Two support results for the Kalai–Smorodinsky solution in small object division markets

We discuss two support results for the Kalai–Smorodinsky bargaining solution in the context of an object division problem involving two agents. Strategic interaction determines an allocation of objects, so that evaluation with individual utilities constitute the payoffs in the derived games. These allocations of objects are obtained through individual demand in a specific market for objects. For the first support result, games in strategic form are derived that exhibit a unique Nash equilibrium and equilibrium payoffs equal the Kalai–Smorodinsky solution of the underlying bargaining problem. The second result uses subgame perfect equilibria of a game in extensive form. Again, payoffs in any subgame perfect equilibrium coincide with the Kalai–Smorodinsky solution.