Talks

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

We present a model of opinion formation game resource limited utility-maximizing agents interacting over a social network. The opinion dynamics is the result of each agent simultaneously revising its opinion by gradient ascent of its utility function. We analyze the evolution of opinions, including boundedness of opinions, convergence to an equilibrium and oscillatory behavior. In some special cases, we comment on the relative dominance of the agents on the steady state opinions. We also establish connections to Nash equilibria and prices of anarchy.

Bio: Pavan Tallapragada is an Associate Prof. in the Robert Bosch Centre for Cyber Physical Systems at the Indian Institute of Science. His research interests are broadly in multi-agent systems and control, including in multi-robot control, multi-agent reinforcement learning and dynamics of social systems.

Animals in the natural world face many choices, and their decisions with respect to food and habitat have major consequences for their fitness. Many factors influence these behavioural decisions, including the ecological and life history context of individuals. I will present our work analysing how females of a cosmopolitan and generalist pest — the red flour beetle Tribolium castaneum — choose where and how to lay eggs. When presented with a choice of an optimal (wheat flour) vs. a non-optimal resource (finger millet), females sometimes allocate more eggs in finger millet. However, we find that this preference depends on their age and density context, and is tuned to optimize distinct fitness components for their offspring, likely mediated via differential nutrient provisioning. During laboratory evolution in wheat-finger millet habitats, the founder female context also determines evolutionary changes in decision-making, though these maternal effects decline over time. Importantly, founder context also influenced population size and the effect of an inadvertent parasitic infection in our experiment. Our work highlights the role of ecological context in driving female decision-making, and demonstrates some wide-ranging effects of founder context on adaptation and trait evolution.

We present a tensor-network-based classical algorithm (equipped with guarantees) for simulating $n$-qubit quantum circuits with arbitrary single-qubit noise. Our algorithm represents the state of a noisy quantum system by a particular ensemble of matrix product states from which we stochastically sample a pure quantum state. Each single qubit noise process acting on a pure state is then represented by the ensemble of states that achieve the minimal average entanglement (the entanglement of formation) between the noisy qubit and the rest of the system. This approach provides a connection between the entanglement of formation and the accuracy of the simulation algorithm. For a given maximum bond dimension $\chi$ and circuit, our algorithm comes with an upper bound on the simulation error (in total variation distance), runs in $poly(n,\chi)$-time and improves upon related prior work (1) in scope: by extending from the three commonly considered noise models to general single qubit noise (2) in performance: by employing a state-dependent locally-entanglement-optimal unraveling and (3) in conceptual contribution: by showing that the fixed unraveling used in prior work becomes equivalent to our choice of unraveling in the special case of depolarizing and dephasing noise acting on a maximally entangled state. This is joint work with Simon Cichy, Paul K. Faehrmann, Lennart Bittel and Jens Eisert.

Beginning with the intimate relationship between recursive algorithms and dynamical systems, I shall describe some common dynamics that serve as templates for `stateless' learning. This will be followed by reinforcement learning for dynamic systems, using Markov decision processes as a test case.

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).