Sequential Persuasion Dynamics

• Sequential persuasion is a dynamic process where information is released in stages, enabling senders to design multi-step experiments that evolve with prior outcomes.
• Dynamic commitment in sequential persuasion requires senders to adhere to a series of experiments, with later stages adapting based on receiver responses and historical signals.
• Constrained information technologies and learning-based methods in sequential persuasion optimize sender strategies, balancing immediate impact with long-term influence in settings like economic models and AI systems.

Sequential persuasion denotes a family of information-design and influence problems in which disclosure unfolds across stages rather than through a single signal. Across the literature, the sequential element can arise because a sender composes a sequence of feasible experiments, because persuasion is embedded in a sequential game or a finite-horizon Markovian environment, because the sender learns while persuading, or because later receivers reinterpret the sender’s policy in light of observed history. In the classical Bayesian benchmark, providing information sequentially is never valuable, but this irrelevance disappears once experiments are constrained, continuation payoffs matter, or receivers update non-Bayesianly or history-dependently (Azrieli et al., 13 Aug 2025, Ni et al., 2023, Wu et al., 2022, Ko, 3 Aug 2025).

1. Conceptual scope

The literature uses “sequential persuasion” for several related, but non-equivalent, objects. One line studies finite or infinite sequences of feasible experiments, with each next experiment chosen as a function of earlier outcomes (Ni et al., 2023). A second line places persuasion inside sequential games with imperfect information or inside multi-phase trial trees whose future experiments depend on realized past outcomes (Celli et al., 2019, Su et al., 2021). A third line embeds persuasion in a Markovian control problem, where current recommendations influence future states and therefore future persuasion opportunities (Wu et al., 2022). A fourth line studies repeated interactions in which the sender learns the environment, builds reputation, or faces receivers whose interpretation of the signal policy changes with public history (Arieli et al., 2023, Bacchiocchi et al., 2024, Ko, 3 Aug 2025).

These formulations matter because the standard one-shot reduction is fragile. In the classic Bayesian case, a sequence of signals can be collapsed into a single experiment, so timing has no independent value (Azrieli et al., 13 Aug 2025). By contrast, timing becomes payoff-relevant when the sender is restricted to a feasible experiment set, when later experiments are determined exogenously, when the sender gradually learns the state, or when the receiver is a conservative Bayesian or a suspicious model selector rather than a literal Bayesian updater (Ni et al., 2023, Su et al., 2021, Arieli et al., 2024, Ko, 3 Aug 2025).

2. Dynamic commitment and obedience

Sequential persuasion typically preserves the canonical commitment structure of Bayesian persuasion, but commitment is now to a dynamic policy rather than to a one-shot experiment. In the dynamic product-adoption model of “Persuading while Learning,” the sender’s posterior process $X=(X_t)_{t=0,1,\dots,T}$ is a discrete-time Markov martingale on $[0,1]$, and the receiver adopts only if $\mathbb E[X_t\mid \tau=t]\ge l$. The sender’s control variable is a dynamic revelation policy, equivalently a randomized stopping rule $\tau$, and under Blackwell order preserving kernels there exists an optimal interval stopping rule. In the random-walk case, if the sender is sufficiently impatient, the greedy policy is optimal and is outcome-equivalent to full transparency up to the moment of adoption (Arieli et al., 2024).

Once the receiver also acts in a sequential environment, obedience itself becomes temporally layered. In “Bayesian Persuasion with Sequential Games,” a single sender interacts with multiple receivers whose actions are of a priori unknown types in a sequential game with imperfect information, and the analysis distinguishes ex ante from ex interim persuasiveness. The computational boundary is sharp in the available result: computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers, whereas for games with two receivers an optimal ex ante persuasive signaling scheme can be computed in polynomial time (Celli et al., 2019).

In settings with farsighted receivers, obedience cannot be reduced to a static posterior-best-response constraint. “Sequential Information Design: Learning to Persuade in the Dark” defines persuasiveness against deviation policies that may stop obeying at some recommendation history and then optimize the continuation problem on the induced subgame. The paper’s single-point-deviation decomposition and persuasive polytope are the core tractability devices: they convert dynamic obedience into a finite collection of linear constraints that support polynomial-time optimization in the known-prior case (Bernasconi et al., 2022).

