<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We analyse <italic>Give and Take</italic>, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to <italic>Give and Take</italic> is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a built-in punishment action. This game allows us to study cooperation in sharing an indivisible and durable resource. Since there are multiple strategies to cooperate, <italic>Give and Take</italic> provides a base to investigate coordination under implicit or explicit agreements. We discuss its position in face of other games and real world situations that are better modelled by it. The paper presents an in-depth analysis of the game for the range of admissible parameter values. We show that, when taking is costly for both players, cooperation emerges as players prefer to give the resource.</p></abstract>

We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a built-in punishment action. This game allows us to study cooperation in sharing an indivisible and durable resource. Since there are multiple strategies to cooperate, Give and Take provides a base to investigate coordination under implicit or explicit agreements. We discuss its position in face of other games and real world situations that are better modelled by it. The paper presents an in-depth analysis of the game for the range of admissible parameter values. We show that, when taking is costly for both players, cooperation emerges as players prefer to give the resource.

The <italic>Give and Take</italic> Game: Analysis of a Resource Sharing Game

BioISI—Biosystems & Integrative Sciences Institute, Faculty of Sciences University of Lisbon, Campo Grande, 1749-016 Lisbon, Portugal

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The  Game: Analysis of a Resource Sharing Game

We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and...

The Give and Take Game: Analysis of a Resource Sharing Game

Publicado en línea: 30 dic 2015

Páginas: 753 - 767

Recibido: 23 jul 2014

DOI: https://doi.org/10.1515/amcs-2015-0054

Palabras clave
two player game, cooperation agreements, social behaviours, resource model

© 2015 Pedro Mariano et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Give and Take Game: Analysis of a Resource Sharing Game

Publicado en línea: 30 dic 2015

Páginas: 753 - 767

Recibido: 23 jul 2014

DOI: https://doi.org/10.1515/amcs-2015-0054

Palabras clavetwo player game, cooperation agreements, social behaviours, resource model

© 2015 Pedro Mariano et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Palabras clave
two player game, cooperation agreements, social behaviours, resource model