Issue: 2015/Vol.25/No.1, Pages 33-54
ELIMINATION OF DOMINATED STRATEGIES AND INESSENTIAL PLAYERS
Mamoru Kaneko
, Shuige Liu
Cite as: M. Kaneko, S. Liu. Elimination of dominated strategies and inessential players. Operations Research and Decisions 2015: 25(1), 33-54. DOI 10.5277/ord150103
Abstract
We study the process, called the IEDI process, of iterated elimination of (strictly) dominated strategies and inessential players for finite strategic games. Such elimination may reduce the size of a game considerably, for example, from a game with a large number of players to one with a few players. We extend two existing results to our context; the preservation of Nash equilibria and order-independence. These give a way of computing the set of Nash equilibria for an initial situation from the endgame. Then, we reverse our perspective to ask the question of what initial situations end up at a given final game. We assess what situations underlie an endgame. We give conditions for the pattern of player sets required for a resulting sequence of the IEDI process to an endgame. We illustrate our development with a few extensions of the battle of the sexes.
Keywords: dominated strategies, inessential players, iterated elimination, order-independence, estimation of initial games
Received: 30 September 2014 Accepted: 19 January 2015