There are three physical countrywide LTE/3G/GSM networks in Finland: Telia/Sonera, Elisa and DNA. They then carry some MVNOs so there are more places where you can actually buy a SIM card than just these three.
Most people buy their phone here separately from the operator contract, so there are much fewer contract phones than e.g. in the U.S. Thus there is competition for phone sales, and competition for operator contracts, separately.
Telia/Sonera is the former state monopoly, Elisa grew out of Helsinki telephone association/company, and DNA is a merger of small countryside operators. Sonera has the best coverage throughout the country, DNA curiously enough has the best coverage in urban areas.
Of course, we can still always say that there is not enough competition between operators, as their prices tend to converge. Consumer advocates usually have only two kinds of messages: either all prices are nearly the same ("competition is not working!") or there are large disparities in prices ("competition is not working!").