Tourist arrival forecasting with game-theoretic social influence weighting and deep learning

Ali Nikseresht

cs.LGJul 4, 2025

Tourist arrival forecasting with game-theoretic social influence weighting and deep learning

Authors: Ali Nikseresht

Organizations: School of Computer Science, Georgia Institute of Technology, Atlanta, GA 30332, United States

Abstract

In the era of Industry 5.0, data-driven decision-making has become indispensable for planning in service systems such as tourism. This paper proposes a non-linear hybrid approach for forecasting tourist arrivals to Hong Kong from five major source markets before COVID-19 and to Sanya, China, through the COVID-19 shock. The method integrates multiple sources of Internet big data and employs a cooperative game-theoretic algorithm to identify coalitions of opinion leaders on social media, whose content then receives larger weights. The Empirical Wavelet Transform (EWT), applied causally, manages nonstationary attributes, and a Stacked Bi-directional Long Short-Term Memory (Stacked BiLSTM) network tuned by Bayesian optimization generates the forecasts. We prove that the Shapley values of the underlying trust-weighted coverage game have a closed form and that the coalition of maximal synergy can be found exactly in polynomial time. Relative to the same network fed only with past arrivals, Internet big data reduce the one-step-ahead root mean squared error by 4.1-41.7% across the Hong Kong markets and opinion-leader weighting by a further 10.1-49.4%, against 5.3% and 8.7% for Sanya. The approach compares favorably with published benchmarks and remains robust under volatile conditions, which suggests uses in logistics, supply chains and production planning.

Figures & tables

Figure 1: (a) Historical monthly time series of the tourist arrivals to Hong Kong from the five chosen source markets, August 2012 to May 2019, and (b) historical monthly tourism demand data in Sanya, January 2011 to October 2021. Shaded areas mark the test windows (last 20% of each series).

Figure 2: Holistic data mining and goal-oriented Internet big data analytics framework.

Panel of Figure 3 — Figure 3: (a) A sample of EWT executed on the tourism demand data (the arrivals from the U.S. for case one, six modes on a normalized time axis). (b) Walk-forward (rolling-origin) evaluation with causal decomposition. At every origin the scaling, the interpolation and the EWT use only the data available at that origin.

Figure 4: Categorization of the trust modes among three users

u_{i}

u_{j}

and

u_{k}

Figure 5: Entire procedure of the game-theoretic opinion leader detection algorithm. Steps 1–3 form the trust layer and steps 4–6 the game layer. The closed form of Theorem 1 and the exact algorithm of Theorem 2 replace the enumeration of permutations and coalitions.

Figure 6: Architecture of the proposed Stacked BiLSTM. Each block holds a forward and a backward LSTM cell that read the same input, both directions run inside the input window, which ends at the forecast origin

t

, and the readout joins the last forward state with the last backward state.

Hyperparameter functionality	Symbol	Value range	Search scale
No. of units in each layer	$N_{u}$	$\{60,\dots,250\}$	integer
No. of layers	$N_{l}$	$\{1,\dots,8\}$	integer
Initial learning rate	$N_{lr}$	$[10^{-2},\,1]$	logarithmic
$L_{2}$ regularization	$N_{L2}$	$[10^{-10},\,10^{-2}]$	logarithmic
Drop-out rate	$N_{d}$	$[0.1,\,0.9]$	linear
Learning method	$N_{lm}$	{BiLSTM, LSTM}	categorical

Table 1: BiLSTM hyperparameters and corresponding value ranges, which are optimized with the help of the suggested BO algorithm.

Figure 7: The BO algorithm.

Figure 8: Holistic view of the entire execution steps of the developed methodology.

Figure 9: MAPE over the prediction horizon (as a proportion). (a) Mainland China, (b) the U.S., (c) Canada, (d) the U.K. and (e) Australia. “With Internet big data” denotes the full framework, including opinion-leader weighting and the EWT, and “Without Internet big data” the same network fed only with past arrivals.

Mainland China
	Considering opinion leaders			Not considering opinion leaders
Forecast	With	Without	Rel. impr.	With	Without	Rel. impr.
lead time $h$	EWT	EWT	(%)	EWT	EWT	(%)
1	0.0044	0.0048	8.33	0.0050	0.0052	3.85
2	0.0047	0.0052	9.62	0.0056	0.0061	8.20
3	0.0051	0.0055	7.27	0.0055	0.0060	8.33

Table 2: Forecast accuracy improvements when considering and not considering opinion leaders and the EWT analysis (in terms of RMSRE). Relative improvements follow Eq. ( 24 ), with

\mathrm{EM}_{1}

the RMSRE of the variant with the EWT and

\mathrm{EM}_{0}

that of the variant without it.

