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.