Equilibria in Quitting Games and Software for the Analysis

• Main Author: Fischer, Katharina
• Other Authors: Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften
• Format: Doctoral Thesis
• Language: English
• Published: Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden 2013
• Subjects: Stochastische N-Personen Spiele; Quitting Games; N-player stochastic games; quitting games; ddc:510; rvk:SK 860
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-119877; http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-119877; http://www.qucosa.de/fileadmin/data/qucosa/documents/11987/Thesis_Publikation.pdf

A quitting game is an undiscounted sequential stochastic game, with finitely many players. At any stage each player has only two possible actions, continue and quit. The game ends as soon as at least one player chooses to quit. The players then receive a payoff, which depends only on the set of players that did choose to quit. If the game never ends, the payoff to each player is zero. In this thesis we give a detailed introduction to quitting games. We examine the existing results for the existence of equilibria and improve an important result from Solan and Vieille stated in their article “Quitting Games” (2001). Since there is no software for the analysis of quitting games, or for stochastic games with more than two players, we provide algorithms and programs for symmetric quitting games, for a reduction by dominance and for the detection of a pure, instant and stationary epsilon-equilibrium.