In the context of an irrevocable undertaking, a shareholder, especially an institutional shareholder, will usually expect to be released if a competing offer is made at any higher price (a soft undertaking) or, more usually in practice, at a price/value which equals or exceeds a specified price or percentage of the original offer price (a semi-hard undertaking). Increasingly in the case of a soft or semi-hard irrevocable, an offeror will request the opportunity to revise the terms of the offer so that it is at least as favourable (a matching right), as the value of the competing offer, in which case the undertaking will not lapse.
Matching rights may also refer to an arrangement whereby an offeree grants the potential offeror the right, within an agreed timescale, to equal or better any competing bid that might be announced during the offer period and undertakes to recommend that revised offer (subject to certain limited exceptions). These types of matching rights are likely to be caught by the general prohibition on offer-related arrangements under Rule 21.2.
For further information see PCP 2011/1, para 3.6 and PCP 2010/2, para 9.19.