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Two-person cooperative games. (English) Zbl 0050.14102

The following game is considered: let a set \(B\) of pairs \((u_1,u_2)\) of possible payoffs to players 1 and 2 respectively be given. The players choose mixed strategies \(t_i\) (“threats”) independently and inform one another of their choices. Then each of them chooses an amount \(d_i\) (“demands”). The pay-offs to them are the demands, if there is a pair in \(B\) such that \(u_i\geq d_i\) for \(i=1,2\). Otherwise the pay-offs are those belonging to the strategies \(t_i\). The game is analyzed by reducing it to a two-person non-zero sum game, and axiomatically. The author shows that there are optimal threats and optimal demands, suitably defined. The latter are the values of the game to the two players.
Reviewer: S. Vajda

MSC:

91A12 Cooperative games
91A05 2-person games
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