Educational spread as a 'Coordination Game' – theory and application to Portugal

José Pedro Pontes; João Dias

doi:10.3934/jdg.2025002

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2025, Volume 12, Issue 4: 484-495. Doi: 10.3934/jdg.2025002

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Educational spread as a 'Coordination Game' – theory and application to Portugal

José Pedro Pontes^, and
João Dias

ISEG, Universidade de Lisboa and UECE/REM Research Center, Portugal

^*Corresponding author: José Pedro Pontes
^*Corresponding author: José Pedro Pontes

Received: March 2024

Early access: February 9, 2025

Published online: February 9, 2025

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Abstract

This paper examines the recent evolution of higher education in Portugal under the light of an $ n $-person coordination game. We feature two alternative coordination requirements, namely "unanimity", which expresses a cooperative agreement, and "$ k $-coordination", which is driven by efficiency considerations. We find that public policy has driven higher education to fully cover the territory, and in particular individuals living in sparsely populated areas. This orientation might have brought about a loss of scale economies in teaching and, consequently, in the efficiency of tertiary education. This is a plausible explanation for the disconnect between higher education spread and economic growth during the more recent period.

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Mathematics Subject Classification: 62, 91.

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Time period	(1)	(2)	(1) $ - $ (2)
1981–2001	6.4	3.0	3.4
2001–2021	4.8	0.4	4.4
(1) $ \equiv $ average annual growth rate in the share of people older than 15 with a complete higher education degree according to the Censuses. (2) $ \equiv $ average annual growth rate of real per head GDP. Source: PORDATA. INE

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Table 1. Portuguese regions (NUTS3)

Portuguese Regions	$ S_t $	$ S_{t-1} $	$ n_t $
Alto Minho	0.147	0.047	231
Cávado	0.199	0.062	417
Ave	0.141	0.039	418
Oporto Metropolitan Area	0.21	0.081	1736
Alto Tâmega	0.118	0.042	84
Tâmega e Sousa	0.104	0.027	409
Douro	0.148	0.051	184
Terras de Trás-os-Montes	0.166	0.056	107
Oeste	0.155	0.049	364
Região de Aveiro	0.186	0.067	367
Região de Coimbra	0.214	0.083	437
Região de Leiria	0.169	0.052	287
Viseu, Dão, Lafões	0.162	0.055	253
Beira Baixa	0.169	0.054	81
Médio Tejo	0.153	0.053	228
Beiras e Serra da Estrela	0.154	0.052	211
Lisbon Metropolitan Area (NUT2)	0.266	0.12	2870
Alentejo Litoral	0.124	0.039	96
Baixo Alentejo	0.139	0.046	115
Lezíria do Tejo	0.151	0.053	236
Alto Alentejo	0.140	0.047	105
Alentejo Central	0.164	0.059	152
Algarve	0.173	0.065	467
Região Autónoma dos Açores (NUT2)	0.147	0.052	236
Região Autónoma da Madeira (NUT2)	0.165	0.056	251

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Table 2. Larger municipalities within metropolitan areas

Municipalities	$ S_t $	$ S_{t-1} $	$ n_t $
Porto Metropolitan Area	—	—	—
Gondomar	0.166	0.062	164
Maia	0.255	0.099	135
Matosinhos	0.247	0.093	172
Paredes	0.121	0.03	84
Porto	0.353	0.161	232
Santa Maria da Feira	0.157	0.043	137
Valongo	0.176	0.058	95
Vila do Conde	0.176	0.054	81
Vila Nova de Gaia	0.214	0.081	304
Lisbon Metropolitan Area	—	—	—
Almada	0.243	0.103	177
Amadora	0.219	0.095	171
Cascais	0.325	0.071	214
Lisboa	0.412	0.191	546
Loures	0.208	0.087	202
Mafra	0.232	0.066	86
Odivelas	0.234	0.078	148
Oeiras	0.378	0.204	172
Seixal	0.2	0.077	166
Setúbal	0.209	0.09	123
Sintra	0.198	0.094	386
Vila Franca de Xira	0.197	0.07	138

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