Commuting for meetings

Urban congestion causes travel times to exhibit considerable variability, which leads to coordination problems when people have to meet. We analyze a game for the timing of a meeting between two players who must each complete a trip of random duration to reach the meeting, which does not begin until both are present. Players prefer to depart later and also to arrive sooner, provided they do not have to wait for the other player. We find a unique Nash equilibrium, and a continuum of Pareto optima that are strictly better than the Nash equilibrium for both players. Pareto optima may be implemented as Nash equilibria by penalty or compensation schemes.