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The generalized version of Hamilton’s rule

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  • Matthijs van Veelen

    (University of Amsterdam)

Abstract

The main ingredient of this paper is the derivation of the generalized version of Hamilton’s rule. This version is derived with the Generalized Price equation. The generalized version of Hamilton’s rule generalizes the original rule, in the sense that it produces a set of rules; one rule for every different model of how social interactions affect fitnesses. Every such Hamilton-like rule is generally valid; they all correctly determine when altruism, or costly cooperation, will be selected for, whatever model they are combined with. Every such rule, however, only has a meaningful interpretation in combination with the model it belongs to. The classic Hamilton’s rule is the generalized Hamilton’s rule that goes with the linear model. The insight that there are many Hamilton-like rules, all of which are generally valid, but none of which is generally meaningful, helps understand the controversy surrounding Hamilton’s rule, and provides a constructive way to always find a rule that both gets the direction of selection right, and has a meaningful interpretation.

Suggested Citation

  • Matthijs van Veelen, 2024. "The generalized version of Hamilton’s rule," Tinbergen Institute Discussion Papers 24-033/I, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20240033
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    File URL: https://papers.tinbergen.nl/24033.pdf
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    References listed on IDEAS

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    1. Patrick Abbot & Jun Abe & John Alcock & Samuel Alizon & Joao A. C. Alpedrinha & Malte Andersson & Jean-Baptiste Andre & Minus van Baalen & Francois Balloux & Sigal Balshine & Nick Barton & Leo W. Beuk, 2011. "Inclusive fitness theory and eusociality," Nature, Nature, vol. 471(7339), pages 1-4, March.
    2. Martin A. Nowak & Corina E. Tarnita & Edward O. Wilson, 2010. "The evolution of eusociality," Nature, Nature, vol. 466(7310), pages 1057-1062, August.
    3. Matthijs van Veelen & Julián García & Maurice W. Sabelis & Martijn Egas, 2010. "Call for a return to rigour in models," Nature, Nature, vol. 467(7316), pages 661-661, October.
    4. Peter D. Taylor & Troy Day & Geoff Wild, 2007. "Evolution of cooperation in a finite homogeneous graph," Nature, Nature, vol. 447(7143), pages 469-472, May.
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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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