Optimistic and Pessimistic Approaches for Cooperative Games: Insights and Applications

Core Concepts

The author explores the optimistic and pessimistic approaches in cooperative game theory, providing insights into strategic interactions.

Abstract

The content delves into cooperative game theory, focusing on the division of joint value among players. It discusses various models accounting for player cooperation levels and external influences. The paper clarifies the interpretation of optimistic and pessimistic approaches by providing a unified framework. It also explores applications to derive results from existing literature. The authors introduce operators to determine marginal contributions based on best and worst-case scenarios. They argue that ensuring allocations do not exceed optimistic upper bounds is as challenging as surpassing pessimistic lower bounds. The study shows that with negative externalities, both objectives are always feasible. By applying a general model accommodating direct and indirect externalities, two families of coalitional games are built. The relationships between anti-core and core of resulting cooperative games are explored. The study provides insights into well-studied applications like queueing theory, minimum cost spanning tree problems, river sharing problems, pipeline externalities problems, facility location, and knapsack problems. The paper concludes by discussing duality in dual games like bankruptcy claims and airport problems. It establishes connections between optimistic and pessimistic games in various applications.

Stats

Various models account for different levels of player cooperation (Hsiao & Raghavan, 1993). Partition function form games consider behavior of players outside the coalition (K´oczy, 2018). Curiel & Tijs introduced minimarg/maximarg operators for marginal contributions (1991). Shapley value assigns payoff based on agents' marginal contributions (Shapley, 1953). Dual games exhibit coincidence between anti-core of pessimistic game and core of optimistic game (Proposition 2).

Quotes

"Ensuring allocations do not exceed optimistic upper bounds is as challenging as surpassing pessimistic lower bounds." "The anti-core of the optimistic game is always a subset of the core of the pessimistic game." "The minimal transfer rule offers allocations below optimistic bounds but above pessimistic bounds." "The maximal transfer rule offers allocations above pessimistic bounds but not always below optimistic bounds." "Anti-core of the optimistic game is a subset of the core of the pessimistic game."

Key Insights Distilled From

Optimistic and pessimistic approaches for cooperative games

by Ata Atay,Chr... at arxiv.org 03-05-2024

https://arxiv.org/pdf/2403.01442.pdf

Deeper Inquiries

How can cooperative game theory be applied beyond economic contexts

Cooperative game theory can be applied beyond economic contexts in various fields such as political science, environmental studies, and social psychology. In political science, it can help analyze coalition formation among different parties or countries to achieve common goals. Environmental studies can benefit from cooperative game theory by examining issues like resource management, pollution control, and climate change mitigation through collaborative efforts. In social psychology, the theory can be used to understand group dynamics, decision-making processes, and conflict resolution strategies within interpersonal relationships.

What counterarguments exist against using only optimistic or pessimistic approaches in cooperative games

While optimistic and pessimistic approaches provide valuable insights into strategic interactions in cooperative games, using only one approach may not capture the full complexity of real-world scenarios. One counterargument against solely relying on these approaches is that they oversimplify the dynamics of cooperation by assuming extreme perspectives. In reality, players may exhibit a combination of optimistic and pessimistic behaviors depending on the context and their individual preferences. By considering a broader range of strategies and attitudes towards cooperation, a more nuanced understanding of cooperative games can be achieved.

How does understanding water sharing problems contribute to broader discussions on resource allocation

Understanding water sharing problems contributes to broader discussions on resource allocation by highlighting the complexities involved in equitable distribution and efficient utilization of limited resources. These problems often involve multiple stakeholders with competing interests who must collaborate to manage shared resources sustainably. By studying water sharing issues through the lens of cooperative game theory, insights can be gained into negotiation strategies, incentive mechanisms for cooperation, and potential solutions for resolving conflicts over resource allocation. This knowledge is transferable to other resource management challenges across different sectors where collaboration among diverse actors is essential for achieving optimal outcomes while ensuring fairness and sustainability.