♟️ 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 silentB confesses
A stays silentA: 1yr, B: 1yrA: 10yr, B: 0yr
A confessesA: 0yr, B: 10yrA: 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

TypeDescriptionExample
SimultaneousBoth players choose at same timePricing, product launch
SequentialPlayers choose in turnNegotiation, 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

SituationAdvantageExample
Commitment mattersFirst moverCapacity expansion to deter entry
Learning/adaptation mattersSecond moverSeeing competitors’ mistakes
Scale/network effectsFirst moverMarketplace 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


🏫 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