The evolutionary dynamics of costly signaling

Josef Hofbauer () and Christina Pawlowitsch ()
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Josef Hofbauer: University of Vienna
Christina Pawlowitsch: University Paris-Panthéon-Assas

International Journal of Game Theory, 2025, vol. 54, issue 1, No 23, 53 pages

Abstract: Abstract The theory of costly signaling (Spence in Q J Econ 87:355–374, 1973) is a well-established paradigm in economics and theoretical biology, where it is also known as the Handicap Principle (Zahavi J Theor Biol 53:205–214, 1975). Nevertheless, while costly-signaling games have been extensively studied in classical game theory (focused on Nash equilibrium and its refinements), evolutionary dynamics in costly-signaling games are relatively unexplored. This paper gives a comprehensive account of evolutionary dynamics in two canonical classes of games with two states of nature, two signals, and two possible reactions to signals: a model with differential signaling costs (similar to Spence’s model) and a model with differential benefits from success (similar to Milgrom and Roberts’s in J Polit Econ 94:796–821, 1986, respectively Grafen’s J Theor Biol 144:517–546, 1990, model). We first use index theory to give a necessary condition for the dynamic stability of the equilibria in these games. Then, we study the replicator dynamics and the best-response dynamics. Along the way, we relate our findings to classical equilibrium refinements that test for the plausibility of beliefs off the equilibrium path.

Keywords: Costly-signaling games; Handicap Principle; Index theory; Replicator dynamics; Periodic orbits; Center manifold; Chain recurrence; Best-response dynamics; Equilibrium refinement; Never-a-weak-best-response criterion; ‘Divinity’; Intuitive criterion (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00182-025-00927-5

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