A Compositional Game to Fairly Divide Homogeneous Cake

The author argues that even homogeneous cake, which has no differences in player valuations, can raise interesting mechanism design questions. Abel Jansma introduces a compositional game based on iterated cake-cutting in which, for a homogeneous cake, a Nash equilibrium gives each of n players 1/n of the cake using just n-1 cuts, so each player receives a contiguous piece. Naive composition of the "I cut you choose" rule produces an exponentially unfair distribution with a Gini coefficient approaching 1, while the proposed Biggest Player rule removes this cost and achieves decentralised, asynchronous fairness at linear Robertson-Webb complexity. The game is also implemented in Haskell and the Open Game engine.