1. Evolutionary Stability in Bayesian Routing Games
Oliver Schulte Petra Berenbrink
Simon Fraser University
Stuff to bring: paper draft, game theory book, references

2. Modelling User Communities
A system provides users with access to resources, e.g. a network.
Centralized planning: gather requests, compute optimal allocation.
“Anarchy”: users individually choose resources, e.g. routes for messages.
Individual choice strategic interactions (≈ traffic models).
Evolutionary Stability in Bayesian Network Games

3. Evolutionary Stability in Bayesian Network Games
Central Allocation
Users
Messages
Network
500K
Router
250K 
750K
Evolutionary Stability in Bayesian Network Games

4. Evolutionary Stability in Bayesian Network Games
Individual Choice
Users
Messages
Network
500K
250K
Example: airlines make you do your own check-in
750K
Evolutionary Stability in Bayesian Network Games

5. Motivation for Game-Theoretic Modelling
Use game theory to predict outcome of “selfish” user choices (Nash equilibrium)
Assess “price of anarchy”
Improve network design
Evolutionary Stability in Bayesian Network Games

6. Evolutionary Stability in Bayesian Network Games
Outline
World 1  n+n  p+p+e-+e- is possible
World 2  n+n  p+p+e-+e- is not possible
n+n  p+p+e-+e- never occurs
Evolutionary Stability in Bayesian Network Games

7. Evolutionary Stability in Bayesian Network Games
Parallel Links Model
Evolutionary Stability in Bayesian Network Games

8. Parallel Links Model as a Game
Evolutionary Stability in Bayesian Network Games

9. Evolutionary Stability in Bayesian Network Games
Stable Equilibrium
Bilaniuk and Sudarshan (1969): “There is an unwritten precept in modern physics, often facetiously referred to as Gell-Mann’s Totalitarian Principle… `Anything which is not prohibited is compulsory’. Guided by this sort of argument we have made a number of remarkable discoveries from neutrinos to radio galaxies.”
Ford (1963): “Everything which can happen without violating a conservation law does happen.”
Evolutionary Stability in Bayesian Network Games

10. Hawk vs. Dove As A Population Game
World 1  n+n  p+p+e-+e- is possible
World 2  n+n  p+p+e-+e- is not possible
n+n  p+p+e-+e- never occurs
Evolutionary Stability in Bayesian Network Games

11. Population Interpretation of Nash Equilibrium
Evolutionary Stability in Bayesian Network Games

12. Evolutionary Stability
Kane (1986): “What is interesting is that, in committing themselves to plenitude in this restricted form, modern physicists are committing themselves to the principle that what never occurs must have a sufficient reason or explanation for its never occurring.”
Nobel Laureate Leon Cooper (1970): “In the analysis of events among these new particles, where the forces are unknown and the dynamical analysis, if they were known, is almost impossibly difficult, one has tried by observing what does not happen to find selection rules, quantum numbers, and thus the symmetries of the interactions that are relevant.”
Feynmann (1965): ”The reason why we make these tables [of conserved quantities] is that we are trying to guess at the laws of nuclear interaction, and this is one of the quick ways of guessing at nature.”
Evolutionary Stability in Bayesian Network Games

13. Evolutionary Stability in Bayesian Network Games
Bayesian Routing Game
Evolutionary Stability in Bayesian Network Games

14. Characterization of ESS in Bayesian Routing Game
I see! 2v  2p + 2e is impossible.
Particle Review 2005: 2v  2p + 2e- observed
Particle Review 2004: no 2v  2p + 2e-
Particle Review 2003: no 2v  2p + 2e-
Particle Review 2002: no 2v  2p + 2e-
This problem is real
I must find a conservation law that explains this.
Evolutionary Stability in Bayesian Network Games

15. Necessary Condition: same speed, same behaviour
Evolutionary Stability in Bayesian Network Games

16. Single Task, Uniform Links: Unique Uniform ESS
Hypothetical Scenario
observed reactions
not yet observed reactions
-  - + n -  m- + nm m-  e- + nm + ne n  e- + ne + p p + p  p + p + 
n  e- + ne
p + p  p + p +  + 
entailed
Evolutionary Stability in Bayesian Network Games

17. Strong Necessary Condition: No double overlap
Evolutionary Stability in Bayesian Network Games

18. >2 Tasks, Uniform Speeds: No ESS
Evolutionary Stability in Bayesian Network Games

19. Clustering are typical ESS’s
ESS leads to niches.
Evolutionary Stability in Bayesian Network Games

20. Does A Clustered Equilibrium Exist?
Evolutionary Stability in Bayesian Network Games

21. Evolutionary Stability in Bayesian Network Games
Future Work
Evolutionary Stability in Bayesian Network Games

22. Evolutionary Stability in Bayesian Network Games
Conclusion
Evolutionary Stability in Bayesian Network Games