Bayesian Persuasion
We investigate a game between a sender and receiver (the agents). While the sender has access to a stochastic process X, which is called, borrowing the terminology from Information Theory and Stochastic Filtering Theory, the (unobservable) signal process, the receiver only knows the process M, that is the message the sender is providing to him. Thus, the sender's filtration is the full information filtration, while the receiver has access to a restricted set. In this setting, each player aims at solving a stochastic control problem with an ergodic criterion and addressing a standard problem in Bayesian persuasion: the receiver prefers the (unobservable) state variable X to be as close as possible to a target value xa while the sender tries to influence him to make sure that the state X stays close to a given threshold xl. The outcome of this scenario gives rise to a (stochastic) Stackelberg game with asymmetry of information, where the leader and the follower correspond to the sender and the receiver, respectively. We address and solve this first case exploiting tools from linear filtering. The existing literature on this topic is quite limited, offering various opportunities for further research and exploration. Our ongoing work includes an extension involving two senders and a large population of receivers, constituting a two-layer game structure. Initially, we seek to establish an equilibrium for the receivers using mean field game techniques. Subsequently, we integrate this solution into the senders' objectives, leading to the resolution of a Nash equilibrium in the two-player game played between the senders. Furthermore, this formalisation naturally lends itself to different practical applications. While we have identified a few potential ones, such as signalling for electricity demand-response, carbon footprint reduction, and assessing the information content of dividends, we believe that numerous additional applications remain undiscovered. This is a currently ongoing joint work with Prof. René Aïd, Prof. Giorgia Callegaro and Prof. Luciano Campi.
Area: IS14 - Stochastic Control and Game-theoretic Models in Economics and Finance (Giorgio Ferrari)
Keywords: Bayesian persuasion, mean field game, Stackelberg equilibrium
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