Generation to Generation by Gersick, Davis, Hampton, and Lansberg
The biggest caveat for this book is that the authors appear to be consultants to family businesses, and not actually the scions of family businesses. That said, the authors forward a tripartite model of family-business roles: ownership, business, and family. The insight being that people switch roles fluidly, and the various goals for each role can often be at ends.
Were one to envision a family business as a game, there would appear to be three paths to success: acquiring more ownership, developing the family somehow, or growing the business. Given this setup, what would a game designer do?
Say we had a Settlers of Catan-like game where Prestige points could come from either of the three paths. In Settlers, players can build their own roads and cities, and when they get road-locked, they can still continue building their cities so they have their own sense of accomplishment. It seems likely a game designer would have some interesting comments on structuring family business dymanics.
The authors detail precious few management hacks to help with the role management problems they've detailed. E.g. using an amulet (instead of a conch) which rotates after invocation and grants the holder an immediate win on any decision, or establishing a primus inter pares type system.
The authors seem to leave much to family culture and business travails. I'd prefer to ask: How do we structure the family business so that everyone can help out in many different ways, see their good work develop, and have the overall result forward the groups' goals? That may just be my German side, though.