Finding probabilities of non-empty cores of four-sided assignment game theory in the housing market.

摘要

This dissertation is a continuing investigation of a multi-sided assignment game theory known as four-sided assignment games. This dissertation investigated the probabilities of core probabilities of given player coalitions (buyers, sellers, real estate agents, and mortgage lenders) in the four-sided housing market. This dissertation focuses on what happens to the core in the four-sided housing market when buyers and sellers are allowed to increase and real estate agents and mortgage lenders are fixed at two players. Computer algorithms based on mathematical concepts and theories were used to find the non-empty core probability of each game. Results show that a four-sided assignment game in the housing market can have empty cores and that the probability of non-empty cores increases as the numbers of players increase. Results may be generalized to include all multi-sided assignment games which follow patterns similar to those of three and four-sided assignment games. Finally, conclusions are presented and further research areas discussed.