Example of a game without a value: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Robinh
clarification of caption
en>Robinh
. . . but OTOH the notation could be improved
 
Line 1: Line 1:
In [[game theory]], the Helly metric is used to assess the distance between two [[Strategy_(game_theory)|strategies]]. It is named for [[Eduard Helly]].
They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. It is very easy to customize plugins according to the needs of a particular business. The Word - Press Dashboard : an administrative management tool that supports FTP content upload 2. If you are using videos on your site then this is the plugin to use. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed. <br><br>purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. Apart from these, you are also required to give some backlinks on other sites as well.  If you cherished this write-up and you would like to obtain extra data pertaining to [http://emailsite.de/wordpress_dropbox_backup_5022041 backup plugin] kindly go to the internet site. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. To turn the Word - Press Plugin on, click Activate on the far right side of the list. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. Wordpress template is loaded with lots of prototype that unite graphic features and content area. <br><br>As a open source platform Wordpress offers distinctive ready to use themes for free along with custom theme support and easy customization. I'm a large fan of using Word - Press to create pretty much any sort of web page. Offshore Wordpress development services from a legitimate source caters dedicated and professional services assistance with very simplified yet technically effective development and designing techniques from experienced professional Wordpress developer India. Extra investment in Drupal must be bypassed as value for money is what Drupal provides. As with a terminology, there are many methods to understand how to use the terminology.
 
Consider a game <math>\Gamma=\left\langle\mathfrak{X},\mathfrak{Y},H\right\rangle</math>, between player I and II.  Here, <math>\mathfrak{X}</math> and <math>\mathfrak{Y}</math> are the sets of [[pure strategy|pure strategies]] for players I and II respectively; and <math>H=H(\cdot,\cdot)</math> is the payoff function.
 
(in other words, if player I plays <math>x\in\mathfrak{X}</math> and player II plays <math>y\in\mathfrak{Y}</math>, then player I pays <math>H(x,y)</math> to player II).
 
The '''Helly metric''' <math>\rho(x_1,x_2)</math> is defined as
 
:<math>
\rho(x_1,x_2)=\sup_{y\in\mathfrak{Y}}\left| H(x_1,y)-H(x_2,y)\right|.
</math>
 
The metric so defined is symmetric, reflexive, and satisfies the [[triangle inequality]].
 
The Helly metric measures distances between strategies, not in terms of the differences between the strategies themselves, but in terms of the consequences of the strategies. Two strategies are distant if their payoffs are different.  Note that <math>\rho(x_1,x_2)=0</math> does not imply <math>x_1=x_2</math> but it does imply that the ''consequences'' of <math>x_1</math> and <math>x_2</math> are identical; and indeed this induces an [[equivalence relation]].
 
If one stipulates that <math>\rho(x_1,x_2)=0</math> implies <math>x_1=x_2</math> then the topology so induced is called the [[natural topology]].
 
The metric on the space of player II's strategies is analogous:
 
:<math>
\rho(y_1,y_2)=\sup_{x\in\mathfrak{X}}\left| H(x,y_1)-H(x,y_2)\right|.
</math>
 
Note that <math>\Gamma</math> thus defines ''two'' Helly metrics: one for each player's strategy space.
 
==Conditional compactness==
 
Notation (definition of an <math>\epsilon</math>-net). A set <math>X_\epsilon</math> is an <math>\epsilon</math>-net in the space <math>X</math> with metric <math>\rho</math> if for any <math>x\in X</math> there exists <math>x_\epsilon\in X_\epsilon</math> with <math>\rho(x,x_\epsilon)<\epsilon</math>.
 
A metric space <math>P</math> is '''conditionally compact''' if for any <math>\epsilon>0</math> there exists a ''finite'' <math>\epsilon</math>-net in <math>P</math>.
 
A game that is conditionally compact in the Helly metric has an <math>\epsilon</math>-optimal strategy for any <math>\epsilon>0</math>.
 
==Other results==
 
If the space of strategies for one player is conditionally compact, then the space of strategies for the other player is conditionally compact (in their Helly metric).
 
==References==
N. N. Vorob'ev 1977.  ''Game theory lectures for economists and systems scientists''. Springer-Verlag (translated by S. Kotz).
 
[[Category:Game theory]]
 
{{gametheory-stub}}

Latest revision as of 10:03, 25 July 2014

They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. It is very easy to customize plugins according to the needs of a particular business. The Word - Press Dashboard : an administrative management tool that supports FTP content upload 2. If you are using videos on your site then this is the plugin to use. It's as simple as hiring a Wordpress plugin developer or learning how to create what is needed.

purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. Apart from these, you are also required to give some backlinks on other sites as well. If you cherished this write-up and you would like to obtain extra data pertaining to backup plugin kindly go to the internet site. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring.

Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. To turn the Word - Press Plugin on, click Activate on the far right side of the list. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way.

Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. Wordpress template is loaded with lots of prototype that unite graphic features and content area.

As a open source platform Wordpress offers distinctive ready to use themes for free along with custom theme support and easy customization. I'm a large fan of using Word - Press to create pretty much any sort of web page. Offshore Wordpress development services from a legitimate source caters dedicated and professional services assistance with very simplified yet technically effective development and designing techniques from experienced professional Wordpress developer India. Extra investment in Drupal must be bypassed as value for money is what Drupal provides. As with a terminology, there are many methods to understand how to use the terminology.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Example_of_a_game_without_a_value&oldid=261833"