Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/308706 
Year of Publication: 
2023
Citation: 
[Journal:] Dynamic Games and Applications [ISSN:] 2153-0793 [Volume:] 13 [Issue:] 4 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 1156-1193
Publisher: 
Springer US, New York, NY
Abstract: 
The prisoner's dilemma, the snowdrift game, and the stag hunt are two-player symmetric games that are often considered as prototypical examples of cooperative dilemmas across disciplines. However, surprisingly little consensus exists about the precise mathematical meaning of the words "cooperation" and "cooperative dilemma" for these and other binary-action symmetric games, in particular when considering interactions among more than two players. Here, we propose definitions of these terms and explore their evolutionary consequences on the equilibrium structure of cooperative dilemmas in relation to social optimality. We show that our definition of cooperative dilemma encompasses a large class of collective action games often discussed in the literature, including congestion games, games with participation synergies, and public goods games. One of our main results is that regardless of the number of players, all cooperative dilemmas—including multi-player generalizations of the prisoner's dilemma, the snowdrift game, and the stag hunt—feature inefficient equilibria where cooperation is underprovided, but cannot have equilibria in which cooperation is overprovided. We also find simple conditions for full cooperation to be socially optimal in a cooperative dilemma. Our framework and results unify, simplify, and extend previous work on the structure and properties of cooperative dilemmas with binary actions and two or more players.
Subjects: 
Cooperation
Social dilemmas
Cooperative dilemmas
Multiplayer games
Evolutionarily stable strategy
Bernstein transforms
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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