Quasi-Perfect Stackelberg Equilibrium

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasi-perfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings---that is, settings where a leader can commit to a strategy---which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes

Comparing Typical Opening Move Choices Made by Humans and Chess Engines

The opening book is an important component of a chess engine, and thus computer chess programmers have been developing automated methods to improve the quality of their books. For chess, which has a very rich opening theory, large databases of high-quality games can be used as the basis of an opening book, from which statistics relating to move choices from given positions can be collected. In order to find out whether the opening books used by modern chess engines in machine versus machine competitions are ``comparable'' to those used by chess players in human versus human competitions, we carried out analysis on 26 test positions using statistics from two opening books one compiled from humans' games and the other from machines' games. Our analysis using several nonparametric measures, shows that, overall, there is a strong association between humans' and machines' choices of opening moves when using a book to guide their choices.Comment: 12 pages, 1 figure, 6 table

An "informationally robust equilibrium" for two-person nonzero-sum games

Game Theory;Equilibrium Theory

An analysis of winning streak's effects in language course of “Duolingo” *

This paper explores the effects of the winning streak on users' motivation and engagement in Duolingo's language course. The winning streak has been used in sport and video games to describe a consecutive number of successful actions and increase players' attention to complete their goal. Similarly, in gamified education system, the winning streak is employed as a game element to boost up motivation of learners. By applying game refinement theory as an assessment method, enjoyment of two user groups in Duolingo is measured to compare. The results indicate that the winning streak can boost up learners' motivation and attention to complete their goals. It also expressed that the winning streak is more significant for advanced learners who are in the high level of milestone than those who are in the low level of milestone