Elimination of Dominated Strategies and Inessential Players

• Autorzy: Mamoru Kaneko , Shuige Liu
• Języki publikacji: EN

Abstrakty

EN

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 orderindependence. 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. (original abstract)

Słowa kluczowe

EN

Game theory; Application of game theory; Strategic games

PL

Teoria gier; Zastosowanie teorii gier; Gry strategiczne

• Czasopismo: Operations Research and Decisions
• Rocznik: 2015
• Tom: 25
• Numer: nr 1
• Strony: 33--54

Twórcy

autor

Mamoru Kaneko

• Waseda University, Shinjuku-ku, Tokyo

autor

Shuige Liu

• Waseda University, Shinjuku-ku, Tokyo

Bibliografia

• [1] APT K.R., Direct proofs of order independence, Economics Bulletin, 2011, 31, 106-115.
• [2] BÖRGERS T., Pure strategy dominance, Econometrica, 1993, 61, 423-430.
• [3] GILBOA I., KALAI E., ZEMEL E., On the order of eliminating dominated strategies, Operations Research Letters, 1990, 9, 85-89.
• [4] KANEKO M., KLINE J.J., Understanding the other through social roles, to be published in International Game Theory Review, 2015.
• [5] MASCHLER M., SOLAN E., ZAMIR S., Game Theory, Cambridge University Press, Cambridge 2013.
• [6] MERTENS J.F., Stable equilibria - a reformulation II. The geometry, and further results, Mathematics of Operations Research, 1991, 16, 694-753.
• [7] MOULIN H., Game Theory for the Social Sciences, 2nd revised Ed., New York University Press, New York 1986.
• [8] NASH J.F., Non-cooperative games, Annals of Mathematics, 1951, 54, 286-295.
• [9] NEWMAN M.H.A., On theories with a combinatorial definition of equivalence, Annals of Mathematics, 1942, 43, 223-243.
• [10] MYERSON R.B., Game Theory, Harvard University Press, Cambridge 1991.
• [11] OSBORNE M., RUBINSTEIN A., A Course in Game Theory, The MIT Press, Cambridge 1994.

Identyfikatory

DOI

10.5277/ord150103