Attending Meetings: The Use of Mixed Strategies
Attending Meetings: The Use of Mixed Strategies

Summary/Abstract: We consider a game in which each of n players is invited to a meeting, and has to decide whether or not to attend the meeting. A quorum has to be at-tained if the meeting is to have the power of making binding decisions. We consider all possible preferences of the players. These preferences are assumed to be the same for all players. Restricting ourselves to symmetric Nash equilibria, we identify three different classes of preferences. In a first class the game has a unique Nash equilibrium, defined in mixed strategies. In a second class the game has two Nash equilibria, defined in pure strategies. In a final class of preferences the game has a Nash equilibrium in pure strategies, and possibly also in mixed strategies. If there is a mixed strategy Nash equilibrium, we show that the equilibrium probability of attending the meeting increases when the quorum increases. Furthermore, if the number of players becomes very large, this equilibrium probability tends to the value of the quorum. Finally, we show how the underlying game structure can also be used in other applications.

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