Interconnected gears with a shrinking circle symbolizing strategic interactions and economic challenges.

Unlocking Cooperation: How Overlapping Generations Can Redefine Game Theory

Lena Kashyap in Business & Economy December 2025 • 4 min read.

"Explore the groundbreaking research that reveals how overlapping generations and strategic interactions shape economic outcomes, challenging traditional game theory assumptions."

In the world of economics, understanding how people cooperate (or don't) is crucial. Game theory provides a set of tools to analyze strategic interactions. But what happens when these interactions aren't one-off events, but rather ongoing relationships between successive generations? This is where the concept of overlapping generations (OLG) comes in, adding a layer of complexity that mirrors real-world scenarios.

Imagine a business where employees work for a set period before retiring, their roles then taken by new recruits. Or consider communities where each generation builds upon the legacy of the last. These scenarios are classic examples of OLG, and they have profound implications for how cooperation can be sustained over time. Unlike traditional game theory, where players might only interact once, OLG introduces the idea of repeated interactions, but with a twist: the players are constantly changing.

New research is shedding light on how these overlapping relationships affect the potential for cooperation. By studying the 'feasible payoff set' in OLG repeated games, economists are uncovering surprising insights into the factors that promote or hinder collaboration. This understanding has implications for businesses, policy-making, and any situation where long-term strategic planning is essential.

What is the Feasible Payoff Set and Why Does it Matter?

Interconnected gears with a shrinking circle symbolizing strategic interactions and economic challenges.

In game theory, the 'feasible payoff set' represents all the possible outcomes that players can achieve through strategic interactions. Think of it as the range of potential rewards (or costs) that can result from different choices. In traditional repeated games, economists often focus on the convex hull of stage game payoffs, which are the immediate rewards or penalties of each player’s actions. However, in OLG games, the picture becomes more intricate.

The overlapping structure allows players to achieve average discounted payoffs that lie outside the typical convex hull. This happens because, while players might share the same discount factor (how much they value future rewards compared to present ones), they discount payoffs differently based on their position in the lifecycle. A younger player might prioritize long-term gains, while an older player might focus on immediate benefits.

Characterizing Feasible Payoffs: The research completely characterizes the set of feasible payoffs for OLG games, considering fixed discount factors and interaction lengths. This leads to a closed-form understanding of the feasible payoff set.
Comparative Statics: The study offers new insights into how the feasible payoff set changes with respect to the discount factor and the length of interaction.
Counterintuitive Findings: Surprisingly, the feasible payoff set can shrink as players' discount factors increase. This challenges traditional assumptions about patience always leading to greater cooperation.
Monotonicity Conditions: The research identifies the conditions under which this shrinking effect is strict, providing a nuanced understanding of when increased patience hinders, rather than helps, cooperation.

These findings are significant because they challenge the conventional wisdom that more patient players will always lead to greater cooperation. In OLG settings, the dynamics are more complex, and strategies need to account for the changing incentives of each generation.

The Future of Cooperation: Implications and Further Research

This research opens new avenues for understanding cooperation in dynamic environments. By providing a clearer picture of the feasible payoff set in OLG games, it offers a valuable benchmark for analyzing equilibrium behavior and designing strategies that promote long-term collaboration. Further research can build on these findings by exploring the role of asymmetric information, reputation, and evolving social norms in shaping cooperation across generations. As our world becomes increasingly interconnected and interdependent, understanding these dynamics will be crucial for building sustainable and prosperous societies.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2303.12988,

Title: Characterizing The Feasible Payoff Set Of Olg Repeated Games

Subject: econ.th

Authors: Daehyun Kim, Chihiro Morooka

Published: 22-03-2023

Everything You Need To Know

What is the core concept of 'overlapping generations' (OLG) in the context of game theory, and how does it differ from traditional game theory?

In the realm of game theory, 'overlapping generations' (OLG) introduce the idea of repeated interactions across generations, such as in a business with employee turnover or in communities. Unlike traditional game theory, where interactions are often one-off events, OLG incorporates the concept of ongoing relationships between successive generations. This change creates a dynamic environment where players are constantly changing, and their incentives and priorities evolve, influencing the potential for cooperation. The OLG model is more complex than traditional game theory and allows for a more realistic representation of real-world scenarios where cooperation is sustained over time.

How does the 'feasible payoff set' function in Overlapping Generations games, and why is it crucial for understanding cooperation in these scenarios?

The 'feasible payoff set' in OLG games represents all possible outcomes players can achieve through their strategic interactions. This set, which includes the range of potential rewards or costs, is crucial for understanding cooperation because the overlapping structure allows players to achieve average discounted payoffs that lie outside the typical convex hull. Because of the different positions in the lifecycle, players discount payoffs differently. Younger players might focus on long-term gains, while older players might prioritize immediate benefits. It completely characterizes the set of feasible payoffs for OLG games considering fixed discount factors and interaction lengths. Understanding the feasible payoff set helps analyze equilibrium behavior and design strategies to promote long-term collaboration.

What are the key insights about discount factors within the context of Overlapping Generations, and how do they challenge conventional wisdom?

Within Overlapping Generations (OLG), the study offers new insights into how the feasible payoff set changes concerning the discount factor. Surprisingly, the feasible payoff set can shrink as players' discount factors increase. This counterintuitive finding challenges the conventional wisdom that patience always leads to greater cooperation. The research identifies the conditions under which this shrinking effect is strict, providing a nuanced understanding of when increased patience hinders, rather than helps, cooperation. This contrasts traditional views and highlights the complexity of cooperation dynamics in OLG settings.

How does the research on Overlapping Generations contribute to a better understanding of cooperation in businesses and long-term strategic planning?

The research on Overlapping Generations (OLG) has significant implications for businesses and long-term strategic planning by providing a clearer picture of the feasible payoff set. Businesses can better analyze equilibrium behavior and design strategies that promote long-term collaboration, such as understanding how different generations of employees value present versus future rewards. The research challenges the traditional assumptions that more patient players always lead to greater cooperation. In OLG settings, the dynamics are more complex, and strategies need to account for the changing incentives of each generation, allowing for a deeper understanding of how cooperation can be sustained over time and ultimately impacting the long-term success of the business.

What are some potential avenues for future research based on the findings related to Overlapping Generations and cooperation, and what is the broader significance of this research?

The research on Overlapping Generations (OLG) opens new avenues for understanding cooperation in dynamic environments. Future research can build on the findings by exploring the role of asymmetric information, reputation, and evolving social norms in shaping cooperation across generations. This could lead to a more nuanced understanding of how these factors influence the feasible payoff set and equilibrium behavior in OLG games. The broader significance of this research lies in its potential to help build sustainable and prosperous societies, particularly in an increasingly interconnected and interdependent world. By providing a clearer picture of the dynamics of cooperation, this research offers a valuable benchmark for designing strategies to promote long-term collaboration across generations.