Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and solution (...) technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks. (shrink)

Brams’ paradox of new members and Shenoy’s paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley–Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.