Cooperation, Competition, and Common Pool Resources in Mean Field Games

Explore the intersection of game theory and resource management in this mathematical conference talk that examines how cooperation and competition dynamics affect common pool resources within mean field games frameworks. Learn about the tragedy of the commons phenomenon, first introduced by Hardin in 1968, and discover how Nobel laureate Elinor Ostrom's research on mutual restraint challenges traditional assumptions about resource overuse. Understand why standard mean field games inevitably lead to the tragedy of the commons due to their fully non-cooperative nature, and examine proposed solutions that incorporate mixtures of selfishness and altruism to better model real-world scenarios. Delve into different equilibrium concepts including mixed individual mean field games and mixed population mean field games, both incorporating common pool resources to capture altruistic tendencies at individual levels and populations mixing cooperative and non-cooperative individuals. Study the mathematical characterization of equilibrium through forward backward stochastic differential equations, and analyze a practical fisheries example where fish stock serves as the common pool resource. Examine existence and uniqueness results while reviewing experimental findings that demonstrate these theoretical concepts in action.