How to Play 3x3 Games: A Strategy Method Experiment

R. Selten, K. Abbink, J. Buchta, A. Sadrieh

Research output: Working paperDiscussion paperOther research output

270 Downloads (Pure)

Abstract

Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages27
Volume2002-39
Publication statusPublished - 2002

Publication series

NameCentER Discussion Paper
Volume2002-39

Fingerprint

Strategy method
Experiment
Pure strategy equilibrium
Tournament
Cascade
Integer

Keywords

  • game theory
  • experimental economics

Cite this

Selten, R., Abbink, K., Buchta, J., & Sadrieh, A. (2002). How to Play 3x3 Games: A Strategy Method Experiment. (CentER Discussion Paper; Vol. 2002-39). Tilburg: Microeconomics.
Selten, R. ; Abbink, K. ; Buchta, J. ; Sadrieh, A. / How to Play 3x3 Games : A Strategy Method Experiment. Tilburg : Microeconomics, 2002. (CentER Discussion Paper).
@techreport{6ef71dcd3f974d13b75a206a2609a2a4,
title = "How to Play 3x3 Games: A Strategy Method Experiment",
abstract = "Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51{\%} in the first to 74{\%} in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).",
keywords = "game theory, experimental economics",
author = "R. Selten and K. Abbink and J. Buchta and A. Sadrieh",
note = "Pagination: 27",
year = "2002",
language = "English",
volume = "2002-39",
series = "CentER Discussion Paper",
publisher = "Microeconomics",
type = "WorkingPaper",
institution = "Microeconomics",

}

Selten, R, Abbink, K, Buchta, J & Sadrieh, A 2002 'How to Play 3x3 Games: A Strategy Method Experiment' CentER Discussion Paper, vol. 2002-39, Microeconomics, Tilburg.

How to Play 3x3 Games : A Strategy Method Experiment. / Selten, R.; Abbink, K.; Buchta, J.; Sadrieh, A.

Tilburg : Microeconomics, 2002. (CentER Discussion Paper; Vol. 2002-39).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - How to Play 3x3 Games

T2 - A Strategy Method Experiment

AU - Selten, R.

AU - Abbink, K.

AU - Buchta, J.

AU - Sadrieh, A.

N1 - Pagination: 27

PY - 2002

Y1 - 2002

N2 - Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).

AB - Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).

KW - game theory

KW - experimental economics

M3 - Discussion paper

VL - 2002-39

T3 - CentER Discussion Paper

BT - How to Play 3x3 Games

PB - Microeconomics

CY - Tilburg

ER -

Selten R, Abbink K, Buchta J, Sadrieh A. How to Play 3x3 Games: A Strategy Method Experiment. Tilburg: Microeconomics. 2002. (CentER Discussion Paper).