Nontransferable Utility Games and Markets: Some Examples
and the Harsanyi Solution
Sergiu Hart
Abstract
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
"λtransfer 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.

Econometrica 53 (1985), 6, 14451450