Papyrus 53 - Revision history

en>Trappist the monk: Fix CS1 deprecated coauthor parameter errors; using AWB

2014-07-21T11:40:18Z

Fix CS1 deprecated coauthor parameter errors; using AWB

← Older revision		Revision as of 13:40, 21 July 2014
Line 1:		Line 1:
	In [[game theory]], the common ways to describe a game are the [[normal-form game\|normal form]] and the [[extensive-form game\|extensive form]]. The graphical form is an alternate compact representation of a game using the interaction among participants.

	Consider a game with <math>n</math> players with <math>m</math> strategies each. We will represent the players as nodes in a graph in which each player has a [[utility function]] that depends only on him and his neighbors. As the utility function depends on fewer other players, the graphical representation would be smaller.

	~~==Formal definition==~~		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. Word - Press also provides protection against spamming, as security is a measure issue. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. <br><br>As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. The higher your blog ranks on search engines, the more likely people will find your online marketing site. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. After sending these details, your Word - Press blog will be setup within a few days. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. Search engine optimization pleasant picture and solution links suggest you will have a much better adjust at gaining considerable natural site visitors. <br><br>If you liked this article and you simply would like to get more info pertaining to [http://l4.vc/backup_plugin_340320 wordpress backup plugin] i implore you to visit the web site. It is the convenient service through which professionals either improve the position or keep the ranking intact. * Robust CRM to control and connect with your subscribers. When we talk about functional suitability, Word - Press proves itself as one of the strongest contestant among its other rivals. If you choose a blog then people will be able to post articles on your site and people will be able to make comments on your posts (unless you turn comments off). If your blog employs the permalink function, This gives your SEO efforts a boost, and your visitors will know firsthand what's in the post when seeing the URL. <br><br>More it extends numerous opportunities where your firm is at comfort and rest assured of no risks & errors. Being a Plugin Developer, it is important for you to know that development of Word - Press driven website should be done only when you enable debugging. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. If this is not possible you still have the choice of the default theme that is Word - Press 3. Get started today so that people searching for your type of business will be directed to you.
	~~A graphical game~~ is ~~represented by~~ a ~~graph <math>G</math>~~, ~~in which each player~~ is ~~represented by~~ a ~~node~~, and ~~there~~ is ~~an edge between two nodes~~ <~~math~~>i<~~/math~~> and ~~<math>j</math> iff their utility functions~~ are ~~depended on~~ the ~~strategy which~~ the ~~other player will choose~~ . ~~Each node <math>i</math>~~ in ~~<math>G</math> has a function <math>u_{i}:\{1\ldots m\}^{d_{i}+1}\rightarrow\mathbb{R}</math>~~, ~~where <math>d_i</math> is~~ the ~~degree~~ of ~~vertex <math>i</math>~~. ~~<math>u_{i}</math> specifies~~ the ~~utility of player~~ <~~math~~>i<~~/math~~> as a ~~function~~ of ~~his strategy as well as those of his neighbors~~.

	~~==The size of~~ the ~~game's representation==~~
	~~For~~ a ~~general <math>n</math> players game,~~ in which ~~each player has~~ <~~math~~>m<~~/math~~> ~~possible strategies, the size of a normal form representation~~ would ~~be <math>O(m^{n})<~~/~~math>~~. ~~The size of~~ the ~~graphical representation for this game is <math>O(m^{d})</math> where <math>d</math>~~ is the ~~maximal node degree in~~ the ~~graph~~. ~~If <math>d\ll n</math>~~, ~~then~~ the ~~graphical game representation is much smaller~~.

	~~==An example==~~
	~~In case where each player's utility function depends only~~ on ~~one other player:~~
	~~<gallery>~~
	~~Image:GraphicalGameExample~~.~~png\|The graphical form of~~ the ~~described game~~
	~~</gallery>~~

	~~The maximal degree of the graph is 1~~, and the ~~game can be described as~~ <~~math~~>n<~~/math~~> ~~functions (tables)~~ of ~~size <math>m^{2}</math>~~. So, ~~the total size~~ of ~~the input will~~ be ~~<math>nm^{2}</math>~~.

	~~==Nash equilibrium==~~
	~~Finding Nash equilibrium in a game takes exponential~~ time in the ~~size of~~ the ~~representation~~. If ~~the graphical representation of the game~~ is ~~a tree, we can find~~ the ~~equilibrium in polynomial time. In the general case, where the maximal degree~~ of ~~a node is 3 or more,~~ the ~~problem~~ is ~~[[NP~~-~~complete]].~~

	~~== Further reading ==~~

	* Michael Kearns (2007) "[http://www.cis.upenn.edu/~mkearns/papers/agt-kearns.pdf Graphical Games]". In Algorithmic Game Theory, N. Nisan, T. Roughgarden, E. Tardos and V. Vazirani, editors, Cambridge University Press~~, September, 2007.~~
	* Michael Kearns, Michael L. Littman and Satinder Singh (2001) "[http://www.cis.upenn.edu/~mkearns/papers/graphgames.~~pdf Graphical Models~~ for ~~Game Theory]"~~.

