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SIGNALING GAMES: Dynamics and Learning

SIGNALING GAMES: Dynamics and Learning. NASSLI 2016 Friday. Networks. Local signaling on networks Emergence of a Signaling Network Signaling Games with Multiple Senders and Receivers. 1. Local Signaling on Networks. Local Signaling: Zollman PhilSci (2005). Simplest Lewis Signaling Game

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SIGNALING GAMES: Dynamics and Learning

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  1. SIGNALING GAMES:Dynamics and Learning NASSLI 2016 Friday

  2. Networks • Local signaling on networks • Emergence of a Signaling Network • Signaling Games with Multiple Senders and Receivers

  3. 1. Local Signaling on Networks

  4. Local Signaling: ZollmanPhilSci(2005) Simplest Lewis Signaling Game played on a 100 by 100 grid. Play with each neighbor both a sender and receiver. Imitate the best dynamics.

  5. Pre-play signaling in the Stag Hunt

  6. Add 2 signals Players exchange signals and then play Stag Hunt, with strategies contingent on signal received. <Signal to send, Act if Signal 1 received, Act if Signal 2 received> Each player plays with each neighbor. Imitate the best dynamics.

  7. A Patchwork of Types but…

  8. A Patchwork of Types but… Everyone hunts Stag

  9. A Patchwork of Types but… Everyone hunts Stag and a population of all Hare hunters can be invaded by using a “secret handshake”

  10. Local Signaling: Wagner Erkenntnis(2009) 1. Repeats Zollman’s setup with problematic cases. more states unequal state probabilities 2. Generalizes the local interaction to other network structures.

  11. Local Signaling: More States Replicator Local Interaction 3 states 95% 100% 4 states 24% 100%

  12. Local Signaling: Unequal Pr • More convergence to all signaling • If not, small pockets of non-signaling.

  13. Local Signaling on a Graph Torus Cycle Wheel

  14. Regions of Meaning (10,000 agents) Torus 9 Cycle 462 Wheel 1

  15. Small World Clustering Coefficient -- Emergence of Signaling Characteristic Path Length -- One language These are combined in small world networks.

  16. 2. Signaling Games with Multiple Senders and Receivers

  17. Multiple Senders and Receivers •→•←•(Many Senders) •←•→•(Many Receivers) •→•→•(Chains) Skyrms Phil. Trans. Royal Society B (2009)

  18. The simplest signaling chain 2 states, 2 signals, 2 acts states equiprobable, N actors

  19. Reinforcement

  20. Learning the simplest Chain Each player has an urn for each stimulus containing a ball for each response. Repeated trials with reinforcement of the balls drawn on a trial.

  21. Simulations and Analysis Simulations Modular learning is better PhD thesis “Broken Telephone” Jonathan Kariv U. Penn. Math.

  22. Probe and Adjust

  23. Sketch of playing the chain game with Probe and Adjust Each player remembers what happened last time for each input. State of the system: A set of maps from inputs to outputs, one for each player.

  24. Sketch of playing the chain game with Probe and Adjust Assume: (1) No contiguous probes. (2) In between probes every state is exercised.

  25. Sketch of playing the chain game with Probe and Adjust So: (1) For each situation, the state of the system contains a transit from that state to an act. (Define in the obvious way; follow the arrows.) (2) The transit has been used.

  26. Can you prove that Probe and Adjust always learns to signal in a binary signaling chain?

  27. What about other simple games with multiple senders and receivers?Can you analyze with probe and adjust?

  28. Chondromyces crocatus

  29. Quorum Signaling Pre-play signaling with many players sending and receiving. Finite Population Model Pacheco, Vasconselos, Santos, Skyrms PLoS Comp. Biology (2015)

  30. 3. Emergence of a Signaling Network

  31. Bala-Goyal Game Everyone has a piece of information (equal value) Everyone can pay others to get their information. Information is passed on without degradation. The ring is the unique efficient equilibrium. Best response with inertia dynamics learns the ring.

  32. Probe and Adjust 2 levels of analysis - no simultaneous probes - simultaneous probes allowed

  33. Probe and AdjustNo Simultaneous ProbesOperates on individual acts. • Huttegger and Skyrms (2012) in Signaling Commitment and Emotion. • Probe and Adjust learns the ring.

  34. Probe and AdjustSimultaneous Probes AllowedOperates on Strategies • Huttegger, Skyrms and Zollman (2013) Erkenntnis. Ring is stochastically stable.

  35. Medium Run

  36. Learning to Network: Reinforcement Another Epistemic Network Game Simulations with Reinforcement Learning

  37. Barrett-Mohseni-Skyrms Game An individual can either consult nature directly to get information, or consult another individual. Some individuals are better at getting the truth from nature.

  38. 1. All communicate perfectly • What are the optimal networks?

  39. Network Structure 1

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