Reciprocation Effort Games

Gleb Polevoy; Mathijs De Weerdt

doi:10.1007/978-3-319-76892-2_4

Reciprocation Effort Games

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Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.

Original language	English
Title of host publication	Artificial Intelligence
Subtitle of host publication	29th Benelux Conference, BNAIC 2017, Revised Selected Papers
Editors	B. Verheij, M. Wiering
Place of Publication	Cham
Publisher	Springer
Pages	46-60
Number of pages	15
ISBN (Electronic)	978-3-319-76892-2
ISBN (Print)	978-3-319-76891-5
DOIs	https://doi.org/10.1007/978-3-319-76892-2_4
Publication status	Published - 2018
Event	29th Benelux Conference on Artificial Intelligence: 29th Benelux Conference on Artificial Intelligence - Groningen, Netherlands Duration: 8 Nov 2017 → 9 Nov 2017 Conference number: 29 http://bnaic2017.ai.rug.nl/

Publication series

Name	Communications in Computer and Information Science
Publisher	Springer
Volume	823
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	29th Benelux Conference on Artificial Intelligence
Abbreviated title	BNAIC 2017
Country/Territory	Netherlands
City	Groningen
Period	8/11/17 → 9/11/17
Internet address	http://bnaic2017.ai.rug.nl/

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

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.

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10.1007/978-3-319-76892-2_4

Polevoy-Weerdt2018_Chapter_ReciprocationEffortGamesFinal published version, 411 KB

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title = "Reciprocation Effort Games",

abstract = "Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.",

author = "Gleb Polevoy and {De Weerdt}, Mathijs",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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.; 29th Benelux Conference on Artificial Intelligence : 29th Benelux Conference on Artificial Intelligence, BNAIC 2017 ; Conference date: 08-11-2017 Through 09-11-2017",

year = "2018",

doi = "10.1007/978-3-319-76892-2_4",

language = "English",

isbn = "978-3-319-76891-5",

series = "Communications in Computer and Information Science",

publisher = "Springer",

pages = "46--60",

editor = "B. Verheij and Wiering, {M. }",

booktitle = "Artificial Intelligence",

url = "http://bnaic2017.ai.rug.nl/",

}

Polevoy, G & De Weerdt, M 2018, Reciprocation Effort Games. in B Verheij & M Wiering (eds), Artificial Intelligence : 29th Benelux Conference, BNAIC 2017, Revised Selected Papers. Communications in Computer and Information Science, vol. 823, Springer, Cham, pp. 46-60, 29th Benelux Conference on Artificial Intelligence, Groningen, Netherlands, 8/11/17. https://doi.org/10.1007/978-3-319-76892-2_4

Reciprocation Effort Games. / Polevoy, Gleb; De Weerdt, Mathijs.
Artificial Intelligence : 29th Benelux Conference, BNAIC 2017, Revised Selected Papers. ed. / B. Verheij; M. Wiering. Cham: Springer, 2018. p. 46-60 (Communications in Computer and Information Science; Vol. 823).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - De Weerdt, Mathijs

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N2 - Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.

AB - Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.

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Reciprocation Effort Games

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