Explaining higher education progress through risk dominance in an n-person coordination (Stag Hunt) game

In this paper, we use HARSANYI and SELTEN (1988)’s risk dominance concept to explain the growth in the Portuguese higher education system during two time periods: 1998 2005 and 2005-2018. During the first time period, the high annual growth rate in tertiary schooling (8.2%) can be accounted for by a n – person, k – coordination Stag Hunt game framework. Hence, the progress in university education can be described as the outcome of a noncooperative game, where youngsters and their families can take decisions without needing to communicate previously. By contrast, during 2005-2018, the former coordination game seems inadequate to rationalize the continued progress in college schooling at an annual rate of 5%, since the wage premium of tertiary education fell drastically (more than 20%) during the same interval. Hence, we switch to an “unanimity” game as framework of analysis. Within such a game, the widespread tertiary enrolment can be accounted for a diminishing “unanimity” requirement, derived from a shrinking demography and the sheer cumulative effect of past spread of college education. We apply here NASH (1950, 1953)’s intuition that the selection of an equilibrium point within an unanimity game is a tool for modelling the outcome of a game, where the players discuss in order to reach an agreement. Hence, we can describe the rise in college education in Portugal in the more recent time period as the outcome of a cooperative process, leading to a wide policy consensus.