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The Give and Take game: Analysis of a resource sharing game

Mariano P., Correia L.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 4

753--767

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.

Partner Selection Using Reputation Information in n-player Cooperative Games

Mariano P., Correia L.

Journal of Telecommunications and Information Technology

2014

nr 4

53--60

To study cooperation evolution in populations, it is common to use games to model the individuals interactions. When these games are n-player it might be di cult to assign defection responsibility to any particular individual. In this paper the authors present an agent based model where each agent maintains reputation information of other agents. This information is used for partner selection before each game. Any agent collects information from the successive games it plays and updates a private reputation estimate of its candidate partners. This approach is integrated with an approach of variable sized population where agents are born, interact, reproduce and die, thus presenting a possibility of extinction. The results now obtained, for cooperation evolution in a population, show an improvement over previous models where partner selection did not use any reputation information. Populations are able to survive longer by selecting partners taking merely into account an estimate of others' reputations.