What is the role of interbank markets and central banks in coping with banking crises? In experiments using an agent-based framework with multiple banks and an interbank market. I found that when banks cannot interact, then runs in isolated banks occur with a higher frequency than when banks have equal market shares. That is, there are no runs escalating to systemic panics. In contrast, if one bank has a market share twice as big as the rest, runs spread. The presence of a central bank may unexpectedly increase the occurrence of bank runs. Institutional complexity helps to reduce the frequency of bank runs. Hence, decentralized institutional structures perform better than centralized ones.