people join tennis clubs for a fixed free per year, which entitles them to play as much as they want without charge. because people who pay these feeds play more tennis than others( who can use free public courts), this means sucnk cost matter for decision. right?

The concept you are referring to is called "sunk cost." Sunk costs are costs that have already been incurred and cannot be recovered. In the case of joining a tennis club, the fixed fee you pay per year is a sunk cost because once paid, it cannot be recovered, regardless of how much or how little you actually play.

However, sunk costs do not directly affect your decisions going forward. When deciding whether to play at a tennis club or use free public courts, the key consideration should be the marginal cost, which refers to the additional cost incurred by playing an additional game of tennis.

In this case, since the fee paid for the tennis club membership is a sunk cost, it should not be factored into the decision. Whether you play at the tennis club or use public courts, the fixed fee remains the same. Therefore, the only costs that matter for the decision are the marginal costs, such as transportation expenses or the time required to commute to the different locations.

It's important to make decisions based on the additional costs and benefits that will arise from that point onwards, rather than being influenced by costs that have already been incurred and cannot be recovered.