@article{bcfa880245334ce181ff88c716adfa03,

title = "On the order of eliminating dominated strategies",

abstract = "It is known that different orders of eliminating dominated strategies in n-person games may yield different reduced games. We give conditions which guarantee that the reduced game is unique. For finite games, the conditions include the well-known cases of strict dominance, and in a slightly weaker form, of regular dominance for zero sum and similar games.",

keywords = "game theory, strategy domination",

author = "I. Gilboa and E. Kalai and E. Zemel",

note = "Funding Information: where N=(1,2 ..... n} (n>~l) is the set of players. Gi~ ~J is a set of strategies for player i, GiNGJ=J~ for i#:j, and h':G:=I-IiENGi--*R is the payoff (utility) function of player i. A strategy x of player i is said to strictly dominate strategy y iff for every strategy profile of the other players the payoff to i when using x is strictly higher than when using y. The strategy x of i is said to weakly dominate y iff for every strategy profile of his opponents the payoff to i with x is no less than with y. Finally, the strategy x is said to dominate y iff it weakly dominates it and in addition for some strategy profile of the opponents, x yields a strictly higher payoff than y. Common sense seems to indicate that players would not use dominated strategies. Thus, one may wish to eliminate at the outset such strategies. Clearly, the elimination of dominated strategies for one player may create new dominations for the other players, and so on. Continuing in this manner, one may finally arrive at a reduced game, i.e., one which does not contain any further * NSF Grant No. IRI-8814672 is gratefully acknowledged. ** This research was partly supported by NSF Economics Grant No. SES-8720342.",

year = "1990",

month = mar,

doi = "10.1016/0167-6377(90)90046-8",

language = "English (US)",

volume = "9",

pages = "85--89",

journal = "Operations Research Letters",

issn = "0167-6377",

publisher = "Elsevier",

number = "2",

}