Solution of the meeting time choice problem for $n$ persons

We consider a game-theoretic model of negotiations of n persons about a meeting time. The problem is to determine the time of the meeting, with the consensus of all players required to make a final decision. The solution is found by backward induction in the class of stationary strategies. Players' wins are represented by piecewise linear functions having one peak. An subgame perfect equilibrium for the problem in the case of $\delta \leqslant \frac{1}{2}$ is found in analytical form.