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

Sergiu Hart

(Acrobat PDF file)

In the last few years, some examples have purportedly exhibited some difficulties with the game theoretic concept of "value" in the nontransferable utility case. These examples (see Roth [1980] and Shafer [1980]) and the ensuing controversy (see Aumann [1985], Roth [1986], Aumann [1986]) have almost exclusively deaalt with the NTU value introduced by Shapley (also known as the "λ-transfer value"). However, prior to the definition of this concept, Harsanyi [1959, 1963] has presented another solution for this class of games, which has received much less attention.
Our purpose is to compute the Harsanyi solutions for the examples of Roth and Shafer. It turns out that the difficulties "disappear," and there is much agreement with what we intuitively expect the outcome to be.