Honesty is the Best Policy ... or is it? Demand Management for Probabilistic Service Options

Daniela Sailer; Robert Klein; Claudius Steinhardt

cs.LGOct 15, 2026

Honesty is the Best Policy ... or is it? Demand Management for Probabilistic Service Options

Authors: Daniela Sailer, Robert Klein, Claudius Steinhardt

Organizations: Chair of Analytics & Optimization, University of Augsburg · Chair of Business Analytics & Management Science, University of the Bundeswehr Munich

Abstract

To enable well-informed customer choices and redistribute demand across service options, providers can display probabilities regarding predicted service levels at the time of booking, effectively offering probabilistic service options. In many service settings, the underlying truthful probabilities endogenously depend on the system state, rather than being static product attributes controlled by the provider. While customers rely on this information when making decisions, they cannot readily verify its accuracy. Consequently, providers may be tempted to manipulate the displayed probabilities to guide customers' choices in their favor, creating a novel lever for demand management. In this work, we model the resulting problem as a sequential decision process, define truthful probabilities recursively, and introduce transparency constraints that limit their distortion. Because the exact computation of truthful probabilities is intractable for realistic settings, we develop an adapted reinforcement learning algorithm to approximate them. Furthermore, we propose a sampling-based mixed-integer program to optimize the information communicated by the provider in each state. Our framework enables providers to gauge the benefits of dynamically disclosing probabilistic information at the time of booking and sheds light on incentives for manipulation. Our computational study is motivated by out-of-home delivery, i.e., the delivery to parcel lockers or shops, and reveals a trade-off between individual-level transparency and aggregate customer utilities.

Figures & tables

			CS			(%)					(pp)
Policy $\pi$		$\tau$	Total	$\Delta$ %	pc	LS	RR	$\underline{\text{LU}}$	$\overline{\text{LU}}$	DC	IN	AE
FF	NO	–	-19,996.5	0.0	-4.9	86.6	13.4	59.8	96.6	–	–	–
	GP	–	-19,950.2	0.2	-4.9	78.9	0.0	75.5	90.4	–	–	–
	EU/LA	0	-17,439.2	12.8	-4.3	85.6	5.5	69.1	96.7	94.9	0.0	0.8
	EU	1	-17,408.6	12.9	-4.3	85.5	5.2	69.7	96.6	94.7	1.1	0.6
	LA	1	-16,551.2	17.2	-4.1	82.3	2.7	76.3	92.0	91.4	19.9	0.4

Table 1: Performance metrics for the base setting.

	Negative		Positive
$\pi^{\textbf{LA}}(1)$	Share	Mean	Share	Mean
FF	11.3	-29.2	1.5	5.0
MY	9.4	-15.7	8.9	4.4

Table 2: Probability distortion.

Figure 1: State-dependent truthful probabilities and their distortion.

Policy $\pi$		$\tau$	PP	PB	OO
FF	NO	–	84.0	16.0	0.0
	LA	0	80.4	6.5	13.1
		1	75.0	2.9	22.0
MY	NO	–	84.0	16.0	0.0
	LA	0	79.2	9.5	11.2
		1	77.2	6.4	16.5

Table 3: Group shares (%).

	Utility loss $(\text{CR}>0)$							Utility gain $(\|\text{CR}<0\|)$
$\pi^{\textbf{LA}}(1)$	Total	Share	Mean	Q1	Q2	Q3	Max.	Total	Share	Mean	Q1	Q2	Q3	Max.
FF	1,257.2	12.2	2.5	0.8	1.7	3.3	20.4	2,139.5	7.2	7.3	3.1	6.6	10.4	24.4
MY	1,122.2	8.9	3.1	1.0	2.1	4.1	19.2	1,940.4	7.6	6.3	2.0	5.3	9.4	23.1

Table 4: Regret distribution.

Figure 5: Redirection rates.

			CS			(%)					(pp)
$\beta_{L}$	$\pi^{\text{LA}}$	$\tau$	Total	$\Delta$ %	pc	LS	RR	$\underline{\text{LU}}$	$\overline{\text{LU}}$	DC	IN	AE
0	FF	0	-23,076.3	7.6	-5.7	78.6	4.5	41.7	94.4	94.8	0.0	0.6
		1	-22,449.2	10.1	-5.5	76.0	2.1	47.9	90.2	91.7	17.2	0.3
	MY	0	-22,448.6	4.2	-5.5	79.3	7.3	44.6	94.0	90.1	0.0	2.9
		1	-21,966.3	6.3	-5.4	78.2	4.8	44.1	92.3	89.8	9.9	2.0
4	FF	0	-11,356.1	23.3	-2.8	90.4	5.7	85.6	97.3	93.0	0.0	0.7

Table 5: Performance metrics for varying locker utility constant

\beta_{L}

Figure 6: Performance of policy

\pi^{\text{LA}}_{\text{MY}}(\tau)

in setting

\beta_{L}=4

			CS			(%)					(pp)
$I$	$\pi^{\text{LA}}$	$\tau$	Total	$\Delta$ %	pc	LS	RR	$\underline{\text{LU}}$	$\overline{\text{LU}}$	DC	IN	AE
15	FF	0	-18,561.6	15.4	-3.1	84.3	5.1	64.9	96.5	93.9	0.0	0.6
		1	-17,552.3	20.0	-2.9	80.5	2.3	71.3	93.0	91.6	22.2	0.2
	MY	0	-18,000.5	8.8	-3.0	84.3	8.7	55.7	95.5	88.7	0.0	3.4
		1	-16,867.1	14.6	-2.8	84.2	6.1	67.1	94.9	88.4	12.6	2.3
20	FF	0	-21,359.6	21.3	-2.6	86.7	6.7	66.0	99.5	93.1	0.0	0.7

