Abstract:

Justice, as a concept and practice, has been closely related to the evolution and development of human societies. Fair division is an aspect of justice that has long been addressed and considered in almost all cultural and juridical contexts. In general, fair division addresses the way that sets of items can be distributed among individuals so that they all feel satisfied with the share they received. Justice and fairness imply stability. When stability is achieved, plenty of resources are released and become available for other beneficial resource-requiring activities. Fair division can also be seen as a game where players, i.e., individuals, valuate items differently.

In this work, we present “Fair ‘n square”, a game suite intended to serve mainly educational and training purposes. “Fair ‘n square” contains two serious, ergodic fair-division games which let players familiarize with terms, concepts and techniques from algorithmic game theory. In these games, “Bankruptcy problem” and “Sealed bids”, we address two interesting fair-division problems, namely “the bankruptcy problem” and “the method of sealed bids”, respectively, and implement solution approaches suggested in the literature which guarantee that all individuals receive a fair share. In particular, the approach suggested for the bankruptcy problem was first described in Talmud and was formally proved recently via game-theoretic arguments. According to the statement of “the bankruptcy problem”, the objective is to divide in a fair way an insufficient amount of divisible items (e.g., money units) among individuals with different claims. The method of sealed bids can be used for the fair division of indivisible (i.e., discrete) items (e.g., an apartment) among individuals who valuate these items differently. Apart from their theoretical and educational interest, these methods are also of practical interest and can be exploited in law-related real-world scenaria like for example dividing an estate among creditors when the total debts claimed exceed the existing estate or for the purposes of inheritance sharing when beneficiaries assign different values to the available items.

Our game suite contains several levels of increasing difficulty together with an introductory training level and an auxiliary level which enable players to cross-check how the methods work on their own input. The suite has been developed using the popular 3D computer graphics game engine Unreal Engine and it is currently offered as a windows application in english and greek. “Fair ‘n square” has an easy-to-use interface and can run on a standard computer without requiring advanced skills on behalf of the players.

Keywords:

Application, education, training, fair division, game theory, the bankruptcy problem, the method of sealed bids, Unreal Engine.