Cost of cooperation for scheduling meetings

Scheduling meetings among agents can be represented as a game - the Meetings Scheduling Game (MSG). In its simplest form, the two-person MSG is shown to have a price of anarchy PoA) which is bounded by 0.5. The PoA bound provides a measure on the efficiency of the worst Nash Equilibrium in social (or global) terms. The approach taken by the present paper introduces the Cost of Cooperation (CoC) for games. The CoC is defined with respect to different global objective functions and provides a measure on the efficiency of a solution for each participant (personal). Applying an "egalitarian" objective, that maximizes the minimal gain among all participating agents, on our simple example results in a CoC which is non positive for all agents. This makes the MSG a cooperation game. The concepts are defined and examples are given within the context of the MSG. Although not all games are cooperation games, a game may be revised by adding a mediator (or with a slight change of its mechanism) so that it behaves as a cooperation game. Rational participants can cooperate (by taking part in a distributed optimization protocol) and receive a payoff which will be at least as high as the worst gain expected by a game theoretic equilibrium point.