Recipes for Structural Fairness in Games

Abstract

Background. Although fairness is central to society and to games that are taken seriously, the structural aspect of fairness has not been addressed as a problem of games.

Aim. To resolve the problem of structural fairness in multi-player, multi-episodic games, especially for business games that are transaction based, where sales result from individual transactions rather than from formulae that aggregate and allocate modeled-market demand.

Method. Mathematics and examples are used to clarify positions, present proofs, and show application.

Argument. Structural fairness is of three kinds: positional, order, and arrival.

Finding. For fixed number of parties, positional rotation assures complete positional fairness, whereas order rotation assures both complete positional fairness and complete order fairness, but only when number-of-party and number-of-episode conditions are satisfied. For variable number of parties, arrival rotation assures fairness to parties added last. The classic Gold and Pray model can be modified to allow supply to affect demand by applying order rotation to stock outs.

Application. The rotational procedures apply to business games with modeled and real markets, and may apply to all games with a scoring system that is taken seriously.

Conclusion. Games can be structurally fair, but the game that is structurally fair must be a multi-episodic game that incorporates fairness into its design. For assuring structural fairness, proportional and random methods are generally inferior to rotation.