Order of Commitments in Bayesian Persuasion with Partial-informed Senders

TL;DR

This paper examines how the order of commitments in sequential Bayesian persuasion with partially informed senders affects equilibrium outcomes, revealing conditions under which different payoff profiles emerge.

Contribution

It provides necessary and sufficient conditions for when commitment order impacts payoffs in two-sender persuasion games with partial information.

Findings

Different payoff profiles occur if senders are willing to collaborate in some states.

Credible threats by the second sender when committing first influence the other sender's signaling strategy.

Order of commitment affects equilibrium payoffs under specific conditions.

Abstract

The commitment power of senders distinguishes Bayesian persuasion problems from other games with (strategic) communication. Persuasion games with multiple senders have largely studied simultaneous commitment and signalling settings. However, many real-world instances with multiple senders have sequential signalling. In such contexts, commitments can also be made sequentially, and then the order of commitment by the senders -- the sender signalling last committing first or last -- could significantly impact the equilibrium payoffs and strategies. For a two-sender persuasion game where the senders are partially aware of the state of the world, we find necessary and sufficient conditions to determine when different commitment orders yield different payoff profiles. In particular, for the two-sender setting, we show that different payoff profiles arise if two properties hold: 1) the two senders are willing to collaborate in persuading the receiver in some state(s); and 2) the sender signalling second can carry out a credible threat when committing first such that the other sender's room to design signals gets constrained.