Thursday, 26th of November
13:00-13:05 Introductory remarks by Mark Golden
13:05-13:30 Mauricio del Razo | Biochemical reaction-diffusion: a multiscale and open systems approach
13:30-13:55 Janusz Meylahn | Tacit Collusion By Self-learning Algorithms In Duopoly
13:55-14:20 Joint coffee tea break
14:20-14:45 Soroush Rafiee Rad | Characterizing Probabilistic Models with A Symmetry Axiom
14:45-15:10 Wout Merbis | Many-body stochastic systems on complex networks
15:10-15:30 Discussion moderated by Mark Golden
Biochemical reaction-diffusion: a multiscale and open systems approach | 13:05-13:30
Mauricio del Razo, DIEP fellow
Biochemical reaction systems in living cells constantly exchange material and energy with their environment. Namely, they operate in an open non-equilibrium setting. Furthermore, these systems are inherently multiscale; cellular signaling alone involves six orders of magnitude in length-scales and eighteen orders of magnitude in time-scales. These scales are tightly coupled such that a single-point mutation in a protein can disturb the biochemical interactions at a macroscopic level. It is thus fundamental to develop theoretical and computational frameworks for biochemical reaction-diffusion systems in open and multiscale settings. In this work, we will present some of our recent advances towards this goal.
We design an algorithm, which can be employed by two firms in a duopoly, that guarantees convergence to the optimal price (the collusive price when it is profitable to collude and the Nash equilibrium otherwise). Furthermore, implementation of the algorithm against an opponent not employing the algorithm guarantees convergence to the best response, given that the opponent's strategy falls within a broad class of reaction functions. The results hold under the mild assumptions on the demand model. These are satisfied by the linear demand model. The implementation of the algorithm would be legal under current EU competition law, and so poses a threat for consumer welfare. Much of the debate surrounding this topic has relied on speculation regarding the possibility of such collusion. Our algorithm provides solid ground for such speculation.
Tacit Collusion By Self-learning Algorithms In Duopoly | 13:30-13:55
Janusz Meylahn, DIEP fellow
Characterizing Probabilistic Models with A Symmetry Axiom | 14:20-14:45
Soroush Rafiee Rad, DIEP fellow
We investigate probabilistic models for a set of first order axioms that are defined in terms of probabilistic inference processes. We study conditions under which such models are well defined and show how a symmetry axiom can uniquely characterize these models.
Many processes in Nature are stochastic; a randomly determined process evolving by the master equation. In this talk, we will formulate an understanding of the stochastic processes involved in epidemiological modelling on networks, in close analogy to many-body quantum systems. We describe the exact state of the population as a tensor product of individual probability spaces. A natural set of operators which act on these individual probability spaces is found and bilocal interactions (i.e. transition rate matrices) are constructed by taking tensor products of these operators. In this way, we are able to define and study exact microscopic versions of many compartmental models familiar from epidemiology and population dynamics. We show how, in simple settings, it is possible to find exact solutions to the master equation for finite population sizes. We comment on several possible research directions which rely on adapting tools and techniques from many-body quantum systems and quantum information to the case at hand and other stochastic many-body systems.
Many-body stochastic systems on complex networks| 14:45-15:10
Wout Merbis, DIEP researcher