Game Theory: Repeated Game vs. One-Shot Game

📌 “In a one-shot game, you think once. In a repeated game, you think about the future.” The shadow of future interactions changes everything in strategic decision-making.

Game theory studies how rational players make decisions. The structure of the game—whether it is played once or repeatedly—has a huge impact on the strategies and outcomes. This article explains the fundamental differences.

What is a One-Shot Game?

A one-shot game is played only once. Players make their moves simultaneously or in sequence, and then the game ends. There is no future interaction, so players only consider the immediate payoff.

Example 1 The Prisoner's Dilemma (One-Shot)

Two prisoners are interrogated separately. They can either Cooperate (stay silent) or Defect (confess). The payoff matrix is:

Prisoner's Dilemma Payoffs
Player A \ Player B	Cooperate	Defect
Cooperate	Both get 1 year	A gets 3 years, B goes free
Defect	A goes free, B gets 3 years	Both get 2 years

🔍 Explanation: In a one-shot game, the dominant strategy for each player is to Defect. Even though mutual cooperation yields a better outcome (1 year each), the fear of being betrayed leads to the worse Nash equilibrium (2 years each). Future punishment is impossible.

Example 2 Rock-Paper-Scissors Tournament Final

Imagine the final match of a Rock-Paper-Scissors tournament. You play one round against your opponent to decide the champion. There is no second chance.

🔍 Explanation: This is a pure one-shot game. Your strategy is based entirely on predicting your opponent's single move. You cannot adapt or learn from previous rounds within this match. The outcome is final.

What is a Repeated Game?

A repeated game is the same base game played multiple times over a period. Players remember past actions and can use future rounds to reward cooperation or punish betrayal. This possibility enables cooperative outcomes that are impossible in one-shot games.

Example 1 The Repeated Prisoner's Dilemma

The same two prisoners face the same dilemma every day for a month. Their sentences are added up at the end.

🔍 Explanation: Now, a player can use a tit-for-tat strategy: start by cooperating, and then copy whatever the other player did in the previous round. If Player B defects on Day 1, Player A can defect on Day 2 as punishment. The threat of future retaliation makes mutual cooperation a stable and rational outcome.

Example 2 Business Partnership

Two companies repeatedly negotiate supply contracts. If one company cheats on quality or price in one deal, the other can refuse to work with them in the next deal.

🔍 Explanation: This repeated interaction builds trust and encourages fair play. The fear of losing future profitable deals prevents short-term cheating. The relationship itself becomes a valuable asset that enforces cooperation.

Key Differences at a Glance

Repeated Game vs. One-Shot Game
Aspect	One-Shot Game	Repeated Game
Time Horizon	Single interaction	Multiple interactions over time
Strategy Focus	Immediate payoff	Long-term payoff & reputation
Cooperation	Often irrational (e.g., Prisoner's Dilemma)	Can be rational and stable
Equilibrium	Static Nash Equilibrium	Dynamic equilibria (e.g., Grim Trigger, Tit-for-Tat)
Information Use	Only initial knowledge	Learning from past rounds

⚠️ Common Pitfalls and Misunderstandings

Pitfall 1: Assuming repeated games always lead to cooperation. Cooperation is only sustainable if the future is important enough (high enough discount factor). If the game is ending soon, players may start defecting.
Pitfall 2: Confusing the game structure. A series of one-shot games with different players is NOT a repeated game. A repeated game involves the same players facing each other again.
Pitfall 3: Overlooking the Folk Theorem. This theorem states that in infinitely repeated games, almost any payoff outcome can be an equilibrium if players are patient enough. This means many outcomes are possible, not just one.

Why the Difference Matters

Understanding whether a situation is a one-shot or repeated game helps predict behavior. In business, diplomacy, and everyday life, we often unconsciously switch between these modes. Recognizing the structure allows for better strategy.

Trade Agreements: Treaties are repeated games. Cheating can lead to trade wars, so nations are incentivized to cooperate.
Online Marketplaces: Seller reviews create a "pseudo-repeated" game. A seller with a long-term reputation (high rating) is less likely to cheat a single buyer.
Traffic Laws: Your daily commute is a repeated game with other drivers. Consistent rules (like stopping at red lights) emerge because we encounter each other repeatedly.