  A recently introduced concept of "cooperative equilibrium", based on the
assumption that players have a natural attitude to cooperation, has been proven
a powerful tool in predicting human behaviour in social dilemmas. In this
paper, we extend this idea to more general game models, termed "Pareto
solvable" games, which in particular include the Nash Bargaining Problem and
the Ultimatum Game. We show that games in this class possess a unique pure
cooperative equilibrium. Furthermore, for the Ultimatum Game, this notion
appears to be strongly correlated with a suitably defined variant of the
Dictator Game. We support this observation with the results of a behavioural
experiment conducted using Amazon Mechanical Turk, which demonstrates that our
approach allows for making statistically precise predictions of average
behaviour in such settings.
