### Abstract

Let G=〈I,J,g〉 be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which players 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per-stage payoff when the two automata face off.We are interested in the cases in which player 1 is " smart" in the sense that k is large but player 2 is " much smarter" in the sense that m≫k. Let S(g) be the value of G where the second player is clairvoyant, i.e., would know player 1's move in advance.The threshold for clairvoyance is shown to occur for m near min(I,J)k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).

Original language | English (US) |
---|---|

Pages (from-to) | 165-168 |

Number of pages | 4 |

Journal | Games and Economic Behavior |

Volume | 69 |

Issue number | 1 |

DOIs | |

State | Published - May 2010 |

### Fingerprint

### Keywords

- C44
- C73
- D83

### ASJC Scopus subject areas

- Economics and Econometrics
- Finance

### Cite this

*Games and Economic Behavior*,

*69*(1), 165-168. https://doi.org/10.1016/j.geb.2009.05.007

**Complexity and effective prediction.** / Neyman, Abraham; Spencer, Joel.

Research output: Contribution to journal › Article

*Games and Economic Behavior*, vol. 69, no. 1, pp. 165-168. https://doi.org/10.1016/j.geb.2009.05.007

}

TY - JOUR

T1 - Complexity and effective prediction

AU - Neyman, Abraham

AU - Spencer, Joel

PY - 2010/5

Y1 - 2010/5

N2 - Let G=〈I,J,g〉 be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which players 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per-stage payoff when the two automata face off.We are interested in the cases in which player 1 is " smart" in the sense that k is large but player 2 is " much smarter" in the sense that m≫k. Let S(g) be the value of G where the second player is clairvoyant, i.e., would know player 1's move in advance.The threshold for clairvoyance is shown to occur for m near min(I,J)k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).

AB - Let G=〈I,J,g〉 be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which players 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per-stage payoff when the two automata face off.We are interested in the cases in which player 1 is " smart" in the sense that k is large but player 2 is " much smarter" in the sense that m≫k. Let S(g) be the value of G where the second player is clairvoyant, i.e., would know player 1's move in advance.The threshold for clairvoyance is shown to occur for m near min(I,J)k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).

KW - C44

KW - C73

KW - D83

UR - http://www.scopus.com/inward/record.url?scp=77951642478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951642478&partnerID=8YFLogxK

U2 - 10.1016/j.geb.2009.05.007

DO - 10.1016/j.geb.2009.05.007

M3 - Article

VL - 69

SP - 165

EP - 168

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

IS - 1

ER -