from Democritus toSignaling Networks

The word is the shadow of the deed.- Democritus

DemocritusThe Laughing Philosopher

400BC

Democritus Laughing, by Hendrick ter Brugghen, 1628

Proclus states that Pythagoras and Epicurus agree with Cratylus, but Democritus and Aristotle agree with Hermogenes, the former that names arise by nature, the latter that they arise by chance.

�In that gathering of men, at a time when utterance of sound was purely individual, from daily habits they fixed on articulate words just as they happened to come; then, from indicating by name things in common use, the result was that in this chance way they began to talk, and thus originated conversation with one another.�

VitruviusThe Ten Books of Architecture Bk2, Ch1

27 BC

1. Can meaningful communication arise spontaneously?

1. Can meaningful communication arise spontaneously?

2. Results robust?

1. Can meaningful communication arise spontaneously?

2. Results robust?

3. Can the Game Evolve?

1. Can meaningful communication arise spontaneously?

2. Results robust?

3. Can the Game Evolve?

4. Signaling on Networks

1. Can meaningful communication arise spontaneously?

2. Results robust?

3. Can the Game Evolve?

4. Signaling on Networks

5. Can the Network Evolve?

The Simplest Lewis Signaling Game

Nature flips a fair coin to choose state 1 or 2.

Sender observes the state & sends signal A or B.

Receiver observes the signal and guesses the state.

Correct guess pays off 1 to both; otherwise nothing.

1. EMERGENCE of MEANINGFUL SIGNALS

Meaningful?

“In the beginning was information.The word came later.”

Fred DretskeKnowledge and the Flow of Information

Information

Emergence?

Dynamics

Herrnstein-Roth-Erev

Reinforcement Learning

Probability of a specific choice is proportional to accumulated rewards from that choice in the past.

Herrnstein, R. J. �On the Law of Effect.� Journal of the Experimental Analysis of Behavior 13: 243-266, 1970.

Roth and Erev GEB 1995. Erev and Roth AER 1998.

Simulation

Theorem

Convergence to a signaling system with probability 1.

Argiento, Pemantle, Skyrms and Volkov. Stochastic Proc. Appl. (2009).

(Parallel results in Evolutionary Dynamics)

Experiments

Subjects in an economics lab learn to signal spontaneously.

Blume, DeJong, Kim, Sprinkle (1998) Experimental evidence on the evolution of meaning of messages in sender-receiver games. Am. Econ. Rev.

Blume, DeJong, Neumann, Savin (2002) Learning and communicationin sender-receiver games: and econometric investigation. J. Appl. Econ.

2. Robust?

Nature’s die is not fair

N states, N signals, N acts

N states, M signals, N acts

Nature’s die is not fair- pooling equilibria may be stable

N states, N signals, N acts- partial pooling equilibria (some stable)

N states, M signals, N acts- signaling systems may not be conventions

Donaldson, Lachmann, Bergstrom (2007) Journal of Theoretical Biology

Here Dynamic Analysis is more nuanced

Efficient signaling can emerge, but is not guaranteed.

Hu, Skyrms, Tarres “Reinforcement Learning in a Signaling Game”

Hofbauer and Huttegger “Feasibility of Communication in Binary Signaling Games” JTB (2008) [Also 3by3by3 Games (2015)]

Huttegger, Skyrms, Tarres and Wagner “Some Dynamics of Signaling Games” PNAS (2014)

Experiments Track Theory

Brunner, O.Connor, Rubin, Huttegger “David Lewis in the Lab – Experimental Results on the Emergence of Meaning” Synthese (2014/2018)

Efficient signaling can emerge, but is not guaranteed.

3. Can the game itself evolve?

Inventing New Signals

• Alexander, Skyrms, Zabell (2011) Dynamic Games and Applications.

Previous Urn Model + “Mutator”

1. No New Signal Tried2. New Signal Tried, but unsuccessful.3. New signal tried with success.

Learning to Signal with Invention

3 by 3 by 3 states equiprobable

2 by 2by 2 probabilities probability .9

Self-Assembling Games

Barrett & Skyrms BJPS 2017

4. Signaling on Networks

Lattice

• Kevin Zollman “Talking to Neighbors” PhilSci (2005)

Regional Meaning on a Lattice

Also Pre-play signaling in Stag Hunt Games promotes Coopertion

Small World Networks

Elliott Wagner “Communication and structured correlation.” Erkenntnis (2009)

Signaling Chains 1

“Signalling chains with probe and adjust learning”

- Giorgio Gosti

Connection Science 2017

Signaling Chains 2

“Broken Telephone: An Analysis of a Reinforcement Process”

-Johnathan Kariv

PhD Thesis MathematicsPenn

Dynamic Networks

5. Can the Network Itself Evolve?

Reinforcement:

Skyrms and Pemantle (2000) “A Dynamic Model of Social Network Formation” PNAS

A RINGBala and Goyal (2000) “A Non-cooperative Model of Network Formation” Econometrica(Best Response with Inertia)

Skyrms and Huttegger (2013) “Emergence of a Signaling Network with Probe and Adjust” in Cooperation and its Evolution.

