Skip to main content
SpringerLink
Log in

The change of signaling conventions in social networks

  • Original Article
  • Published:
AI & SOCIETY Aims and scope Submit manuscript

Abstract

To depict the mechanisms that have enabled the emergence of semantic conventions, philosophers and researchers particularly access a game-theoretic model: the signaling game. In this article I argue that this model is also quite appropriate to analyze not only the emergence of a semantic convention, but also its change. I delineate how the application of signaling games helps to reproduce and depict mechanisms of semantic change. For that purpose I present a model that combines a signaling game with innovative reinforcement learning; in simulation runs I conduct this game repeatedly within a multi-agent setup, where agents are arranged in social network structures. The results of these runs are contrasted with an attested theory from sociolinguistics: the ‘weak tie’ theory. Analyses of the produced data target a deeper understanding of the role of environmental variables for the promotion of (1) semantic change or (2) solidity of semantic conventions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. In a game-theoretic sense, ‘unconsciousness’ of agents signifies that they do not deduce a particular decision, but rather learn it by optimizing behavior.

  2. Note: in the literature under discussion this phenomenon is solely called ‘convention’ (or sometimes ‘norm’). I label it ‘behavioral convention’ to distinguish this phenomenon from more communication-related types of conventions.

  3. A good overview of subsequent studies that concern different particular network typologies is given in Airiau et al. (2014).

  4. For the definition of these network properties I refer to Jackson’s Social and Economic Networks (Jackson 2008), Chapter 2.

  5. Weak ties are links that have a low strength, often defined by frequency or multiplexity of the connection. Weak ties connect mostly detached communities.

  6. Note that centrality in a network can be defined in multiple ways, as introduced in Sect. 4.4.

  7. \(\varDelta (X)\) denotes the set of all probability distributions over a random variable X.

  8. Informally spoken, the information state came to the sender’s mind. In game theory we say that the state is chosen by an invisible participant, called nature N.

  9. Note that the number of balls is just a metaphor for better comprehensibility of the principle and, therefore, the incremental value per urn can be \(\in \mathbb {R}\).

  10. For a discussion and comparison of reinforcement learning and Fictitious Play in signaling game playing agents, see, e.g., Mühlenbernd (2011).

  11. For a definition of expected utilities over strategy pairs, see, e.g., Mühlenbernd (2011). Note that signaling systems maximize expected utilities; therefore, they are optimal according to such a value function.

  12. As mentioned earlier, signaling systems are Nash equilibria over expected utilities and evolutionary stable strategies. Furthermore, in combination with the current reinforcement learning setup, agents that have learned a signaling system stick with it with a zero probability to change.

  13. It was shown for experiments with three-agent populations that the force of innovation and communicative success reveal a significant negative correlation.

  14. Note that optimal number \(n'\) defines the number of messages which are necessary to create a signaling system.

  15. For the definition of these network properties I refer to Jackson’s Social and Economic Networks (Jackson 2008), Chapter 2.

  16. e.g., the ‘weak tie’ theory assumes a high negative correlation of an agent’s tie strength (TS, see Definition 4) and her contribution to innovation, i.o.w. to start new regions of signaling conventions.

  17. The mutual intelligibility value MI reproduces the expected utility for two different strategy pairs. For the definition see Mühlenbernd and Nick (2014), Definition 3.

  18. Data points are the agents’ features; for 10 simulation runs with 500 agents each.

  19. Due to the fact that some numbers are hard to spot, all values of these Pearson-correlations are also given in Table 3 (Appendix).

  20. An open issue here is to test the ‘weak tie’ theory when the strength of a tie is defined in other ways (cf. Mühlenbernd and Quinley 2017).

