two of company T’s (the “target”). Before the offer, A’s stock was selling for RM50 per share and T’s stock RM20 per share.

If all of T’s shareholders accept the deal, its shares should climb to RM25. If T’s stock only rises to RM24, a merger arbitrage opportunity arises – investors can acquire two shares of company T for RM48 and sell one share of company A for RM50.

They can then exchange their two T shares for one A share, cover their short, and make a risk-free profit of RM2.

2. Save when buying a car

Instead of going to a dealership and bargaining with a salesperson, game theory can be used to save you money on your vehicle purchase.

Start by locating each dealership within a specified radius that has the car you want. Then contact each one with an offer to make a purchase within a specific time frame, and ask each dealer to submit a quote.

Some dealers may reply saying they do not negotiate over the phone or by email, but most will try outbidding the others by offering a better price.

3. Negotiate real estate

Game theory is frequently used in real estate. In multi-offer transactions, you have three options if you submit a bid and the real estate agent reveals you are up against competing offers.

You can choose to keep your original offer, withdraw it, or increase your bid. The latter alternative is essential to win, since the property would go to the highest bidder.

You should bid the maximum amount within your budget, based on the worth you place on the home, and live with your decision regardless of the outcome. Even if you don’t win, you would know you made the best decision during the process.

In relation to personal finance, it’s best to focus on the basics when applying game theory: understand the rules, predict possible outcomes, and make the best decisions.

This article first appeared in MyPF. Follow MyPF to simplify and grow your personal finances on Facebook and Instagram.