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Learning to signal: Analysis of a micro-level reinforcement model

Author

Listed:
  • Argiento, Raffaele
  • Pemantle, Robin
  • Skyrms, Brian
  • Volkov, Stanislav

Abstract

We consider the following signaling game. Nature plays first from the set {1,2}. Player 1 (the Sender) sees this and plays from the set {A,B}. Player 2 (the Receiver) sees only Player 1's play and plays from the set {1,2}. Both players win if Player 2's play equals Nature's play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as follows. Each node of the decision tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination.

Suggested Citation

  • Argiento, Raffaele & Pemantle, Robin & Skyrms, Brian & Volkov, Stanislav, 2009. "Learning to signal: Analysis of a micro-level reinforcement model," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 373-390, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:373-390
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    References listed on IDEAS

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    1. Bonacich, Phillip & Liggett, Thomas M., 2003. "Asymptotics of a matrix valued Markov chain arising in sociology," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 155-171, March.
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    Cited by:

    1. Penélope Hernández & Bernhard von Stengel, 2014. "Nash Codes for Noisy Channels," Operations Research, INFORMS, vol. 62(6), pages 1221-1235, December.
    2. Jason McKenzie Alexander & Brian Skyrms & Sandy Zabell, 2012. "Inventing New Signals," Dynamic Games and Applications, Springer, vol. 2(1), pages 129-145, March.
    3. Zachary Fulker & Patrick Forber & Rory Smead & Christoph Riedl, 2022. "Spontaneous emergence of groups and signaling diversity in dynamic networks," Papers 2210.17309, arXiv.org, revised Jan 2024.
    4. Conor Mayo-Wilson & Kevin Zollman & David Danks, 2013. "Wisdom of crowds versus groupthink: learning in groups and in isolation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 695-723, August.
    5. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.

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