Figure 1
Boltzmann division for homogeneous and heterogeneous cake-cutting problems. (a) Homogeneous cake cutting, in which \(\tilde{N}\) is the total number of cake units, Ej is the division potential of player j, and Pj is the Boltzmann probability that a cake unit is allocated to player j. (b) Heterogeneous cake cutting, in which \(\tilde{N}^{i}\) is the total number of cake units with flavor i, \(w_{j}^{i}\) is the weight factor expressing player j’s preference for flavor i, and \(P_{j}^{i}\) is the Boltzmann probability that a cake unit of flavor i is allocated to player j.
