Sanjari Kalantri

I analyse a dynamic model of persuasion in which a long-lived Sender provides information about an evolving state to a sequence of short-lived Receivers who choose between two actions, high and low. In each period, the Sender has a weak ordinal preference for the high action over the low and the good state over the bad, whereas each Receiver wants the high action only in the good state. Importantly, each Receiver’s action affects the state the next one faces, creating intertemporal externalities: the high action may either improve or worsen the future state. When the high action improves the future state, the Sender’s ordinal preferences alone ensure that the optimal policy is the one that induces the high action with maximal probability each period. When the high action worsens the future state, the optimal policy depends on the cardinal features of the Sender’s preferences: it may maximise the probability of the high action or of the low action, fully reveal the state (eliminating any uncertainty), or leave the Receiver uncertain of the state after every disclosure. Beyond what the Sender discloses, the optimal policy also determines when she discloses, and whether disclosure eventually stops.

I analyse a dynamic cheap-talk model in which a long-lived sender provides information about an evolving state to a sequence of short-lived receivers making binary decisions. States evolve endogenously based on the action taken by the receiver. I also assume that there are no conflicts of interest between the sender and the receivers in the stage-game. While a non-informative equilibrium always exists, full revelation is an equilibrium in the stage-game too. I then characterize the equilibria in the dynamic game, depending on the strength and direction of the externalities. In the dynamic game, under moderate externalities, partially revealing equilibria may exist, but the non-informative equilibrium is the unique equilibrium when the externalities are too strong.

In standard principal-agent models, a risk-neutral principal designs a wage schedule as a function of output (which is observable) to incentivise a risk-averse agent to exert high effort (which is unobservable). In our setup, the agent has Yaari preferences, i.e., she applies a probability distortion function to the output probabilities, rather than a utility function to the wages. In the binary action case, we show that simple bonus contracts are optimal. We also do comparative statics with respect to various parameters: the minimum wage, agent's reservation wage, degree of risk aversion of the agent, and the informativeness of the signal (output).