This interactive environment is called "Bird-Do-Or-Die" where users compete or collaborate to either save or kill the bird(s). This is best played over a period of time. People should use their asynchronous free time to either protect or kill the bird - competing against other users over longer durations.
The network model here is ideally a many-to-many setup - where people form teams to work on saving/and or killing the bird over time. This also makes the system asynchronous - where people can work on increasing the bridge blocks over time, which then others must overcome to kill the bird. The roles are essentially oppositional - where people work to defeat the other's work.