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.info:eu-repo/semantics/publishedVersio

Linking Strategic Interaction and Bargaining Theory. The Harsanyi - Schelling Debate on the Axiom of Symmetry

This paper analyses the early contributions of John Harsanyi and Thomas C. Schelling to bargaining theory. In his work, Harsanyi (1956) draws Nash’s solution to two-person cooperative games from the bargaining model proposed by Zeuthen (1930). Whereas Schelling (1960) proposes a multi-faceted theory of conflict that, without dismissing the assumption of rational behaviour, points out some of its paradoxical consequences. Harsanyi and Schelling’s contrasting views on the axiom of symmetry, as postulated by Nash (1950), are then presented. The analysis of this debate illustrates that, although in the early 1960s two different approaches to link strategic interaction and bargaining theory were proposed, only Harsanyi’s insights were fully developed later. Lastly, the causes of this evolution are assessed.bargaining, game theory, symmetry

A Game-Theoretic Analysis of the Off-Switch Game

The off-switch game is a game theoretic model of a highly intelligent robot interacting with a human. In the original paper by Hadfield-Menell et al. (2016), the analysis is not fully game-theoretic as the human is modelled as an irrational player, and the robot's best action is only calculated under unrealistic normality and soft-max assumptions. In this paper, we make the analysis fully game theoretic, by modelling the human as a rational player with a random utility function. As a consequence, we are able to easily calculate the robot's best action for arbitrary belief and irrationality assumptions

Non-cooperative Games

Non-cooperative games are mathematical models of interactive strategic decision situations.In contrast to cooperative models, they build on the assumption that all possibilities for commitment and contract have been incorporated in the rules of the game.This contribution describes the main models (games in normal form, and games in extensive form), as well as the main concepts that have been proposed to solve these games.Solution concepts predict the outcomes that might arise when the game is played by "rational" individuals, or after learning processes have converged.Most of these solution concepts are variations of the equilibrium concept that was proposed by John Nash in the 1950s, a Nash equilibrium being a combination of strategies such that no player can improve his payoff by deviating unilaterally.The paper also discusses the justifications of these concepts and concludes with remarks about the applicability of game theory in contexts where players are less than fully rational.noncooperative games

Three alternative (?) stories on the late 20th-century rise of game theory

The paper presents three different reconstructions of the 1980s boom of game theory and its rise to the present status of indispensable tool-box for modern economics. The first story focuses on the Nash refinements literature and on the development of Bayesian games. The second emphasizes the role of antitrust case law, and in particular of the rehabilitation, via game theory, of some traditional antitrust prohibitions and limitations which had been challenged by the Chicago approach. The third story centers on the wealth of issues classifiable under the general headline of "mechanism design" and on the game theoretical tools and methods which have been applied to tackle them. The bottom lines are, first, that the three stories need not be viewed as conflicting, but rather as complementary, and, second, that in all stories a central role has been played by John Harsanyi and Bayesian decision theory.game theory; mechanism design; refinements of Nash equilibrium; antitrust law; John Harsanyi

An experimental study of costly coordination

This paper reports data for coordination game experiments with random matching. The experimental design is based on changes in an effort-cost parameter, which do not alter the set of Nash equilibria nor do they alter the predictions of adjustment theories based on imitation or best response dynamics. As expected, however, increasing the effort cost lowers effort levels. Maximization of a stochastic potential function, a concept that generalizes risk dominance to continuous games, predicts this reduction in efforts. An error parameter estimated from initial two-person, minimum-effort games is used to predict behavior in other three-person coordination games