Fair, Individually Rational and Cheap Adjustment

Consider the practical goal of making a desired action profile played, when the planner can only change the payoffs, bound by stringent constraints. Applications include motivating people to choose the closest school, the closest subway station, or to coordinate on a communication protocol or an investment strategy. Employing subsidies and tolls, we adjust the game so that choosing this predefined action profile becomes strictly dominant. Inspired mainly by the work of Monderer and Tennenholtz, where the promised subsidies do not materialise in the not played profiles, we provide a fair and individually rational game adjustment, such that the total outside investments sum up to zero at any profile, thereby facilitating easy and frequent usage of our adjustment without bearing costs, even if some players behave unexpectedly. The resultant action profile itself needs no adjustment. Importantly, we also prove that our adjustment minimises the general transfer among all such adjustments, counting the total subsidising and taxation.