The change of signaling conventions in social networks

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.

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Notes

  1. 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. 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. 3.

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

  4. 4.

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

  5. 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. 6.

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

  7. 7.

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

  8. 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. 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. 10.

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

  11. 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. 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. 13.

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

  14. 14.

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

  15. 15.

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

  16. 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. 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. 18.

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

  19. 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. 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).

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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)

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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

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Keywords

  • Signaling game
  • Reinforcement learning
  • Multi-agent account
  • Social network structure
  • Mechanisms of language change