Game Theory

What is Game Theory?

Game theory is the study of how people make decisions when the outcome depends not only on their own choices but also on the choices of others.

For example, instead of asking a question like:

• "What should I do?"

Game Theory would ask:

• "What should I do, knowing that others are listening, choosing or reacting?"

Game Theory is applied in many circumstances:

• Competition
• Cooperation
• Risk vs reward

Why does Game Theory matter?

Game theory matters because life is interactive: our choices affect others, and their responses affect us.

Without Game Theory, people often:

• Assume others will act logically or fairly
• Focus only on their own benefit
• Don't understand how incentives (see below) change behaviour

This shows that people often assume others will be "fair" when they might actually be "strategic".

Game Theory helps us see:

• Interdependent actions: how our decisions are linked to "other players"
• Decision making: how individuals make strategic decisions when outcomes depend on interdependent choices
• Potential outcomes: the strategic interactions between multiple "players" and the potential outcomes that are likely to arise from their choices

Nash Equilibrium

What is Nash Equilibrium?

• Nash Equilibrium is a situation in a game where each player chooses the best possible strategy, given the strategies chosen by all the other players.
• Each player assumes that the other players' choices remain fixed.
• In this situation, no single player has an incentive to change their strategy on their own.
• If one player were to change their strategy while the others did not, their outcome would not improve.
• It is a stable state where no player can benefit by changing their strategy alone.

Example of Nash Equilibrium

Two shops sell the same product. Each shop must choose either a High Price or a Low Price.

• If both choose High Price, both earn a good result.
• If one chooses Low Price and the other High Price, the shop with the low price attracts more customers and does better.
• If both choose Low Price, both earn less than if they had chosen high prices.

Nash Equilibrium explanation

Assuming Shop A chooses Low Price, Shop B will follow and also reduce its prices. In this situation, market share remains the same, but A and B both make less money.

Assuming Shop A chooses High Price, B does better by choosing Low Price, taking market share.

However, if A and B both choose High Price, their market share remains the same and they both make more money.

So it is in A and B's interest to cooperate in this scenario by fixing a higher price. However, this may result in illegal activity because of price fixing.

When both shops choose Low Price, neither shop can improve its outcome by changing its price alone.

Conclusion: both choosing Low Price is a Nash Equilibrium, because neither shop's individual action will result in that shop improving its position.

Incentives Shaping Behaviour

Incentives are rewards or consequences that influence the way people act. If you change the reward, you will also change the person's behaviour.

People tend to choose options that:

• Maximise rewards
• Minimise risks or punishments

Example: if students are only rewarded for their test scores, they may:

• Compete instead of helping each other
• Focus on memorising rather than truly understanding the topic

Analogy: just as a sailor adjusts their sails to capture the wind, individuals shift their actions to match the rewards or penalties they expect to receive.

The Evolution of Trust in Game Theory

1. Repeated Interactions

Trust keeps a relationship going, but you need the knowledge of possible repeated interactions that could occur in the future before trust can evolve.

2. Win-Win Possibilities

Trust requires a non-zero-sum game, where it is possible for both players to be better off. This contrasts with a zero-sum game, where one person's gain is always another's loss.

In zero-sum games, incentive structures reward short-term self-interest and exploitation, since cooperation provides no lasting benefits.

In non-zero-sum games, incentives change: cooperation can increase total value, and personal choices move from "How do I beat the other player?" to "How do we both benefit over time?"

3. Low Miscommunication

If the level of miscommunication is too high, trust will break down. But when there is a little bit of miscommunication, it pays to be tolerant and more forgiving.

To find out more, visit: ncase.me/trust

The Prisoner's Dilemma

The Prisoner's Dilemma shows that rational choices and a lack of trust can lead to worse outcomes.

Each player has two choices:

• Cooperate with each other
• Act in self-interest (defect)

Even though cooperation helps both players, the fear of being taken advantage of often pushes people to defect.

Trust is risky, but in many cases, without trust you can end up worse off.

The Cold War: A Real-Life Example of the Prisoner's Dilemma

During the Cold War, the USA and USSR were repeatedly building nuclear weapons.

Each country feared that the other might attack if they stopped building these weapons, so neither backed down.

Both countries may have been safer if they had cooperated, but distrust made them keep competing.

This is a real-life example of the Prisoner's Dilemma: mistrust can lead to worse results for everyone.

Apple vs Samsung

Tech companies like Apple and Samsung are in constant competition. They make strategic choices about:

• Pricing
• Product releases
• New features

Choices:

• Cooperate: avoid price cuts and focus on innovation
• Compete: cut prices or "copy" features to gain profit

Outcome:

• If both cooperate, they both gain healthy profits
• If one competes whilst the other cooperates, the company competing will gain more market share
• If both compete, profits will drop

Insight: just like the Prisoner's Dilemma, companies must balance short-term gains against long-term benefits.

Where is Game Theory Used?

• Economics: pricing, competition, auctions
• Law: courtroom strategies and criminal law
• Politics: alliances, voting strategies and campaigning
• Military: strategy and defence
• Sports and gaming: developing optimal strategies for each player, understanding how to bet, and poker

Game Theory in Real Life

Everyone uses Game Theory in life, but you probably just don't realise it!

Examples:

1. Should I do all the work in this group project, or should I wait to see what others do?
2. Should I tell the truth, or say what people want to hear?
3. Should I help someone now, or will they take advantage of me in the future?

Game Theory helps you think about actions, consequences and trust.

Misunderstandings in Game Theory

Acting selfishly

People often assume that acting selfishly will lead to the best result for them.

But on many occasions, acting selfishly leads to worse outcomes for everyone, even yourself.

For example, if everyone in a group project wants to carry on with their own idea, the team will fall apart. Cooperation can actually give you better results too.

Oversimplifying

Game Theory is not just about "winning". Many situations have many possible outcomes, uncertainty and changes in behaviour.

Oversimplifying can lead to bad decisions.

In competitive situations, is it truly rational to trust your opponent?

What I Have Learnt and Why It Is Important

• I have learnt that game theory explains how people and organisations make decisions when their outcomes depend on each other.
• Concepts such as Nash Equilibrium show why people stick with certain strategies, even if the result isn't ideal for them.
• Game Theory highlights how strategic thinking and incentives can result in cooperation or even conflict.
• This is important because these ideas apply to real-life situations like politics, competition in business and everyday decision making.
• Understanding game theory helps us predict and understand behaviour, and helps create systems that encourage cooperation instead of conflict.