Abstract
A possible rationale for victory displays—which are performed by the winners of contests but not by the losers—is that the displays are attempts to decrease the probability that the loser of a contest will initiate a future contest with the same individual. We explore the logic of this “browbeating” rationale with a game-theoretic model, which extends previous work by incorporating the effects of contest length and the loser’s strategic response. The model predicts that if the reproductive advantage of dominance over an opponent is sufficiently high, then, in a population adopting the evolutionarily stable strategy or ESS, neither winners nor losers signal in contests that are sufficiently short; and only winners signal in longer contests, but with an intensity that increases with contest length. These predictions are consistent with the outcomes of recent laboratory studies, especially among crickets, where there is now mounting evidence that eventual winners signal far more frequently than losers after fighting, and that post-conflict displays are more likely to be observed after long contests.
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Notes
- 1.
In general, strategy v is an ESS if it does not pay a potential mutant to switch from v to any other strategy, and v need not satisfy the strong condition f(v, v) > f(u, v) for all u≠v. If there is at least one alternative best reply u such that f(u, v) = f(v, v) but v is a better reply than u to all such u (f(v, u) > f(u, u)), then v is called a weak ESS. For our model, however, any ESS is a strong ESS, as is typical of continuous games ([18], p. 408).
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We are grateful to Lauren Fitzsimmons and two anonymous reviewers for constructive feedback on earlier versions of the manuscript.
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Mesterton-Gibbons, M., Sherratt, T.N. (2013). Signalling Victory to Ensure Dominance: A Continuous Model. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_2
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