Table 6: Performance metrics for varying network size

I

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$i\in\mathcal{I}=\mathcal{I}^{-}\cup\mathcal{I}^{+}$	Service outcomes, partitioned into base outcomes $\mathcal{I}^{-}$ and premium outcomes $\mathcal{I}^{+}$
$Q_{i}$	Capacity of premium outcome $i\in\mathcal{I}^{+}$
$j\in\mathcal{J}=\mathcal{J}^{P}\cup\mathcal{J}^{D}$	Service options, partitioned into probabilistic service options $\mathcal{J}^{P}$ and deterministic service options $\mathcal{J}^{D}$
$(i_{j}^{-},i_{j}^{+})$	Base outcome $i_{j}^{-}\in\mathcal{I}^{-}$ and premium outcome $i_{j}^{+}\in\mathcal{I}^{+}$ of probabilistic service option $j\in\mathcal{J}^{P}$
$i_{j}$	Service outcome $i_{j}\in\mathcal{I}^{-}$ of deterministic service option $j\in\mathcal{J}^{D}$
$t\in\mathcal{T}$	Point in time
$p_{j}$	Displayed probability for premium outcome of probabilistic service option $j\in\mathcal{J}^{P}$

Appendix

Table 12

Feature	Min.	Max.	Interpretation
$t^{A}$	$1$	$T$	Number of within-day time periods until allocation $T+1-t_{k}$
$O^{+}$	$0$	$T$	Number of pending orders for service option $j$ with a higher priority for allocation than order $o$
$C^{d}$	$0$	$Q_{i_{j}^{+}}$	Number of occupied capacity units in locker $i_{j}^{+}$ with elapsed storage duration of $d$ days
$x^{l},y^{l}$	$\underline{x},\underline{y}$	$\bar{x},\bar{y}$	Coordinates of locker $i_{j}^{+}$
$s$	$\underline{s_{i}}$	$\overline{s_{i}}$	Expected demand share of locker $i_{j}^{+}$
$\Delta v$	$\underline{\Delta v}$	$\overline{\Delta v}$	Deterministic utility component difference $v_{i_{j}^{+}}-v_{i_{j}^{-}}$ for order $o$

Appendix

Table 8: Feature overview.

Information Design

Information design studies how to choose what signals people or algorithms receive to shape decisions, incentives, and outcomes.

See all 15 papers

The Limits of Manipulation within Personalized Incentive Policies
Oct 9, 2026Andrea Araldo, Alessa Mayer, Ravi Seshadri +1Demand Response
SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, 91120 Palaiseau, France · Institut Polytechnique de Paris · Technical University of Denmark +2
The Value of Information in Resource-Constrained Pricing
Mar 26, 2026Ruicheng Ao, Jiashuo Jiang, David Simchi-LeviDynamic Pricing Decision-Making under Uncertainty
Institute for Data, Systems, and Society, Massachusetts Institute of Technology · Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology · Department of Civil and Environmental Engineering and Operations Research Center, MIT
From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms
Dec 28, 2025Rui Ai, David Simchi-Levi, Feng ZhuCausal Effect Estimation Instrumental Variable Estimation
MIT

Oct 9, 2026J/K move · Enter open · S save

The Limits of Manipulation within Personalized Incentive Policies

Andrea Araldo, Alessa Mayer, Ravi Seshadri, Amir Brudner

SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, 91120 Palaiseau, France · Institut Polytechnique de Paris · Technical University of Denmark+2

Demand Response

Open paper AskPDF arXiv

Demand management policies aim to shift individual behavior toward sustainable choices (e.g., goods, transport modes). Personalized incentive policies tailor subsidies to agents' needs and constraints, but personalization also exposes the regulator to agents' strategic manipulative behavior. The extent to which agents can profitably manipulate such policies remains poorly understood, which limits their applicability. This paper establishes analytically the conditions under which manipulation benefits the agent. We formalize a Stackelberg game in which an agent may simulate a different profile to extract higher incentives from a regulator. Previous work typically assumes that the regulator would instantaneously classify agents into the simulated user profile. In contrast, we explicitly model the regulator's process of learning the agent profile, based on observed past behavior. This makes manipulation harder, since it forces the agent to consistently behave according to a simulated profile, thus renouncing following their true preferences. Manipulative agents thus incur a Cost of Manipulation, which has typically been neglected. By accounting for it, we get a counterintuitive finding: although classification uncertainty reduces personalization accuracy, it may benefit the regulator by deterring manipulation. We establish an upper bound on the agent's gain from manipulation, which becomes stricter as profiles become harder to distinguish for the regulator. Simulations on the London Passenger Mode Choice dataset illustrate this deterrence effect. The framework can therefore be used to stress-test the robustness of personalized incentive policies before deployment.

Abstract

Information Design

Explore similar work

The Limits of Manipulation within Personalized Incentive Policies

The Value of Information in Resource-Constrained Pricing

From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms