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

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

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

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

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

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

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

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

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

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

Population Interpretation of Nash Equilibrium Evolutionary Stability in Bayesian Network Games

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

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

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

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

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

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

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

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

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

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

Evolutionary Stability in Bayesian Network Games Conclusion Evolutionary Stability in Bayesian Network Games