Cs-621 Theory Gems

So far, we were focusing on “static” analysis of games. That is, we considered scenarios in which the game and utilities of all the players are fixed and known and our task is only to predict possible outcomes of that game when some (or all) the players are acting rationally. Today, we turn the tables: there is no predefined game, only players that have some utilities. However, the key point is that these utilities are private. That is, we have no access to them (we only know a universe they are coming from) – so, in particular, when players claim to have some utility function there is no way for us to know if they are telling the truth. Our goal now is to design a game that compels players that are acting rationally (with respect to their private utilities) to choose an outcome that maximizes the social welfare, i.e., a one that maximizes the sum of (private) utilities of all the players. (Note that an outcome that maximizes the social welfare might not necessarily be optimal from the point of view of any particular player. So, the difficulty here is to ensure that the social-welfare outcome is still the preferable one for all the players and, furthermore, to do it in a way that does not even require us to know what their actual utilities are.)