Dynamic stability and basins of attraction in the Sir Philip Sidney game

We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics (i.e. standard evolutionary dynamics); however, the latter states are more likely in cases where honest signalling should apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium.

[1]  R. Johnstone,et al.  Begging and bleating: the evolution of parent-offspring signalling. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[2]  A. Grafen,et al.  The continuous Sir Philip Sidney game: a simple model of biological signalling. , 1992, Journal of theoretical biology.

[3]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[4]  Steven Hamblin,et al.  When will evolution lead to deceptive signaling in the Sir Philip Sidney game? , 2009, Theoretical population biology.

[5]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[6]  John Maynard Smith.  Honest signalling: the Philip Sidney game , 1991, Animal Behaviour.

[7]  A. Zahavi.  Mate selection-a selection for a handicap. , 1975, Journal of theoretical biology.

[8]  M. Spence.  Job Market Signaling , 1973 .

[9]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

[10]  R. Hayes,et al.  The Evolution of Animal Communication. Reliability and Deception in Signalling Systems , 2006 .

[11]  David G. Haskell.  Experimental evidence that nestling begging behaviour incurs a cost due to nest predation , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[12]  P. O'Carroll,et al.  Beyond the Tower of Babel , 2002 .

[13]  G. Bachman,et al.  The energetic cost of begging behaviour in nestling house wrens , 1998, Animal Behaviour.

[14]  R. Cressman.  Evolutionary Dynamics and Extensive Form Games , 2003 .

[15]  A. Grafen.  Biological signals as handicaps. , 1990, Journal of theoretical biology.

[16]  Carl T. Bergstrom,et al.  Signaling among relatives. III. Talk is cheap. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[17]  S. Nowicki,et al.  The Evolution of Animal Communication: Reliability and Deception in Signaling Systems: Reliability and Deception in Signaling Systems , 2005 .

[18]  Josef Hofbauer,et al.  Feasibility of communication in binary signaling games. , 2008, Journal of theoretical biology.

[19]  C. Orengo,et al.  A rapid method of protein structure alignment. , 1990, Journal of theoretical biology.

[20]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[21]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[22]  Carl T. Bergstrom,et al.  Signalling among relatives. II. Beyond the tower of Babel. , 1998, Theoretical population biology.

[23]  Carl T. Bergstrom,et al.  Signalling among relatives. I. Is costly signalling too costly , 1997 .

[24]  Rufus A. Johnstone,et al.  Dishonesty and the handicap principle , 1993, Animal Behaviour.

[25]  The limits to cost-free signalling of need between relatives , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[26]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.