Sequentially two-leveled egalitarianism for TU games: Characterization and application

A new linear value for cooperative transferable utility games is introduced. The recursive definition of the new value for an n-person game involves a sequential process performed at n - 1 stages, applying the value to subgames with a certain size k,1 ≤ k < n, combining with the rule of two-leveled egalitarianism (additive normalization) in order to guarantee the efficiency property for the new value, sequentially two-leveled egalitarianism, shortly S ₂EG value, applied to subgames of size k + 1. The new value will be characterized in various ways. The S ₂EG value differs from the Shapley value since, besides efficiency, linearity, and symmetry, it verifies an additional property with respect to so-called scale-dummy player (replacing dummy player property). Consequently, the S ₂EG value of a game may be determined as the solidarity value of the per-capita game (incorporating the proportional rule due to different levels of efficiency). Various potential representations of the new value are established. In the application to a land corn production economy, it yields allocations, in which the landlord's interest coincides with striving for a maximum production level. For economies with the linear production function, not only the unique landlord but also all the workers have incentives to increase the scale of the economy.