Game theory

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

It combines ideas from:

• mathematics,
• economics,
• psychology,
• political science,
• and strategy.

The “game” does not necessarily mean sports or video games.
A “game” means any situation where:

1. there are multiple decision-makers (“players”),
2. each has choices (“strategies”),
3. and each person’s result (“payoff”) depends on what everyone does.

Simple Example: Prisoner’s Dilemma

Two criminals are arrested separately.

Each has two choices:

• stay silent,
• or betray the other.

Outcomes

Player A	Player B	Result
Silent	Silent	both get light punishment
Betray	Silent	betrayer goes free, other gets heavy punishment
Silent	Betray	opposite
Betray	Betray	both get medium punishment

Even though cooperation gives a better combined result, fear and self-interest often push both to betray.

This illustrates a central idea of game theory:

Rational individual decisions can create bad collective outcomes.

Important Concepts

1. Strategy

A plan of action.

Example:

• cooperate,
• attack,
• negotiate,
• lower prices,
• raise prices.

2. Payoff

What each player gains or loses:

• money,
• power,
• survival,
• reputation,
• territory, etc.

3. Nash Equilibrium

A stable situation where no player gains by changing strategy alone.

Named after John Nash, whose life inspired the movie A Beautiful Mind.

Example:
If two competing shops settle into prices where neither can improve profit by changing prices alone, that is a Nash equilibrium.

Real-World Uses

Economics & Business

Companies decide:

• pricing,
• advertising,
• market competition,
• mergers.

Example:
Coca-Cola vs PepsiCo price wars.

Politics & War

Countries analyze:

• alliances,
• sanctions,
• nuclear deterrence,
• trade wars.

During the Cold War, game theory was heavily used to study nuclear strategy.

Biology

Animals also “play games”:

• cooperation,
• competition,
• mating behavior,
• survival strategies.

Everyday Life

• salary negotiation,
• traffic behavior,
• dating,
• auctions,
• sports tactics.

Types of Games

Cooperative Games

Players can make binding agreements.

Non-Cooperative Games

Each player acts independently.

Zero-Sum Games

One side’s gain equals the other’s loss.

Example:
Chess.

Non-Zero-Sum Games

Both can gain or lose together.

Example:
Trade agreements.

One Famous Formula

In many strategic situations, probabilities matter. Mixed strategies use probability distributions over choices.

For example, in a simple mixed strategy setup:

$P(A)=p,\;P(B)=1-p$

This means a player chooses strategy A with probability $p$ and strategy B with probability $1-p$.

Main Insight

Game theory tries to answer:

“What is the smartest decision when others are also trying to be smart?”

It explains why:

• wars happen,
• cooperation fails,
• markets compete,
• alliances form,
• and sometimes irrational outcomes emerge from rational behavior.

• Here are some famous and easy-to-understand examples of game theory in real life.

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  1. Price War Between Companies

  Two companies sell the same product.

  Example:
  Apple vs Samsung

  Each can:

  • keep prices high,
  • or cut prices.

  Situation

  Apple	Samsung	Result
  High price	High price	both earn high profit
  Low price	High price	Apple gains customers
  High price	Low price	Samsung gains customers
  Low price	Low price	both earn less

  Problem:
  Even though both prefer high prices, fear of losing customers pushes both toward lowering prices.

  This is similar to the Prisoner’s Dilemma.

  ---

  2. Nuclear Deterrence During the Cold War

  During the Cold War, the United States and Soviet Union both had nuclear weapons.

  Choices:

  • attack,
  • or not attack.

  Logic

  If one attacks first:

  • both may be destroyed.

  So both avoid war.

  This became known as:

  Mutually Assured Destruction (MAD)

  Game theory showed:

  Fear of total destruction can actually prevent war.

  ---

  3. Traffic Example

  Imagine two drivers approaching a narrow road.

  Each can:

  • cooperate,
  • or aggressively move first.

  Driver A	Driver B	Result
  Cooperate	Cooperate	smooth traffic
  Aggressive	Cooperate	aggressive driver wins
  Aggressive	Aggressive	crash/jam

  This explains:

  • traffic jams,
  • road rage,
  • queue-cutting.

  ---

  4. Football Penalty Kick

  In soccer, a striker and goalkeeper both guess.

  Striker:

  • shoot left,
  • or right.

  Goalkeeper:

  • dive left,
  • or right.

  If both choose same side → save.
  Different side → goal.

  Players therefore randomize choices.

  This is called a mixed strategy.

  $P(\text{Left})=p,\;P(\text{Right})=1-p$

  The player intentionally becomes unpredictable.

  ---

  5. Auction Bidding

  Suppose 5 people bid for a rare painting.

  Each person must guess:

  • how much others value it,
  • and how high they may bid.

  If you bid:

  • too low → lose,
  • too high → overpay.

  This is studied in auction game theory.

  Governments use this for:

  • oil fields,
  • telecom spectrum,
  • contracts.

  ---

  6. The “Chicken Game”

  Two cars drive toward each other.

  Choices:

  • swerve,
  • or continue.

  A	B	Result
  Swerve	Continue	A loses pride
  Continue	Swerve	B loses pride
  Swerve	Swerve	both safe
  Continue	Continue	disaster

  This model is often used in:

  • military standoffs,
  • political brinkmanship,
  • crisis diplomacy.

  Analysts sometimes compare crises like the Cuban Missile Crisis to this game.

  ---

  7. Advertising Competition

  Two cola companies decide:

  • advertise heavily,
  • or spend less.

  If both advertise heavily:

  • costs rise,
  • profits fall.

  But if one advertises while the other stays quiet:

  • advertiser gains market share.

  So both keep spending huge amounts.

  ---

  8. Family Example

  Two siblings must clean a room.

  Choices:

  • help,
  • or avoid work.

  If both help:

  • job finishes quickly.

  If one avoids:

  • the other does more work.

  If both avoid:

  • parents become angry.

  This is game theory at home.

  ---

  9. Evolution and Animals

  Game theory is used in biology.

  Example:
  Two deer fighting.

  Choices:

  • fight aggressively,
  • or display strength without fighting.

  Real fighting may cause injury, so animals often evolve “ritual competition” instead of constant deadly fights.

  This is called evolutionary game theory.

  ---

  10. Trade War Between Countries

  Two countries can:

  • cooperate on trade,
  • or impose tariffs.

  If both cooperate:

  • both economies benefit.

  If one imposes tariffs:

  • it may temporarily protect industries.

  If both impose tariffs:

  • trade shrinks,
  • prices rise,
  • both suffer.

  This logic appears in many modern trade disputes.

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  Why Game Theory Matters

  It helps explain:

  • why cooperation is difficult,
  • why conflicts happen,
  • why trust matters,
  • why competition sometimes hurts everyone,
  • and why rational people can create irrational outcomes.

  It is widely used in:

  • economics,
  • military strategy,
  • AI,
  • diplomacy,
  • business,
  • politics,
  • psychology,
  • and even dating apps and online platforms.