Mainland China
	RMSE with social media features			Reduction by Full (%)
Horizon	Full	Attention	Endorsement	vs.	vs.
$h$	set	features	features	Attention	Endorsement
1	973.502	986.087	977.196	1.28	0.38
2	985.103	996.745	989.320	1.17	0.43
3	994.902	1018.003	1007.144	2.27	1.22

Table 3: Comparison of out-of-sample RMSE across different feature set considerations using social media data, without opinion leader detection. The last two columns give the reduction of the full set relative to each single family, computed with Eq. ( 24 ).

Proposed hybrid algorithm
Model	China	U.S.	Canada	U.K.	Australia
Topic modeling + SARIMAX ( Park et al., 2021 ) †	655897	11121	NA	NA	NA
SARIMA-MIDAS ( Hu et al., 2022 ) †	NA	4912.31	1267.96	2526.74	3869.27
(w) without Internet big data	1061.156	1038.809	593.470	780.483	804.962
(b) with Internet big data	948.357	996.411	409.572	506.418	468.938
(l) with Internet big data and opinion leaders	852.957	847.391	279.624	256.417	362.260

Table 4: One-step-ahead RMSE values obtained by state-of-the-art methods and the developed one to forecast tourism demand.

No.	Model	RMSE	MAPE
1	PCA + SVM	37789	0.015
2	KPCA + SVM	37789	0.015
3	ISOMAP + SVM	72784	0.024
4	LLE + SVM_PROPHET	88537	0.035
5	TSNE + SARIMAX_F	217929	0.083
6	Proposed hybrid algorithm , (w) without Internet big data	37058	0.014

Table 5: RMSE and MAPE of five models reported by Hu et al. (2023) and of the developed framework for one-step-ahead forecasts of Sanya tourism demand.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Platform	Type of data	Variables
Search engine data	Google	Search	Search queries, trends and web traffic
	Baidu	Search	Search queries, trends and web traffic
Social media data	TripAdvisor	Volume and valence	Review volume and rating for attractions, hotels and shopping markets, as in Hu et al. (2022)
	Facebook	Volume (attention)	Numbers of comments, posts, likes and shares
		Valence (endorsement)	Average length, sentiment and polarity of comments
	Twitter	Volume (attention)	Numbers of comments, posts, likes and shares

Appendix

Table 1: Summary of the used Internet big data features.

Main keywords and hashtags	Main keywords and hashtags
Tourism-related words (e.g., travel)	Economy-related words (such as growth, rise)
Online tourism-market-related words (e.g., tourism platform)	Customer-related words (such as anger, satisfaction)
Hotel-related words (e.g., The Ritz-Carlton, hotel, room)	Industry-issue-related words (such as brand, market)
Tourist-attraction-related words (e.g., Hong Kong Skyline)	Public-rights-related words (such as transparency, safety, privacy)
General Sanya- and Hong Kong-related words (e.g., hong_kong, government)	Societal-issue-related words (such as family, woman)
Shopping-market-related words (e.g., Stanley Market)	Sanya and Hong Kong political and regulation-related words (such as political, community, authority, policy)

Appendix

Table 2: Main keywords and hashtags whose combinations were used for social media data extraction.

Solution	Payoff structure	Equilibrium	Result
1	zero-sum, strategies $\{\mathsf{o},\mathsf{a}\}$	$(\mathsf{o},\mathsf{o})$ , payoffs $(0,0)$	deadlock (Prop. B.1 )
2	zero-sum, adds agreement $\mathsf{g}$	$(\mathsf{o},\mathsf{o})$ , payoffs $(0,0)$	deadlock (Prop. B.1 )
3	zero-sum part plus common bonus $1/d$ per agreeing player	$(\mathsf{g},\mathsf{g})$ if $1/d>\pi_{\mathsf{o}}+\pi_{\mathsf{g}}$ , $(\mathsf{o},\mathsf{o})$ if $1/d<\pi_{\mathsf{o}}+\pi_{\mathsf{g}}$ , any mixture of $\mathsf{o}$ and $\mathsf{g}$ at equality	cooperation or prisoner’s dilemma (Prop. B.2 )
4	separable, with influence probabilities $p_{A},p_{B}$	dominant strategies, mutual agreement iff Eq. ( 15 ) holds	agreement graph $G^{\mathrm{ag}}$ (Prop. 3 )

Appendix

Table 1: Equilibria of the four pairwise persuasion games.

