Values for cooperative games with incomplete information: An eloquent example

Myerson's [Cooperative games with incomplete information. Int. J. Game Theory 13 (1984) 69-96] extension of the λ-transfer value to cooperative games with incomplete information focuses among other things on the strength of the incentive constraints at the solution for determining the power of coalitions. We construct an intuitive three-player game where the player whose only contribution is to partly release the two other players from the incentive constraints they face when they cooperate, receives a zero payoff according to Myerson's solution. On the contrary, the random order arrival procedure attributes a strictly positive payoff to him. Our example is thus an analog of the banker game of Owen [Values of games without side payments. Int. J. Game Theory 1 (1972) 95-109] that was designed for evaluating Shapley's λ-transfer value under complete information. Asymmetric information now takes up the role that was formerly attributed to the lack of transferability of utilities.