We study a class of non-cooperative aggregative games—referred to as social purpose games—in which the payoffs depend separately on a player’s own strategy (individual bene- fits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assess- ment of a common social benefit across players. We show that these games have a weighted potential, and we investigate its properties. We investigate the payoff structure and the unique- ness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators, while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of strict social pur- pose games. As a particular application, we study a standard formulation of the tragedy of the commons. We show that there emerges a single stable coalition of cooperators that curbs the over-exploitation of the common resource.

Emergent Collaboration in Social Purpose Games / Gilles, Robert P.; Mallozzi, Lina; Messalli, Roberta. - In: DYNAMIC GAMES AND APPLICATIONS. - ISSN 2153-0785. - 13:(2023), pp. 566-588. [10.1007/s13235-022-00457-9]

Emergent Collaboration in Social Purpose Games

Robert P. Gilles;Lina Mallozzi;Roberta Messalli
2023

Abstract

We study a class of non-cooperative aggregative games—referred to as social purpose games—in which the payoffs depend separately on a player’s own strategy (individual bene- fits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assess- ment of a common social benefit across players. We show that these games have a weighted potential, and we investigate its properties. We investigate the payoff structure and the unique- ness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators, while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of strict social pur- pose games. As a particular application, we study a standard formulation of the tragedy of the commons. We show that there emerges a single stable coalition of cooperators that curbs the over-exploitation of the common resource.
2023
Emergent Collaboration in Social Purpose Games / Gilles, Robert P.; Mallozzi, Lina; Messalli, Roberta. - In: DYNAMIC GAMES AND APPLICATIONS. - ISSN 2153-0785. - 13:(2023), pp. 566-588. [10.1007/s13235-022-00457-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/890792
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