(Petrozavodsk, Russia)

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Institute of Applied Mathematical Research, KarRC of the RAS, Russia

We present a game-theoretic model of competitive decision on a meeting time. There are n players who are negotiating the meeting time. The players’ utilities are represented by linear unimodal functions. The maximum values of the utility functions are located at the points i/(n-1), i=0,…,n-1. The final decision will be done if all participants accept the proposal. Players take turns 1, then 2, then 3, …, n. We assume that after each negotiation session, the utility functions of all players will decrease proportionally to d. We will look for a solution in the class of stationary strategies, when it is assumed that the decisions of the players will not change during the negotiation time, i.e. the player i will make the same offer at step i and at subsequent steps n+i, 2n+i, etc. We use the backward induction method. To do this, assume that player n is looking for his best responce, knowing player 1’s proposal, then player (n-1) is looking for his best responce, knowing player n’s solution, etc. The subgame perfect equilibrium in the class of stationary strategies is found in analytical form.