= occurs when the sharing the production of the good by one person increases the value of the good to others.
- Mark Cooper 
(in contrast inclusiveness refers to the fact that increased use of the good increases the value to others)
the "property characterizing goods (or processes of production) where the use of the (produced) good by one individual enhances the use by the others."
- Ignacio de Castro
"Software in many circumstances is more than simply nonrival. Operating systems like Linux in particular, and most software in general, actually are subject to positive network externalities. Call it a network good, or an antirival good (an awkward, but nicely descriptive term). In simpler language, it means that the value of a piece of software to any user increases as more people use the software on their machines and in their particular settings
The point is that open source software is not simply a nonrival good in the sense that it can tolerate free riding without reducing the stock of the good for contributors. It is actually antirival in the sense that the system as a whole postively benefits from free riders.
The twist is this: Under conditions of anti-rivalness, as the size of the Internet-connected group increases, and there is a heterogeneous distribution of motivations with people who have a high level of interest and some resources to invest, then the large group is more likely, all things being equal, to provide the good than is a small group." (http://www.sauria.com/blog/2006/Jun/04)
Ignacio de Castro:
"I am aware that this is Weber´s definition, however I think that it is arguable that the definition could be improved:
Considering antirivalry as the opposite to rivalry, and parting hence from rivalry definnition.
"A purely rival good has the property that its use by one firm or person precludes its use by another; a purely nonrival good has the property that its use by one firm or person in no way limits is use by another" (http://p2pfoundation.net/Anti-rivalry). Wikipedia definition (http://en.wikipedia.org/wiki/Rivalry_%28economics%29#cite_ref-0) emplois the term "consumption" instead of "use": "Rival goods are goods whose consumption by one consumer prevents simultaneous consumption by other consumers". Rivalry refers to use/consumption and, directly, has nothing to do with value (as far as I know).
The opposite term, antirivalry, should imply that " its use by one firm or person ENHANCES its use by another". From variations in the value of the good (to others) when the sharing of the production increases it does not necessarily follow that there are variations in the access to the use/consumption of the good by the rest of individuals.
I would tentatively define antirivalry as the "property characterizing goods (or processes of production) where the use of the (produced) good by one individual enhances the use by the others." It can be argued from this definition that the use of the good by one person increases the production of that good, or that -as in Weber (2004)´s definition, that the sharing of the production increases the value of the good, but both are only a sufficient condition for antirivalry defined as the opposite of rivalry." (email July 2010)
Symbiotic and Networked Anti-Rival Common Goods Challenge Our Current Value Regime
"Making the markets to work efficiently for the so-called anti-rival goods may require a radical departure from our current established thinking. In particular, since data cannot be easily enclosed and since data may gain more value as it is used and combined with other data, data and other anti-rival goods do not easily fit into the fourfold division of goods to private, public, club/toll and common-pool goods. Hence, it has been suggested to extend the fourfold model with network goods and symbiotic goods; In Ostrom's (2009) Institutional Analysis and Design (IAD) terms, it appears that the subtractability of goods may be negative. Weather such goods should be called anti-rival or not is still being argued.
While other potentially anti-rival goods, such as textual knowledge and copyrightable works have existed for a while, their distribution has been bound to rival media, such as books or records, until recently. Digital technologies have arguably led to (almost) zero marginal cost of both copying and even producing such information. For example, for many major digital platforms, the most valuable data may be considered as a by-product.
Furthermore, from an accounting, governance, and compensation point of view, the so-called distributed ledger technologies (DLTs) seem to provide a new way to accounting, securing transactions, and triggering actions. This allows one to design and efficiently implement new governance models and perhaps new ways to quantify value, i.e. introducing new units of account that are non-linear. In particular, we have surmised that to efficiently clear the markets of anti-rival goods, it may be necessary to create new market structures (Nikander & Elo, 2019). In more generic terms, it has been suggested to move from the current annual or monthly double entry accounting to more real time practices (such as using xBRL ) or to use DLTs and 1 other means to establish triple entry bookkeeping (Ijiri, 1989; Skole-Sorensen, 2016)." (email, November 2019)