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Hamilton’s rule in non-additive games

Hamilton’s rule in non-additive games
Hamilton’s rule in non-additive games
Recently a number of authors have questioned both the validity and utility of inclusive fitness. One particular claim is that Hamilton’s rule applies only to additive games. Additive games represent a vanishingly small subset of all games and do not capture a number of interesting qualitative behaviours which are present in non-additive games. Thus, if these criticisms were correct, inclusive fitness would be a severely limited theoretical tool. We show these criticisms are not valid by demonstrating that any symmetric game can be transformed into an additive payoff matrix in such a way that the action of selection remains unchanged. The result comes with a caveat, however, which is that terms in the payoff matrix must themselves be frequency dependent. Despite this, we demonstrate the utility of inclusive fitness by means of applying Hamilton’s rule to two such non-additive games. The central claim of inclusive fitness is that relatedness is the key to cooperation, we show that this remains true even for non-additive games.
inclusive fitness, evolutionary game theory, non-additive games, evolution of cooperation, synergy
1-11
Tudge, Simon
302f675d-7164-47e0-96b0-c85c1f48fddc
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Watson, Richard
ce199dfc-d5d4-4edf-bd7b-f9e224c96c75
Gonzalez, Miguel
e77dc324-ee8a-44a6-806f-23dbad2a3d36
Tudge, Simon
302f675d-7164-47e0-96b0-c85c1f48fddc
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Watson, Richard
ce199dfc-d5d4-4edf-bd7b-f9e224c96c75
Gonzalez, Miguel
e77dc324-ee8a-44a6-806f-23dbad2a3d36

Tudge, Simon, Brede, Markus, Watson, Richard and Gonzalez, Miguel (2014) Hamilton’s rule in non-additive games. Author's Original, 1-11. (Submitted)

Record type: Article

Abstract

Recently a number of authors have questioned both the validity and utility of inclusive fitness. One particular claim is that Hamilton’s rule applies only to additive games. Additive games represent a vanishingly small subset of all games and do not capture a number of interesting qualitative behaviours which are present in non-additive games. Thus, if these criticisms were correct, inclusive fitness would be a severely limited theoretical tool. We show these criticisms are not valid by demonstrating that any symmetric game can be transformed into an additive payoff matrix in such a way that the action of selection remains unchanged. The result comes with a caveat, however, which is that terms in the payoff matrix must themselves be frequency dependent. Despite this, we demonstrate the utility of inclusive fitness by means of applying Hamilton’s rule to two such non-additive games. The central claim of inclusive fitness is that relatedness is the key to cooperation, we show that this remains true even for non-additive games.

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Inclusive_Fitness_and_Game_Theory.pdf - Author's Original
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More information

Submitted date: 13 May 2014
Keywords: inclusive fitness, evolutionary game theory, non-additive games, evolution of cooperation, synergy
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 384981
URI: http://eprints.soton.ac.uk/id/eprint/384981
PURE UUID: e303a74f-8fb0-48c3-a84b-ef3eb7047e6e

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Date deposited: 15 Jan 2016 15:44
Last modified: 14 Jul 2020 16:32

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