Séminaire parisien de Théorie des Jeux

Program for 2023/2024

11:00-12:00 : Julien GRAND-CLEMENT  (HEC) On the connection between stochastic games and robust optimization, with Nicolas Vieille (HEC Paris) and Marek Petrik (University of New Hampshire).

 

Abstract: Robust Markov Decision Processes (RMDPs) are a widely used framework for sequential decision-making under parameter uncertainty. RMDPs have been extensively studied when the objective is to maximize the discounted return, but little is known for average optimality (optimizing the long-run average of the rewards obtained over time) and Blackwell optimality (remaining discount optimal for all discount factors sufficiently close to 1). In this paper, we prove several foundational results for RMDPs beyond the discounted return. We show that average optimal policies can be chosen stationary and deterministic for sa-rectangular RMDPs but, perhaps surprisingly, that history-dependent (Markovian) policies strictly outperform stationary policies for average optimality in s-rectangular RMDPs. We also study Blackwell optimality for sa-rectangular RMDPs, where we show that approximate Blackwell optimal policies always exist, although Blackwell optimal policies may not exist. We also provide a sufficient condition for their existence, which encompasses virtually any examples from the literature. We then discuss the connection between average and Blackwell optimality, and we describe several algorithms to compute the optimal average return. Interestingly, our approach leverages the connections between RMDPs and stochastic games.

10:00-11:00: Dimitrios XEFTERIS  (University of Cyprus) Information Aggregation with Delegation of Votes, with Amrita Dhillon (King’s College London), Grammateia Kotsialou (London School of Economics), Dilip Ravindran (Humboldt University of Berlin), Dimitrios Xefteris (University of Cyprus)


Abstract: Liquid democracy is a system that combines  aspects of direct democracy and representative democracy by allowing voters to either vote directly themselves, or delegate their votes to others. In this paper we study the information aggregation properties of liquid democracy in a setting with heterogeneously informed truth-seeking voters who want the election outcome to match an underlying state of the world and partisan voters. We establish that liquid democracy admits equilibria which improve welfare and information aggregation over direct and representative democracy when voters' preferences and information precisions are publicly or privately known. When precisions are commonly known, we provide sufficient conditions for this improvement being strict and characterize optimal delegation for important classes of committees. Liquid democracy also admits equilibria which do worse than the other two systems. We discuss features of efficient and inefficient equilibria and provide conditions under which voters can more easily coordinate on the efficient equilibria in liquid democracy than the other two systems.




Andy CHOI (Bocconi University)


Divyarthi MOHAN (Tel Aviv University) Communicating with Anecdotes, with Nika Haghtalab, Nicole Immorlica, Brendan Lucier, and Markus Mobius.

We study a communication game between an informed sender and an uninformed receiver. The sender chooses one of her signals about the state of the world (i.e., an anecdote) and communicates it to the receiver who takes an action affecting both players. The sender and receiver both care about the state of the world but are also influenced by personal preferences, so their ideal actions can differ. We characterize perfect Bayesian equilibria. The sender faces a temptation to persuade: she wants to select a biased anecdote to influence the receiver’s action. Anecdotes are still informative to the receiver (who will debias at equilibrium) but the attempt to persuade comes at the cost of precision. This gives rise to informational homophily where the receiver prefers to listen to like-minded senders because they provide higher-precision signals. Communication becomes polarized when the sender is an expert with access to many signals, with the sender choosing extreme outlier anecdotes at equilibrium (unless preferences are perfectly aligned).  This polarization dissipates all the gains from communication with an increasingly well-informed sender when the anecdote distribution is heavy-tailed. Experts can therefore face a curse of informedness: receivers will prefer to listen to less-informed senders who cannot pick biased signals as easily.

Bernhard VON STENGEL (LSE)

Sven RADY (Bonn University)