Geodesic
Solution of the meeting time choice problem for $n$ persons
Contributions to game theory and management, Tome 15 (2022), pp. 303-310

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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.
Keywords: optimal timing, linear utility functions, sequential bargaining, Rubinstein bargaining model, subgame perfect equilibrium, stationary strategies, backward induction. 
@article{CGTM_2022_15_a22,
     author = {Vladimir V. Yashin},
     title = {Solution of the meeting time choice problem for $n$ persons},
     journal = {Contributions to game theory and management},
     pages = {303--310},
     publisher = {mathdoc},
     volume = {15},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2022_15_a22/}
}
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Vladimir V. Yashin. Solution of the meeting time choice problem for $n$ persons. Contributions to game theory and management, Tome 15 (2022), pp. 303-310. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a22/