Huttegger , Skyrms and Zollman (2014) “Probe and Adjust in Information Transfer” Erkenntnis

Stars, etc.

“Self-Assembling Networks” Barrett, Skyrms, Mosheni BJPS forth.

There is lots more to do.

Thank you.

Beyond Common Interest

Opposed InterestsA1 A2 A3

S1 -1, 1 .5, -.5 1, -1

S2 1,-1 -1, 1 .5, -.5

S3 .5, -.5 1,-1 -1, 1

Chaos(structurally stable)

Wagner BJPS 2012, Sato Akiyama, Farmer, PNAS 2002.

Mixed Interests with Differential Signaling Costs

Cycles also occur here in a non-trivial way in:Spence Signaling Game

- Noldeke &Samuelson J. Econ. Th. (1997)- Wagner Games (2013)

Sir Philip Sydney Game - Huttegger & Zollman Proc.Roy.Soc.(2010)

- But signaling system Equilibria are also possible.

Information Transfer

may emerge spontaneously withoutcommon interest

in and out of equilibrium

Cycles around Hybrid Equilibrium

DeceptionSearcy and Nowicki The Evolution of Animal Signals: Reliability and Deception in Signaling SystemsHarper and Maynard Smith Animal SignalsSkyrms SignalsGodfrey-Smith review of SignalsBergstrom “Dealing with Deception in Biology”Fallis "Skyrms on the Possibility of Universal Deception", Philosophical Studies, (forthcoming)McWhirter "Behavioral Deception and Formal Models of Communication" in the British Journal for the Philosophy of Science (forthcoming)

Propositional Content

Birch “Propositional Content in Signaling Systems” Philosophical Studies.

Godfrey-Smith et.all.

Special Journal Issue

Costless Pre-Play Signaling

Robson (1990) “Efficiency in Evolutionary Games” Journal of Evolutionary Biology.

Skyrms (2002) “Signals, Evolution and the Explanatory Value of Transient Information” Philosophy of Science

Santos, Pacheco, Skyrms (2011) “Co-evolution of pre-play signaling and cooperation” Journal of Theoretical Biology

Perturbation: mutation

Pooling equilibria collapse to a single point.Is it dynamically unstable, stable, strongly stable?

It depends. (Hofbauer and Huttegger JTB 2008).

If

a sink, otherwise a saddle. (for small mutation rates).

Synonyms and Bottlenecks: Simulations

N Partial Pooling

3 9.6 %

4 21.9 %

8 59.4 %

Barrett Phil. Sci. 2007

Transient Information in Pre-play Signaling: Stag Hunt

-- Skyrms PhiSci 2002

Structural Stability

A Dynamics (given by a vector field) is

Structurally Unstable

if an arbitrarily small change in the vector field yields a qualitatively different dynamics.

Arbitrarily small difference?

At each point in the simplex, for each component, there is a numerical difference. Take the maximum.

Take the least upper bound of these numbers.

This is the distance between the vector fields.

Qualitatively Different?

Two vector fields are qualitatively the same, i.e.(topologically equivalent) if there is homeomorphism of the simplex to itself that takes the orbits of one into the orbits of the other (preserving sense of the orbits).

Selection-Mutation Dynamics

Hofbauer (1985) J. Math. Bio.

Functional Analysis

Aczél, J.; Daróczy, Z. On Measures of Information and Their Characterizations

Complex Signals• Franke (2013) “Compositionality from Reinforcement

Learning” Proc. G.I.R.L.• Barrett (2009) “Evolution of Coding in Signaling Games” Th. &

Dec.• Steinert-Threlkeld (forth.) “Compositional Signaling in a

Complex World” JLLI.• Nowak and Krakauer (1999) “The Evolution of Language”

PNAS.• Batali (2002) “Negation and Acquisition of Recursive

Grammars…” in Briscoe (ed.)• Barrett, Skyrms & Cochran (2018) “Hierarchinal Models …”

ms.