References

  • Airiau S, Sen S, Villatoro D (2014) Emergence of conventions through social learning: heterogeneous learners in complex networks. Auton Agents Multi-Agent Syst 28(5):779–804

    Article  Google Scholar 

  • Alexander J, Skyrms B, Zabell S (2012) Inventing new signals. Dyn Games Appl 2(1):129–145

    Article  MathSciNet  MATH  Google Scholar 

  • Axelrod R (1984) The evolution of cooperation. Basic Books, New York

    MATH  Google Scholar 

  • Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512

    Article  MathSciNet  MATH  Google Scholar 

  • Barrett JA (2009) The evolution of coding in signaling games. Theory Decis 67:223–237

    Article  MathSciNet  Google Scholar 

  • Barrett JA, Zollman KJS (2009) The role of forgetting in the evolution and learning of language. J Exp Theor Artif Intell 21(4):293–309

    Article  MATH  Google Scholar 

  • Brown G (1951) Iterative solution of games by fictitious play. In: Koopmans T (ed) Activity analysis of production and allocation. Wiley, New York, p 375

    Google Scholar 

  • Bush R, Mosteller F (1955) Stochastic models of learning. Wiley, New York

    Book  MATH  Google Scholar 

  • Centola D, Baronchelli A (2015) The spontaneous emergence of conventions: an experimental study of cultural evolution. Proc Natl Acad Sci 112(7):1989–1994

    Article  Google Scholar 

  • Crawford VP, Sobel J (1982) Strategic information transmission. Econometrica 50:1431–1451

    Article  MathSciNet  MATH  Google Scholar 

  • Croft W (2000) Explaining language change: an evolutionary approach. Longman, Harlow

    Google Scholar 

  • Easley D, Kleinberg J (2010) Networks, crowds, and markets: Reasoning about a highly connecetd world. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Fagyal Z, Swarup S, Escobar AM, Gasser L, Lakkaraju K (2010) Centers and peripheries: network roles in language change. Lingua 120:2061–2079

    Article  Google Scholar 

  • Franke M, Jäger G (2012) Bidirectional optimization from reasoning and learning in games. J Log Lang Inf 21(1):117–139

    Article  MathSciNet  MATH  Google Scholar 

  • Holme P, Kim BJ (2002) Growing scale-free networks with tunable clustering. Phys Rev E 65(2):026107-1–026107-4

    Article  Google Scholar 

  • Huttegger SM (2007) Evolution and the explanation of meaning. Philos Sci 74:1–27

    Article  MathSciNet  Google Scholar 

  • Jackson MO (2008) Social and economic networks. Princeton University Press, Princeton

    Book  MATH  Google Scholar 

  • Ke J, Gong T, Wang WS-Y (2008) Language change and social networks. Commun Comput Phys 3(4):935–949

    MATH  Google Scholar 

  • Koschützki D, Lehmann K, Peeters L, Richter S, Tenfelde-Podehl S, Zlotowski O (2005) Centrality indices. In: Koschützki D, Lehmann K, Peeters L, Richter S, Tenfelde-Podehl S, Zlotowski O (eds) Network analysis, vol 3418. Springer, Heidelberg, pp 16–61

    Chapter  Google Scholar 

  • Labov W (1973) The linguistic consequences of being a lame. Lang Soc 2(1):81–115

    Article  Google Scholar 

  • Labov W (1991) The three dialects of english. In: Eckert P (ed) New ways of analyzing sound change. Academic Press, New York, pp 1–44

    Google Scholar 

  • Labov W (2001) Principles of linguistic change, volume 2: Social factors. Blackwell, Malden

    Google Scholar 

  • Labov W (2010) Principles of linguistic change, volume 3: cognitive and cultural factors. Wiley-Blackwell, Oxford

    Book  Google Scholar 

  • Lewis D (1969) Convention. Harvard University Press, Cambridge

    Google Scholar 

  • Llamas C (2000) Variation in the north-east of England. In: Paper presented at NWAV 29, Michigan State University

  • Milroy J (1996) A current change in british english: variation in (th) in Derby. Newctle Durh Pap Linguistics 4:213–222

    Google Scholar 

  • Milroy J, Milroy L (1985) Linguistic change, social network and speaker innovation. J Linguistics 21(2):339–384

    Article  Google Scholar 

  • Milroy L (1980) Language and social networks. Blackwell, Oxford

    Google Scholar 

  • Milroy L, Gordon M (2003) Sociolinguistics: method and interpretation. Blackwell, Oxford

    Book  Google Scholar 

  • Milroy L, Milroy J (1992) Social network and social class: towards an integrated sociolinguistic model. Lang Soc 21:1–26

    Article  Google Scholar 

  • Mühlenbernd R (2011) Learning with neighbours: emergence of convention in a society of learning agents. Synthese 183(S1):87–109

