A game of timing and visibility
We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x i in the interval [ 0 , 1 ] , and a player's payoff is the distance from its point x i to the next larger point, or to 1 if x i is the largest. For this game, we giv...
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| Published in: | Games and economic behavior Vol. 62; no. 2; pp. 643 - 660 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Duluth
Elsevier Inc
01.03.2008
Elsevier Academic Press |
| Series: | Games and Economic Behavior |
| Subjects: | |
| ISSN: | 0899-8256, 1090-2473 |
| Online Access: | Get full text |
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| Abstract | We consider the following abstraction of competing publications. There are
n players in the game. Each player
i chooses a point
x
i
in the interval
[
0
,
1
]
, and a player's payoff is the distance from its point
x
i
to the next larger point, or to 1 if
x
i
is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the
n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the
n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games. |
|---|---|
| AbstractList | We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point xi in the interval [0,1], and a player's payoff is the distance from its point xi to the next larger point, or to 1 if xi is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games. We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x"i in the interval [0,1], and a player's payoff is the distance from its point x"i to the next larger point, or to 1 if x"i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games. All rights reserved, Elsevier We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x... in the interval [0,1], and a player's payoff is the distance from its point x... to the next larger point, or to 1 if x... is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games. (ProQuest: ... denotes formulae/symbols omitted.) We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x i in the interval [ 0 , 1 ] , and a player's payoff is the distance from its point x i to the next larger point, or to 1 if x i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games. |
| Author | Patt-Shamir, Boaz Lotker, Zvi Tuttle, Mark R. |
| Author_xml | – sequence: 1 givenname: Zvi surname: Lotker fullname: Lotker, Zvi email: zvilo@cse.bgu.ac.il organization: Ben Gurion University, Israel – sequence: 2 givenname: Boaz surname: Patt-Shamir fullname: Patt-Shamir, Boaz email: boaz@eng.tau.ac.il organization: Tel Aviv University, Israel – sequence: 3 givenname: Mark R. surname: Tuttle fullname: Tuttle, Mark R. email: tuttle@acm.org organization: Intel, USA |
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| References | Maynard Smith (bib005) 1974; 47 Baye, Kovenock, de Vries (bib001) Osborne, Rubinstein (bib006) 1994 Fudenberg, Tirole (bib002) 1991 Hotelling (bib004) 1929; 39 Hendricks, Weiss, Wilson (bib003) 1988; 29 Baye (10.1016/j.geb.2007.04.006_bib001) Osborne (10.1016/j.geb.2007.04.006_bib006) 1994 Maynard Smith (10.1016/j.geb.2007.04.006_bib005) 1974; 47 Hendricks (10.1016/j.geb.2007.04.006_bib003) 1988; 29 Fudenberg (10.1016/j.geb.2007.04.006_bib002) 1991 Hotelling (10.1016/j.geb.2007.04.006_bib004) 1929; 39 |
| References_xml | – volume: 29 start-page: 663 year: 1988 end-page: 680 ident: bib003 article-title: The war of attrition in continuous time with complete information publication-title: Int. Econ. Rev. – volume: 39 start-page: 41 year: 1929 end-page: 57 ident: bib004 article-title: Stability in competition publication-title: Econ. J. – year: 1991 ident: bib002 article-title: Game Theory – ident: bib001 article-title: A general linear model of contests. Mimeo – volume: 47 start-page: 209 year: 1974 end-page: 221 ident: bib005 article-title: The theory of games and the evolution in animal conflicts publication-title: J. Theoret. Biol. – year: 1994 ident: bib006 article-title: A Course in Game Theory – year: 1994 ident: 10.1016/j.geb.2007.04.006_bib006 – ident: 10.1016/j.geb.2007.04.006_bib001 – year: 1991 ident: 10.1016/j.geb.2007.04.006_bib002 – volume: 39 start-page: 41 year: 1929 ident: 10.1016/j.geb.2007.04.006_bib004 article-title: Stability in competition publication-title: Econ. J. doi: 10.2307/2224214 – volume: 47 start-page: 209 year: 1974 ident: 10.1016/j.geb.2007.04.006_bib005 article-title: The theory of games and the evolution in animal conflicts publication-title: J. Theoret. Biol. doi: 10.1016/0022-5193(74)90110-6 – volume: 29 start-page: 663 issue: 4 year: 1988 ident: 10.1016/j.geb.2007.04.006_bib003 article-title: The war of attrition in continuous time with complete information publication-title: Int. Econ. Rev. doi: 10.2307/2526827 |
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| Snippet | We consider the following abstraction of competing publications. There are
n players in the game. Each player
i chooses a point
x
i
in the interval
[
0
,
1
]
,... We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point xi in the interval [0,1], and a... We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x... in the interval [0,1], and... We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x"i in the interval [0,1], and... |
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| SubjectTerms | Algorithms Approximation Computational methods Differential equations Economic theory Equilibrium Game theory Games Nash equilibrium Pay-off Studies Time Visibility |
| Title | A game of timing and visibility |
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