3. Sequential experiments and constrained information technologies

A central reason sequence matters is that the sender often cannot implement arbitrary Bayes-plausible experiments. “Sequential Persuasion Using Limited Experiments” formalizes this by restricting the sender to a feasible set $F\subseteq F_0$ of experiments over posterior beliefs. The sender may therefore have to compose information gradually, conditioning the next feasible experiment on the current posterior. For infinite sequences, the supremum sender payoff is characterized by the constrained analogue of concavification,

$v_\infty(p)=\inf\{g(p):g\in G\},$

where $G$ is the set of functions dominating the stage value $v$ and satisfying the Jensen-type inequality induced by every feasible experiment. The paper also shows that when an optimal sequential design exists, there exists an optimal design that is Markovian, so the next experiment depends only on the receiver’s current belief (Ni et al., 2023).

“Bayesian Persuasion in Sequential Trials” studies a closely related but more structured problem: a multi-phase trial tree in which some experiments are chosen by the sender and others are fixed exogenously as determined experiments. In the only non-trivial two-phase binary-state, binary-outcome configuration, the sender designs phase I and both phase-II experiments are determined. The induced continuation behavior on each determined branch collapses to three classes, $\alpha$, $\beta$, and $[0,1]$0, and the best continuation use of a determined experiment $[0,1]$1 is summarized by its persuasion potential

$[0,1]$2

For general multi-phase trial trees, the paper gives a dynamic programming algorithm that recursively combines branch values using the two-phase structural insights (Su et al., 2021).

Sequential structure may also enter through the cost of generating evidence. “Costly Persuasion by a Partially Informed Sender” studies a privately and partially informed sender who chooses a public experiment at a cost equal to the expected reduction of a weighted log-likelihood ratio function of her belief. That cost is microfounded by a Wald sequential sampling problem in which good news and bad news cost differently. The paper’s qualitative divide is between low and high relative cost of good news: if good news is not too costly compared to bad news, there exists a unique separating equilibrium; if good news is sufficiently costlier, the single-crossing property fails, pooling and partial pooling may arise, and in some equilibria the receiver learns less information than in a benchmark with an uninformed sender (Jiang, 2024).

4. Markov, repeated, and learning-based persuasion

The most explicit dynamic-control formulation is the Markov persuasion process. In “Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning,” a sender with informational advantage seeks to persuade a stream of myopic receivers in a finite-horizon Markovian environment with varying priors and utility functions. Planning in this model requires choosing a signaling policy that is simultaneously persuasive stage by stage and optimal in long-run cumulative sender utility. In the known-model case, optimal or $[0,1]$3-optimal policies can be computed through a modified Bellman equation. In the online setting with unknown priors, sender utilities, and transitions, the paper introduces OP4, which combines optimism and pessimism and achieves a sublinear $[0,1]$4-regret upper bound (Wu et al., 2022).

A central impossibility result in the learning literature is that exact persuasiveness cannot, in general, be maintained while the sender learns unknown primitives. “Sequential Information Design: Learning to Persuade in the Dark” proves that no learning algorithm can be persuasive in its repeated extensive-form setting, and therefore replaces exact obedience by sublinear receiver regret. Under full feedback, the paper obtains $[0,1]$5 sender regret and $[0,1]$6 receiver regret. Under bandit feedback, it gives a tradeoff: for any $[0,1]$7, the sender can achieve $[0,1]$8 sender regret and $[0,1]$9 receiver regret, together with a lower bound showing this tradeoff is essentially tight (Bernasconi et al., 2022).

“Markov Persuasion Processes: Learning to Persuade from Scratch” strengthens the unknown-environment dimension by removing sender knowledge of transitions, priors, sender rewards, and receiver rewards. The model is an episodic MPP

$\mathbb E[X_t\mid \tau=t]\ge l$0

and the algorithmic contribution is OPPS, an optimistic persuasive policy search procedure over occupancy measures. Under full feedback, both cumulative regret and cumulative persuasiveness loss scale as $\mathbb E[X_t\mid \tau=t]\ge l$1. Under partial feedback, if $\mathbb E[X_t\mid \tau=t]\ge l$2, OPPS achieves

$\mathbb E[X_t\mid \tau=t]\ge l$3

and a matching lower bound shows that one cannot generally do better while keeping both quantities sublinear (Bacchiocchi et al., 2024).