    Article  MathSciNet  MATH  Google Scholar 

  • Mühlenbernd R, Franke M (2012) Signaling conventions: who learns what where and when in a social network? In: Scott-Phillips T, Tamariz M, Cartmill EA, Hurford J (eds) Proceedings of the 9th international conference on the evolution of language (Evolang IX), pp 242–249

  • Mühlenbernd R, Nick J (2014) Language change and the force of innovation. In: Katrenko S, Rendsvig K (eds) Pristine perspectives on logic, language, and computation, vol 8607. Springer, Heidelberg, pp 194–213

    Chapter  MATH  Google Scholar 

  • Mühlenbernd R, Quinley J (2013) Signaling and simulations in sociolinguistics. In K. Shwayder (ed) University of Pennsylvania working papers in linguistics, vol 19 (article 16)

  • Mühlenbernd R, Quinley J (2017) Language change and network games. Lang Linguistics Compass 11(2):e12235

    Article  Google Scholar 

  • Nettle D (1999) Using social impact theory to simulate language change. Lingua 108(2–3):95–117

    Article  Google Scholar 

  • Roth A, Erev I (1995) Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games Econ Behav 8:164–212

    Article  MathSciNet  MATH  Google Scholar 

  • Russell B (1921) The analysis of mind. Allen & Unwin, London

    MATH  Google Scholar 

  • Salazar N, Rodriguez-Aguilar JA, Arcos JL (2010) Robust coordination in large convention spaces. AI Commun 23:357–372

    Article  MathSciNet  Google Scholar 

  • Shoham Y, Tennenholtz M (1997) On the emergence of social conventions: modeling, analysis, and simulations. Artif Intell 94(1–2):139–166

    Article  MATH  Google Scholar 

  • Skyrms B (2010) Signals: evolution, learning and information. Oxford University Press, Oxford

    Book  Google Scholar 

  • Steels L (2002) Grounding symbols through evolutionary language games. In: Cangelosi A, Parisi D (eds) Simulating the evolution of language. Springer, London, pp 211–226

    Chapter  Google Scholar 

  • Sutton R, Barto A (1998) Reinforcement learning: an introduction. The MIT Press, Cambridge

    MATH  Google Scholar 

  • Trudgill P (1988) Norwich revisited: recent changes in an english urban dialect. Engl World-Wide 9(1):33–49

    Article  Google Scholar 

  • Wagner E (2009) Communication and structured correlation. Erkenntnis 71(3):377–393

    Article  Google Scholar 

  • Wärneryd K (1993) Cheap talk, coordination, and evolutionary stability. Games Econ Behav 5(4):532–546

    Article  MathSciNet  MATH  Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393:440–442

    Article  MATH  Google Scholar 

  • Young HP (1993) The evolution of conventions. Econometrica 2(1):129–145

    MathSciNet  MATH  Google Scholar 

  • Zollman KJS (2005) Talking to neighbors: the evolution of regional meaning. Philos Sci 72(1):69–85

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Linguistics, Eberhard Karls University Tübingen, Wilhelmstr. 19, 72074, Tübingen, Germany

    Roland Mühlenbernd

Authors
  1. Roland Mühlenbernd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roland Mühlenbernd.

Additional information

Special Thanks to Michael Franke, Shane Steinert-Threlkeld, three anonymous reviewers and the ERC Advanced Grant Project Group ‘Language Evolution—the Empirical Turn’ (EVOLAEMP) for comments and discussions.

Appendix: Correlation values

Appendix: Correlation values

See Table 3.

Table 3 Pearson-correlation values (accurate to two decimal places) over 5000 data points (10 simulation runs \(\times\) 500 agents) for all different pairs of features: the static network properties tie strength (TS), degree centrality (DC), closeness centrality (CC), betweenness centrality (BC) and clustering coefficient (CL); and the dynamic behavioral features loyalty (LOY), majority preference (MAJ), interiority (INT), fraternity (FRA), mutual intelligibility (MI), adaptivity (AD), impact (IMP) and innovation skill (INV)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mühlenbernd, R. The change of signaling conventions in social networks. AI & Soc 34, 721–734 (2019). https://doi.org/10.1007/s00146-017-0786-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00146-017-0786-4

Keywords

Search

Navigation