Sperner's lemma and fair division

Fair division is an active research area in Mathematics, Economics, Computer Science, etc. There are many different kinds of fair division problems. These are often named after everyday situations: fair resource allocation, fair cake-cutting, fair chore division, room assignment – rent division, and more. Although many exact and approximative methods for finding fair solutions already exist, the area of fair division still expands and tries to find better solutions for everyday problems. The objective of the thesis was to find, present and compare methods based on Sperner's Lemma, that can be used for solving different fair division problems. The thesis presents next approximative methods: Simmons' approach to cake-cutting, Su's approach to room assignment – rent division and Scarf's method for computation of equilibrium prices. An application with graphical user interface was build, which allows us to try out described methods in different test scenarios.