Signaling Games on Networks

Signaling Games on Networks

• Extension in time & space

• Agents are placed on a social network

• Agents communicate repeatedly with their neighbors

• Agents‘ decisions depend on learning dynamics

Topic 1 Topic 2 Message 2

Message 1

S₁ ^{Topic 1}

Topic 2 Message 2

Message 1 S₂

Invasion & Social Status

• Project: “Language Contact & Change“ (Jason Quinley & Roland Mühlenbernd)

• Research Question: What kind of environmental circumstances explain the emergence of a specific meaning space division in the English language

• Publications:

– Quinley & Mühlenbernd (2012): Conquest, Contact, and Convention:

Simulating the Norman Invasion’s Impact on Linguistic Usage, BRIMS 2012 proceedings, pp. 113-118.

– Mühlenbernd & Quinley (2013): Signaling & Simulations in Sociolinguistics, Pennsylvania Working Papers in Linguistics

Simulating Language Contact

• Salient systematic division of meaning space between words of Germanic and French origin

• Social conditions like the lifestyle of the Anglo-Saxon laborers and the French- speaking nobility causes this divergence

Germanic French

work (Werk) play (plaisir) stone (Stein) jewel (joel) swine (Schwein) pork (porc)

animal meat

"pork"

"swine" animal

meat

"beef"

"cow" animal

meat

"mutton"

"sheep"

animal meat

“fish" animal

meat

"Schwein"

The Context Signaling Game

1. Nature chooses topic (T = {meat, animal})

2. Sender transmits message to Receiver (M = {swine, pork}) 3. Receiver chooses interpretation (A = {meat, animal})

4. Sender and Receiver in context (C= {farm, dinner}) 5. P_C(c) depends on sender‘s social status S_i

6. Context Influences Topics Pr(t| c)

Dinner Farm

Computer simulation

animal meat

"swine" animal

meat

"swine"

animal meat

"pork"

animal meat

"pork"

animal meat

"pork"

"swine" animal

meat

"pork"

"swine"

animal meat

"pork"

"swine"

S_A

S_N

S_E

S_U

Result 1: The whole society learns either S_E or S_U, but both strategies are equiprobable.

Random Replacement

Trial 1: Replace Agents at Random Why?

Are Conventions Pre-Determined?

Result:

• All Learn Convention BUT

• Strategies Equiprobable

• Contact NOT Enough!

Meat or Animal?

swine pork

beef cow

fish fish

Contact Meets Context

Trial 2: Replace Big Nodes with Invaders

Why?

High Status 

- Higher Probability of C

- Higher Probability of T

Result: Convergence to Convention

Factoring in Social Status

animal meat

"pork"

"swine" animal

meat

"pork"

"swine"

S_E S_U

Status S₁ S₂ S₃ S₄ S₅ S₆ S₇ S₈ S₉

Pr(C_d) .1 .2 .3 .4 .5 .6 .7 .8 .9

0 0.2 0.4 0.6 0.8 1

≥ S1 ≥ S2 ≥ S3 ≥ S4 ≥ S5 ≥ S6 ≥ S7 ≥ S8 ≥ S9

Of Nodes and Nobles

Trial 3:

• Replace Hubs with Invaders

• Tie Degree to Status Why?

Preferential Attachment  Scale-Free Social Networks

• Power Law Distribution - Degree

- Wealth

Result:

• Faster Convergence

• Context + Connectivity

Future Research

• Game Dynamics

– Cost vs. Capacity

– Punishment/ Prestige – Norms vs. Conventions – Innovation/ Extinction

• Network Dynamics

– Rewiring

– Bottom-Up Invasion (e.g.

Czech)

Standard Colloquial

závin štrůdl

láhev flaška

kniha bichle

German loans in Czech