The Convergence of Reciprocation: (Extended Abstract)

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People often interact repeatedly: with relatives, through file sharing, in politics, etc. Many such interactions are reciprocal: reacting to the actions of the other. In order to facilitate decisions regarding reciprocal interactions, we analyze the development of reciprocation over time. To this end, we propose a model for such interactions that is simple enough to enable formal analysis, but is sufficient to predict how such interactions will evolve. Inspired by existing models of international interactions and arguments between spouses, we suggest a model with two reciprocating attitudes where an agent's action is a weighted combination of the others' last actions (reacting) and either i) her innate kindness, or ii) her own last action (inertia). We analyze a network of repeatedly interacting agents, each having one of these attitudes, and prove that their actions converge to specific limits. Convergence means that the interaction stabilizes, and the limits indicate the behavior after the stabilization. For two agents, we describe the interaction process and find the limit values. For a general connected network, we find these limit values if all the agents employ the second attitude, and show that the agents' actions then all become equal. In the other cases, we study the limit values using simulations. We discuss how these results predict the development of the interaction and constitute the first step towards helping agents decide on their behavior.
Original languageEnglish
Title of host publicationAAMAS '16 Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems
EditorsC. Jonker, S. Marsella, J. Thangarajah, K. Thuyls
Place of PublicationRichland
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Number of pages2
ISBN (Print)978-1-4503-4239-1
Publication statusPublished - 2016
EventAAMAS 2016 : 15th International Conference on Autonomous Agents and Multiagent Systems - Singapore, Singapore
Duration: 9 May 201613 May 2016
Conference number: 15


ConferenceAAMAS 2016
Abbreviated titleAAMAS
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • agent's influence
  • behavior
  • convergence
  • perron-frobenius
  • reciprocal interaction
  • repeated reciprocation


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