Figure 1: The brokerage coalition of the

u_{2}

u_{7}

and

u_{11}

nodes (shaded) and the coalition of maximal synergy

\{u_{11},u_{12},u_{13},u_{14}\}

for unit trust scores and

c=1

(dashed outline).

Node	Deg.	BC	CC	EC	$\varphi_{i}$	Node	Deg.	BC	CC	EC	$\varphi_{i}$
$u_{1}$	2	26	.238	.098	.917	$u_{9}$	1	0	.246	.107	.750
$u_{2}$	2	56	.333	.306	.833	$u_{10}$	1	0	.224	.077	.750
$u_{3}$	2	36	.263	.270	.833	$u_{11}$	3	58.5	.333	.470	1.167
$u_{4}$	1	0	.185	.076	.750	$u_{12}$	2	4.5	.263	.343	.917
$u_{5}$	3	27	.224	.179	1.583	$u_{13}$	2	2.5	.246	.340	.917
$u_{6}$	1	0	.185	.076	.750	$u_{14}$	3	48.5	.306	.458	1.167

Appendix

Table 2: Exact centralities of the 16-node network of Fig. 1 . Deg. is the degree, BC the unnormalized betweenness, CC the closeness, EC the eigenvector centrality (unit Euclidean norm) and

\varphi_{i}

the Shapley value of the game of Eq. ( 12 ) with unit trust scores and

\kappa=1

(Corollary 1 (ii)).

Figure 2: A sample of two networks’ synergetic coalition, formed by linking their central nodes (OL).

Figure 1: The architecture of the stacked LSTM with dropout layers.

Symbol	Meaning
Forecasting and evaluation
$y_{t}$ , $\hat{y}_{t+h\mid t}$	arrivals in month $t$ and their $h$ -step-ahead forecast made at origin $t$
$h$ , $\mathcal{T}_{h}$	forecast horizon (lead time) and set of evaluated test months
$x_{\min},x_{\max}$ , $x_{\mathrm{low}},x_{\mathrm{high}}$	training range of a series and target range of the scaling
$\mathrm{EM}_{1}$ , $\mathrm{EM}_{0}$	evaluation metric with and without the component under study
$\mathcal{I}_{t}$	information available at origin $t$

Appendix

Table 1: Main notation for forecasting, networks, trust and influence.

Symbol	Meaning
Games, coalitions and weighting
$v$ , $\kappa$ , $\varphi_{i}$	characteristic function, coverage threshold and Shapley value
$\mathsf{o},\mathsf{a},\mathsf{g}$ , $M_{A}$ , $M_{B}$	strategies (original plan, altered plan, agreement) and payoff matrices
$\pi_{\mathsf{o}},\pi_{\mathsf{a}},\pi_{\mathsf{g}}$ , $p_{A}$ , $p_{B}$	payoff parameters and influence probabilities of the two players
$d_{ij}$ , $\zeta_{i}$ , $\lambda$ , $\rho$ , $\epsilon_{d}$	symmetric distance between users, composite centrality and distance parameters
$E^{\mathrm{ag}}$ , $G^{\mathrm{ag}}$	agreement edges and agreement graph

Appendix

Table 2: Main notation for games, coalitions, weighting, decomposition and learning.

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Tourist mobility poses a distinct challenge for urban transportation planning. Unlike resident commuting, tourist travel is largely non-routine, attraction driven, and highly sensitive to trip purpose, travel season, and trip member composition. Existing approaches either measure aggregate tourist spatial patterns without generating individual schedules, or synthesize mobility without tourist specific structure such as trip duration conditioning, month varying attraction demand, and household co-travel rules. To address these challenges, we propose a four stage simulation framework combining month conditioned spatial priors derived from GPS and survey data, trip extent prediction from tourist demographics, distance feasible ward sequence assignment, and LLM-based activity chain generation under household and spatial constraints. GPS data are used only in privacy preserving aggregated form as month conditioned spatial priors, with no individual traces retained or exposed. Experiments on tourism in Tokyo demonstrate that the GPS based tourist cohort extraction recovers spatial visitation signatures consistent with survey references, and our framework produces demographically aligned synthetic schedules whose ward-level visitation shares align closely with both survey distributions and staypoint derived monthly visitation patterns. The results demonstrate the framework's effectiveness as a geographically grounded, demographically aware approach to tourist mobility modeling.

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