Gale and Shapley (1962) proposed that there is a similar game to the marriage problem called "the roommate problem". And, they showed that unlike the marriage problem, the roommate problem may have unstable solutions. In other words, the stability theorem fails for the roommate problem. In this...

In this paper, we propose two new mechanisms operating in two-sided matching games. The first mechanism implements the full set of stable matchings for any preference profile in subgame perfect Nash equilibrium. The second mechanism, derived from the first, implements a Matryoshka Partition for...

In this paper, we propose a new cycle criterion, Cyclical Conflicts (CCs), for preference profiles in two-sided matching markets through a dynamic mechanism. We first show that CCs provide a complete characterization of singleton cores in two-sided matching markets. Secondly, we prove the...