Talks

Equilibrium multiplicity throws up the question of which equilibria are plausible. How can we distinguish between them? We look to understanding equilibria as emergent properties of dynamic processes of behavioral change and consider some classic behavioral rules and applications, such as the best response rule and coordination problems.

The emergence of cooperation among selfish agents that have no incentive to cooperate is a non-trivial phenomenon that has long intrigued biologists, social scientists and physicists. The iterated Prisoner’s Dilemma (IPD) game provides a natural framework for investigating this phenomenon. The spatial version of IPD, where each agent interacts only with their nearest neighbors on a specified connection topology, has been used to  study the evolution of cooperation under conditions of bounded rationality. This talk will explorehow the collective behavior that arises from the simultaneous actions of the agents (implemented by synchronous update) is affected by the connection topology among the interacting agents. The system exhibits three types of collective states, viz., a pair of absorbing states (corresponding to all agents cooperating or defecting, respectively) and a fluctuating state characterized by agents switching intermittently between cooperation and defection. We show that the system exhibits a transition from one state to another simply by altering the connection topology from regular to random, without altering any of the parameters govering the game dynamics, such as temptation payoff or noise. Such topological phase transitions in collective behavior of strategic agents suggest important role that social structure may play in promoting cooperation.

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.

I discuss work in progress on the no-boundary state of the universe in quantum cosmology, emphasizing the key role played by the inclusion of an observer in obtaining a reasonable no-boundary state. For concreteness we focus on a 2d toy model, namely dS JT gravity. This model has avatars of important issues with the wavefunction of the universe in inflationary models. The issues are that the wavefunction predicts a small universe (whereas our universe is rather large), and that it is not normalizable. I show that the non-normalizability is resolved by promoting dS JT gravity to sine dilaton gravity, a type of UV completion of dS JT gravity of which I discuss the cosmological interpretation. I then argue that the issue of predicting a small universe (in this toy model) is resolved by including an observer in the theory. With the observer, the leading contribution is a bra-ket wormhole. The observer's no boundary state is a (maximally mixed) identity matrix, and thus prefers neither small nor large universes.