| Abstract: |
| The tragedy of the commons (TOTC) states that individual incentives result in the overuse of common pool resources (CPRs), which may have detrimental future consequences for everyone. However, in many real-life situations this does not occur, and researchers such as Nobel laureate Elinor Ostrom have suggested that mutual restraint by individuals can prevent it. In mean field games (MFGs), since individuals are insignificant and non-cooperative, TOTC is inevitable. This suggests that MFGs with CPRs must incorporate both selfishness and altruism to better capture real-world behavior. Motivated by this, we discuss equilibrium notions blending cooperative and non-cooperative actions.
We introduce mixed-individual and mixed-population MFGs, together with modeling of CPRs. The former captures altruism at individual levels, while the latter represents a population composed of cooperative and non-cooperative individuals. For both, we outline equilibrium definitions, and their characterization via FBSDEs. We then present a fisheries-inspired example, discussing existence, uniqueness, and experimental results.
Finally, we address the challenge that understanding intervention policies in mixed MFGs requires knowledge of individuals` altruism levels, which are unobservable. We therefore consider how these levels can be learned from data using inverse learning. (Based on works with Mathieu Lauriere, and with Xiaofei Shi, Haoyang Cao) |
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