Optimal Preference Satisfaction for Conflict-Free Joint Decisions

When presented with multiple choices, we all have a preference; we may suffer loss because of conflicts arising from identical selections made by other people if we insist on satisfying only our preferences. Such a scenario is applicable when a choice cannot be divided into multiple pieces owing to the intrinsic nature of the resource. Earlier studies examined how to conduct fair joint decision-making while avoiding decision conflicts in terms of game theory when multiple players have their own deterministic preference profiles. However, probabilistic preferences appear naturally in relation to the stochastic decision-making of humans, and therefore, we theoretically derive conflict-free joint decision-making that satisfies the probabilistic preferences of all individual players. To this end, we mathematically prove conditions wherein the deviation of the resultant chance of obtaining each choice from the individual preference profile (loss) becomes zero; i.e., the satisfaction of all players is appreciated while avoiding conflicts. Further, even in scenarios where zero-loss conflict-free joint decision-making is unachievable, we present approaches to derive joint decision-making that can accomplish the theoretical minimum loss while ensuring conflict-free choices. Numerical demonstrations are presented with several benchmarks.