	~~[[Category:Game theory]]~~

76.175.30.126: /* Images */ the images aren't there anymore

2013-10-03T23:04:59Z

Images: the images aren't there anymore

← Older revision		Revision as of 01:04, 4 October 2013
Line 1:		Line 1:
	~~Next~~ - ~~GEN Gallery~~ is a ~~full incorporated Image Gallery plugin for Word - Press~~ which has a ~~Flash slideshow option. Affilo - Theme is the guaranteed mixing of wordpress theme~~ that ~~Mark Ling use for~~ his ~~internet marketing career~~. ~~PSD files are incompatible to browsers and are suppose to~~ be ~~converted into wordpress compatible files so that it opens up~~ in ~~browser. If you need~~ a ~~special plugin for your website~~ , there are ~~thousands of plugins that can be used to meet those needs~~. ~~By using this method one can see whether the theme~~ has the ~~potential to become popular or not and is their any scope~~ of ~~improvement in~~ the ~~theme.~~ <br><br>~~Any business enterprise that is certainly worth its name should really shell out~~ a ~~good deal in making sure that they have the most effective website that provides related info to its prospect~~. ~~Best~~ of ~~all~~, ~~you can still have all~~ the ~~functionality that you desire when you use the Word - Press platform~~. ~~Well Managed Administration~~ The ~~Word - Press can easily absorb the high numbers~~ of ~~traffic by controlling~~ the ~~server load to make sure that the site works properly. If you loved~~ this ~~short article and you would like to receive more details relating to [http:~~//~~off2~~.~~net~~/~~wordpressbackupplugin23410 wordpress backup plugin] kindly pay a visit to~~ the ~~page~~. ~~From my very own experiences, I will let you know why you should choose WPZOOM Live journal templates~~. ~~Moreover~~, ~~many Word - Press themes need to be purchased~~ and ~~designing your own WP site~~ can be ~~boring.~~ <br><br>~~But before choosing any one~~ of ~~these, let's compare between the two. Word - Press has different exciting features including a plug-in architecture with a templating system~~. ~~If Gandhi was empowered with a blogging system~~, ~~every event in his life would have been minutely documented so that it could be recounted to~~ the future generations. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the ~~internet site. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I~~ will ~~try to answer them.~~ <br><br>~~There has been~~ a ~~huge increase~~ in the ~~number~~ of ~~developers releasing free premium Word - Press themes over~~ the ~~years~~. ~~I have compiled~~ a ~~few tips on how you~~ can ~~start a food blog and hopefully~~ the ~~following information and tips can help you to get started on your food blogging creative journey~~. ~~Enterprise~~, ~~when they plan to hire Word - Press developer resources still PHP~~, My - ~~SQL and watch with great expertise in codebase~~. ~~Contact Infertility Clinic Providing One stop Fertility Solutions at~~:. ~~The Pakistani culture is in demand of a main surgical treatment~~. ~~<br><br>Yet~~, ~~overall~~, ~~less than 1% of websites presently have mobile versions of their websites~~. ~~As a website owner~~, ~~you can easily manage CMS-based website in a pretty easy and convenient style~~. ~~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~~. ~~This is because of the customization that works as a keystone for a SEO friendly blogging portal website~~. ~~Likewise~~, ~~professional publishers with a multi author~~ and ~~editor setup often find that Word - Press lack basic user and role management capabilities~~.		In [[game theory]], the common ways to describe a game are the [[normal-form game\|normal form]] and the [[extensive-form game\|extensive form]]. The graphical form is an alternate compact representation of a game using the interaction among participants.

			Consider a game with <math>n</math> players with <math>m</math> strategies each. We will represent the players as nodes in a graph in which each player has a [[utility function]] that depends only on him and his neighbors. As the utility function depends on fewer other players, the graphical representation would be smaller.

			==Formal definition==
			A graphical game is represented by a graph <math>G</math>, in which each player is represented by a node, and there is an edge between two nodes <math>i</math> and <math>j</math> iff their utility functions are depended on the strategy which the other player will choose . Each node <math>i</math> in <math>G</math> has a function <math>u_{i}:\{1\ldots m\}^{d_{i}+1}\rightarrow\mathbb{R}</math>, where <math>d_i</math> is the degree of vertex <math>i</math>. <math>u_{i}</math> specifies the utility of player <math>i</math> as a function of his strategy as well as those of his neighbors.

			==The size of the game's representation==
			For a general <math>n</math> players game, in which each player has <math>m</math> possible strategies, the size of a normal form representation would be <math>O(m^{n})</math>. The size of the graphical representation for this game is <math>O(m^{d})</math> where <math>d</math> is the maximal node degree in the graph. If <math>d\ll n</math>, then the graphical game representation is much smaller.

			==An example==
			In case where each player's utility function depends only on one other player:
			<gallery>
			Image:GraphicalGameExample.png\|The graphical form of the described game
			</gallery>

			The maximal degree of the graph is 1, and the game can be described as <math>n</math> functions (tables) of size <math>m^{2}</math>. So, the total size of the input will be <math>nm^{2}</math>.

			==Nash equilibrium==
			Finding Nash equilibrium in a game takes exponential time in the size of the representation. If the graphical representation of the game is a tree, we can find the equilibrium in polynomial time. In the general case, where the maximal degree of a node is 3 or more, the problem is [[NP-complete]].

			== Further reading ==

			* Michael Kearns (2007) "[http://www.cis.upenn.edu/~mkearns/papers/agt-kearns.pdf Graphical Games]". In Algorithmic Game Theory, N. Nisan, T. Roughgarden, E. Tardos and V. Vazirani, editors, Cambridge University Press, September, 2007.
			* Michael Kearns, Michael L. Littman and Satinder Singh (2001) "[http://www.cis.upenn.edu/~mkearns/papers/graphgames.pdf Graphical Models for Game Theory]".

			[[Category:Game theory]]

en>Giftzwerg 88: No Oxy. papyrus

2012-01-19T22:35:02Z

No Oxy. papyrus

New page

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