Repeated persuasion also appears in mediated environments. “Reputation-based Persuasion Platforms” studies a platform that first controls the sender’s information about user types and then, in a repeated extension with sequentially arriving myopic users, maintains a reputation for the sender and punishes deviations from truthfulness on a designated subset of signals. The repeated problem is characterized by an incentive constraint that trades off current manipulation against permanent loss of future rents, and the optimal policy combines a truthful segment used for discipline with static segmentation on the residual segment (Arieli et al., 2023). At a higher level of repetition, “Meta-Learning for Repeated Bayesian Persuasion” studies related sequences of OBP and MPP tasks and shows that meta-persuasion algorithms achieve sharper regret rates under natural notions of task similarity while recovering standard single-game guarantees when the task sequence is arbitrary (Turna et al., 20 Mar 2026).

5. History, misspecification, and non-Bayesian updating

Once receivers update non-Bayesianly, sequence itself becomes an independent source of persuasion power. In “Sequential Non-Bayesian Persuasion,” the receiver is a conservative Bayesian whose updated belief is

$\mathbb E[X_t\mid \tau=t]\ge l$4

Under the paper’s period-by-period updating rule, the path of intermediate posteriors matters, so sequential disclosure is no longer reducible to a one-shot experiment. The paper shows gains from sequential persuasion in common-preferences environments, Crawford–Sobel quadratic-loss environments, transparent-motive linear-action settings, and two-action problems. It also proves that if sender and receiver are both biased, the maximal expected payoff under sequential persuasion is the same as in the benchmark where neither is biased (Azrieli et al., 13 Aug 2025).

A different long-run distortion appears in “Persuasion in the Long Run: When history matters.” There, a long-lived sender commits to a stationary information structure, but short-lived receivers compare the announced structure $\mathbb E[X_t\mid \tau=t]\ge l$5 with an uninformative alternative $\mathbb E[X_t\mid \tau=t]\ge l$6 and may switch according to a Bayes factor rule. The dynamic linkage across periods is not through state persistence but through evolving interpretation of the sender’s policy. When receivers cannot infer the state from the sender’s preferred action, they never switch and the one-shot BP-optimal structure remains optimal in the long run. When such inference is possible, however, full disclosure may outperform the BP-optimal structure because suspicious receivers can stop trusting the announced information structure (Ko, 3 Aug 2025).

Nonclassical path dependence also appears in “Targeting in Quantum Persuasion Problems.” In that model, persuasion is implemented by measurements that change the receiver’s cognitive state rather than by standard Bayesian posterior splits. The sender can transform any prior into the completely mixed state $\mathbb E[X_t\mid \tau=t]\ge l$7 with one blind measurement, can induce any target belief with probability at least $\mathbb E[X_t\mid \tau=t]\ge l$8 using two sequential measurements, and, when both prior and target are known pure states, can reach the target with probability at least $\mathbb E[X_t\mid \tau=t]\ge l$9. The first stage is interpreted as a deliberate distraction step that makes later persuasion possible (Danilov et al., 2017).

6. Dialogue, argumentation, and multi-agent influence

Not all sequential-persuasion research is framed as commitment-based information design. “Strategic Argumentation Dialogues for Persuasion” treats persuasion as an online planning problem over multi-turn argumentative dialogue. The persuadee is modeled by beliefs in arguments and concern preferences, the system optimizes the next move by Monte Carlo Tree Search, and the reward combines concern-sensitive dialogue quality with the final belief in the persuasion goal. In experiments with human participants, the belief-and-concern-aware system produced statistically significant belief change, whereas a baseline that chose counterarguments uniformly at random did not (Hadoux et al., 2021).

“Abstract Argumentation / Persuasion / Dynamics” gives a more abstract state-transition account. It extends Dung’s framework with persuasion acts of inducement and conversion, so persuasion changes the currently visible set of arguments over time. Reachable states form a branching transition system, admissibility becomes non-monotonic across transitions, and CTL is used to express temporal properties of argument evolution. This line studies sequential persuasion as dynamics over argument visibility rather than as Bayesian information disclosure (Arisaka et al., 2017).

A recent empirical line studies sequential persuasion behaviorally in multi-agent AI systems rather than as a game-theoretic design problem. “Disagreements in Reasoning: How a Model’s Thinking Process Dictates Persuasion in Multi-Agent Systems” operationalizes persuasion as post-exposure response change, measures it by Persuaded-Rate, Remain-Rate, and Other-Rate, and extends the analysis to multi-hop chains such as $\tau$0. Its central empirical finding is a “Persuasion Duality”: explicit reasoning increases resistance when a model is the persuadee, while exposing that reasoning increases its ability to persuade others. Influence then propagates nonlinearly through agent chains, with both amplification and attenuation depending on chain composition (Zhao et al., 25 Sep 2025).