Sunk costs are costs that have been made and cannot be reversed. In the built environment this concerns building lots that have been bought and the construction costs of an existing building. In principle these costs ought not to influence subsequential decisions. Every subsequent decision should in itself be profit maximizing. That means that only the costs that are to be incurred after the decision matter. In many cases, but not always, that means it is more interesting to continue with existing possessions than to start anew.
When certain costs have been made, that should give a competitive advantage. This holds as the already incurred costs do not matter anymore in subsequent decisions. An existing office can lower its rent a lot more than an office that is not constructed yet. The new office only gets build if the construction costs are also covered by the rent. The threat of lower rents stemming from the existing building stock puts downwards pressure on new construction.
This kind of competition could be considered Stackelberg competition. In Stackelberg competition party A first determines by how much it will supply the market and after that party B decides. That means that party B takes into consideration the amount of supply already available from party A.
In practice many people do seem to take sunk costs into account. When could it be rational to take sunks costs into consideration? To seem consistent to the outside world, it could be rational to consider these costs despite being theoretically irrelevant.
The actual question is: will people take me serious if I quit a project I invested so much in? If not, which means reputational damage, it means sunk costs do matter indirectly. In that case the reputation damage is the extra cost of quitting. The actual sunk costs still do not matter directly in that case. Although, the costs of reputation damage are probably higher when the sunk costs are higher.
Sources and further reading
McAfee, R.P., Mialon, H.M., and Mialon S.H., 2007. Do Sunk Costs Matter?