18.15: Finitely Repeated Games

Repeated games are scenarios where the same game is played multiple times by the same participants. These games are fundamental in understanding how decision-making processes evolve over time.

Finitely Repeated Games: These games occur a specific number of times.

Consider two software firms that are in competition, releasing updates to their software every quarter. Each quarter, these firms must decide on their strategic approach: they can either invest heavily in developing innovative new features or opt to cut costs by implementing only minor fixes and updates.

Strategic Adjustments:

Final Round Strategy: As the final quarter approaches, firms are motivated to cut costs significantly to maximize profits.

Backward Induction: Knowing the final quarter is near, firms anticipate minimal innovation in the final quarter, leading them to reduce investments earlier, potentially starting in the previous quarters.

Long-term Impact: This knowledge pushes the firms to adopt cost-saving strategies ever earlier quarters. Ultimately, both firms adopt cost-saving strategies from the start, despite the potential for higher collective profits through sustained innovation.

By studying repeated games, one gains insight into the dynamic evolution of strategic decision-making, as players of the game strike the balance between competition and cooperation, as well as the impact of game length on player behavior.

Repeated games involve playing the same game multiple times with the same players. These games are crucial in understanding how decisions evolve over time.

Finitely repeated games are played a specific number of times.

Consider two lemonade stands competing from May to August.

At the start of each month, they decide whether to keep the price high for better profit or keep it low to attract more customers.

Assume both stands agree to cooperate by setting a high price.

As the final month approaches, players adjust their strategies, knowing there will be no future rounds for retaliation or cooperation.

By August, both stands are likely to drop their prices to capture more customers.

Each stand expects the other to reduce prices in the final month. So, they might start lowering prices in July.

The logic continues all the way back to the first month, and both stand set a low price from the start.

Knowing the game will eventually end encourages them to adopt a competitive strategy from the start.

This method of solving a game backward is known as backward induction.

• Finitely Repeated Games – These are games that occur a specific number of times.
• Strategic Adjustments – Changes in strategies based on game outcomes.
• Final Round Strategy – A strategy mainly focused on the last round of the game.
• Backward Induction – Process to predict future outcomes based on current game status.
• Long-term Impact – The lasting effect of the strategic decisions made during the game.

• Define Finitely Repeated Games – Understand why and when they occur (e.g., finitely repeated games).
• Contrast Individual round Strategy vs Final Round Strategy – Identify their characteristics (e.g., Backward Induction).
• Explore Examples – Understand the decision-making process in software firms (e.g., Final Round Strategy).
• Explain Backward Induction – Understand predictions based on current game status.
• Apply in Context – Understand the impact of these games on long term strategic planning.

• [Question 1] What are Finitely Repeated Games and how do they influence strategic adjustments?
• [Question 2] How does Final Round Strategy contrast with strategies for other rounds?
• [Question 3] How does Backward Induction impact the long term strategies?

• Students – Dive into the decision-making process in Finitely Repeated Games
• Educators – It provides a clear framework for teaching Game Theory Repeated Games
• Researchers – Understand the evolution of strategic decisions in Repeated Games
• Game Theory Enthusiasts – Gain insights on Backward Induction and its impact on games