Non-transferable Utility Games Research Articles

Values for two-stage games: Another view of the Shapley axioms

This short study reports an application of the Shapley value axioms to a new concept of “two-stage games.” In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some “two-stage majority games” (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roth's (1980) criticism of Shapley's “λ-transfer value” for non-transferable utility (NTU) games. But our analysis has wider scope than Roth's example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for “multi-stage games.”

A note on aspirations in non-transferable utility games

For an important class of non-transferable utility games it is shown by short proofs that the set of aspirations is not empty, and that aspirations are closely related to coalitionally rational payoff distributions.

Values of Voting Games

The Shapley-Shubik index of political power measures the probability that a given player in a simple game is pivotal, with th2 power to turn a losing coalition into a winning coalition. Until now, this index has been applied only to games with transferable utility. This paper considers the case where utility is not transferable. A voting game is a nontransferable utility game with a simple gane structure. The solution of a voting game is its nontransferable utility value. This paper studies the values of such games. In particular, the Shapley-Shubik index is the value for a certain class of voting games. This shows that the measurement of political power does not depend on the transferability of utility.

Nontransferable Utility Games and Markets: Some Examples and the Harsanyi Solution

Nontransferable Utility Games and Markets: Some Examples and the Harsanyi Solution