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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| Vydané v: | Games and economic behavior Ročník 62; číslo 2; s. 643 - 660 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Duluth
Elsevier Inc
01.03.2008
Elsevier Academic Press |
| Edícia: | Games and Economic Behavior |
| Predmet: | |
| ISSN: | 0899-8256, 1090-2473 |
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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. |
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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 |
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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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