♟️ Game Theory
Definition: The study of mathematical models of strategic interaction between rational agents. Used to analyze situations where the outcome for each participant depends on the choices of all.
John von Neumann & Oskar Morgenstern (1944); John Nash (1950) Key courses: Wharton MGEC 612, Booth BUSN 20200, HBS competitive strategy
🔑 Core Concepts
Players, Strategies, Payoffs
Every game has:
- Players: Who is making decisions?
- Strategies: What choices are available?
- Payoffs: What are the outcomes for each combination of choices?
- Information: Is it a complete or incomplete information game?
Nash Equilibrium
“A set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy.” — John Nash (Nobel Prize 1994)
How to find: Ask “Given what my opponent is doing, is this the best I can do?” If yes for all players → Nash Equilibrium.
🎲 The Prisoner’s Dilemma
The most famous game in game theory — illustrates why rational individuals fail to cooperate even when cooperation benefits everyone.
Setup: Two suspects arrested separately for a crime. Each can confess or stay silent.
| B stays silent | B confesses | |
|---|---|---|
| A stays silent | A: 1yr, B: 1yr | A: 10yr, B: 0yr |
| A confesses | A: 0yr, B: 10yr | A: 5yr, B: 5yr |
Nash Equilibrium: Both confess → (5yr, 5yr) But cooperative outcome: Both silent → (1yr, 1yr) — better for both!
Insight: Individually rational behavior leads to collectively suboptimal outcomes. This explains:
- Arms races between countries
- Price wars between competitors
- Overgrazing of common resources (Tragedy of the Commons)
- Advertising wars that increase total cost but not total sales
Escaping the Dilemma
In repeated games, cooperation can emerge:
- Tit-for-Tat: Cooperate first, then mirror opponent’s last move
- Commitment devices: Contracts, bonds, reputation
- Communication: Pre-game coordination
🏢 Game Theory in Business Strategy
Simultaneous vs. Sequential Games
| Type | Description | Example |
|---|---|---|
| Simultaneous | Both players choose at same time | Pricing, product launch |
| Sequential | Players choose in turn | Negotiation, M&A bid |
Dominant Strategies
A strategy that is best regardless of what the opponent does. If found, the answer is clear.
First-Mover vs. Second-Mover Advantage
| Situation | Advantage | Example |
|---|---|---|
| Commitment matters | First mover | Capacity expansion to deter entry |
| Learning/adaptation matters | Second mover | Seeing competitors’ mistakes |
| Scale/network effects | First mover | Marketplace platforms |
📊 Business Applications
Entry Deterrence
An incumbent can commit to aggressive response to deter entry:
- Excess capacity (can flood market if entrant comes)
- Long-term contracts with customers (switching costs)
- Reputation for fighting entry (builds credibility)
Auctions
- First-price sealed bid: Winner’s curse — tendency to overbid
- Second-price (Vickrey): Bid true value; winner pays 2nd highest bid
- English ascending: Most visible; used for art, real estate
- Google AdWords: Second-price auction (now modified)
Price Wars
Why price wars happen and why they destroy value:
- Each firm rationally cuts price expecting to gain share
- All firms cut → all lose margins → prisoner’s dilemma in action
- Exit: Long-term pricing contracts, product differentiation, signaling
🔗 Connected Concepts
- Porter’s Five Forces — Supplier/buyer power is a bargaining game
- Negotiation Strategies — BATNA and ZOPA as game payoffs
- Competitive Advantage — Sustainability depends on game dynamics
- Behavioral Economics Overview — Real people deviate from rational game theory
🏫 School Context
- Wharton: Game theory integrated into competitive strategy; MGEC 612
- Booth: Economics lens — IO theory uses game theory for oligopoly analysis
- HBS: Applied via cases; rarely taught formally but implicit in strategy courses
← 📈 Economics MOC | Related: Negotiation Strategies · Competitive Advantage · Porter’s Five Forces