Why would full employment lead to inflation?

In the past, the return to full employment would bring back inflation as labour costs accelerated (this i s the Phillips curve). But why would full employment inevitably lead to inflation? It is usually thought that, when there is full employment, companies increase wages to try to attract new employees. But this is a non-cooperative equilibrium between companies: each company tries to attract other companies’ employees by raising its wages. At equilibrium, as all companies share the same behaviour, there is merely a generalised increase in wages without any transfer of employment : companies merely pay their employees more without having attracted others. To avoid this unnecessary increase in labour costs, companies can move to a cooperative equilibrium between them whereby they do not raise wages - even at full employment - and do not try to attract other companies’ employees; Even if the non-cooperative equilibrium persists and labour costs accelerate at full employment, if competition in the goods and services markets is strong, companies might not increase their prices and profit margins are squeezed instead of there being inflation. In the recent period in the United States and the euro zone, there has been: A small acceleration in wages and no acceleration in labour cost s in the United States; A small acceleration in labour cost s which has not brought about an acceleration in prices in the euro zone.