Dishonest signalling in a variant of pygmalion game. (English) Zbl 1461.91063
Summary: We present a variation of the pygmalion game, a signalling game played between a population of senders and receivers. Senders have varying quality and can attempt to send a costly signal. Not all signals are successfully delivered or observed; the probability of success increases with the signal strength. The cost of the signal increases with the signal strength and decreases with the sender’s quality. Receivers have no information about senders’ qualities and can only detect the strengths of signals. Nevertheless, receivers have to decide whether to act or not and the receivers’ payoff is higher if they act to senders of higher qualities. The senders’ payoff is 1 if receivers do act and 0 otherwise. We analyse this game and show two kinds of Nash equilibria: (1) senders do not signal and receivers always act and (2) all Senders send the same and relatively strong signals and receivers always act to those signals. Thus, in Nash equilibria, only dishonest signalling occurs. Interestingly, despite the dishonesty, signalling equilibria provide some benefit to receivers – they face a higher proportion of high-quality senders than in the non-signalling Nash equilibrium.
MSC:
| 91A28 | Signaling and communication in game theory |
References:
| [1] | Bassler, BL, How bacteria talk to each other: regulation of gene expression by quorum sensing, Curr Opin Microbiol, 2, 6, 582-587 (1999) |
| [2] | Bergstrom, CT; Lachmann, M., Signalling among relatives. I. Is costly signalling too costly?, Philos Trans R Soc Lond B Biol Sci, 352, 1353, 609-617 (1997) |
| [3] | Biernaskie, JM; Grafen, A.; Perry, JC, The evolution of index signals to avoid the cost of dishonesty, Proc R Soc B, 281, 1790, 20140876 (2014) |
| [4] | Broom, M.; Ruxton, GD, Some mistakes go unpunished: the evolution of “all or nothing” signalling, Evol: Int J Org Evol, 65, 10, 2743-2749 (2011) |
| [5] | Broom, M.; Ruxton, GD, Perceptual advertisement by the prey of stalking or ambushing predators, J Theor Biol, 315, 9-16 (2012) · Zbl 1397.92562 |
| [6] | Broom, M.; Ruxton, GD, On the evolutionary stability of zero-cost pooled-equilibrium signals, J Theor Biol, 323, 69-75 (2013) · Zbl 1314.92176 |
| [7] | Broom, M.; Speed, MP; Ruxton, GD, Evolutionarily stable defence and signalling of that defence, J Theor Biol, 242, 1, 32-43 (2006) · Zbl 1447.92271 |
| [8] | Broom, M.; Ruxton, GD; Schaefer, HM, Signal verification can promote reliable signalling, Proc R Soc B: Biol Sci, 280, 1771, 20131560 (2013) |
| [9] | Davies, NB; Krebs, JR; West, SA, An introduction to behavioural ecology (2012), London: Wiley, London |
| [10] | Grafen, A., Biological signals as handicaps, J Theor Biol, 144, 4, 517-546 (1990) |
| [11] | Hoffman, M.; Hilbe, C.; Nowak, MA, The signal-burying game can explain why we obscure positive traits and good deeds, Nat Hum Behav, 2, 6, 397 (2018) |
| [12] | Holman, L., Costs and constraints conspire to produce honest signaling: insights from an ant queen pheromone, Evolution, 66, 7, 2094-2105 (2012) |
| [13] | Huttegger, SM; Bruner, JP; Zollman, KJ, The handicap principle is an artifact, Philos Sci, 82, 5, 997-1009 (2015) |
| [14] | Isack, HA; Reyer, HU, Honeyguides and honey gatherers: interspecific communication in a symbiotic relationship, Science, 243, 4896, 1343-1346 (1989) |
| [15] | Kane, P.; Zollman, KJ, An evolutionary comparison of the handicap principle and hybrid equilibrium theories of signaling, PLoS ONE, 10, 9, e0137271 (2015) |
| [16] | Kirchner, W.; Lindauer, M.; Michelsen, A., Honeybee dance communication, Naturwissenschaften, 75, 12, 629-630 (1988) |
| [17] | Kodric-Brown, A., Female preference and sexual selection for male coloration in the guppy (Poecilia reticulata), Behav Ecol Sociobiol, 17, 3, 199-205 (1985) |
| [18] | Kodric-Brown, A., Dietary carotenoids and male mating success in the guppy: an environmental component to female choice, Behav Ecol Sociobiol, 25, 6, 393-401 (1989) |
| [19] | Lachmann, M.; Bergstrom, CT, Signalling among relatives: II. Beyond the Tower of Babel, Theor Popul Biol, 54, 2, 146-160 (1998) · Zbl 0947.92020 |
| [20] | Langridge, KV; Broom, M.; Osorio, D., Selective signalling by cuttlefish to predators, Curr Biol, 17, 24, R1044-R1045 (2007) |
| [21] | Lewis, D., Convention (1969), Cambridge: Harvard University Press, Cambridge |
| [22] | Maynard Smith, J., Honest signalling: the Philip Sidney game, Anim Behav, 42, 1034-1035 (1991) |
| [23] | Maynard Smith, J.; Harper, DG, Animal signals: models and terminology, J Theor Biol, 177, 3, 305-311 (1995) |
| [24] | Maynard Smith, J.; Harper, D., Animal signals (2003), Oxford: Oxford University Press, Oxford |
| [25] | Sun, S.; Leshowitz, MI; Rychtář, J., The signalling game between plants and pollinators, Sci Rep, 8, 1, 6686 (2018) |
| [26] | Proctor, CJ; Broom, M.; Ruxton, GD, Modelling antipredator vigilance and flight response in group foragers when warning signals are ambiguous, J Theor Biol, 211, 4, 409-417 (2001) |
| [27] | Ruxton, GD; Speed, MP; Broom, M., Identifying the ecological conditions that select for intermediate levels of aposematic signalling, Evol Ecol, 23, 4, 491-501 (2009) |
| [28] | Schaefer, HM; Ruxton, GD, Plant-animal communication (2011), Oxford: Oxford University Press, Oxford |
| [29] | Skyrms, B., Evolution of signalling systems with multiple senders and receivers, Philos Trans R Soc B: Biol Sci, 364, 1518, 771-779 (2008) |
| [30] | Sun S, Johanis M, Rychtář J (2019) Costly signalling theory and dishonest signalling. J Theor Ecol. 10.1007/s12080-019-0429-0 |
| [31] | Zahavi, A., Mate selection: a selection for a handicap, J Theor Biol, 53, 1, 205-214 (1975) |
| [32] | Zollman, KJ; Bergstrom, CT; Huttegger, SM, Between cheap and costly signals: the evolution of partially honest communication, Proc R Soc B: Biol Sci, 280, 1750, 20121878 (2013) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
