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. We also consider incomplete information scenarios
on the planner's part and infinite games.