#### On the Actual Inefficiency of Efficient Negotiation Methods

##### Luca Barzanti, Marcello Mastroleo

In this contribution we analyze the effect that mutual information has on the actual performance of efficient negotiation methods. Specifically, we start by proposing the theoretical notion of Abstract Negotiation Method (ANM) as a map from the negotiation domain in itself, for any utility profile of the parties. ANM can face both direct and iterative negotiations, since we show that ANM class is closed under the limit operation. The generality of ANM is proven by showing that it captures a large class of well known in literature negotiation methods. Hence we show that if mutual information is assumed then any Pareto efficient ANM is manipulable by one single party or by a collusion of few of them. We concern about the efficiency of the resulting manipulation. Thus we find necessarily and sufficient conditions those make manipulability equivalent to actual inefficiency, meaning that the manipulation implies a change of the efficient frontier so the Pareto efficient ANM converges to a different, hence actually inefficient, frontier. In particular we distinguish between strong and weak actual inefficiency. Where, the strong actual inefficiency is a drawback which is not possible to overcome of the ANMs, like the Pareto invariant one, so its negotiation result is invariant for any two profiles of utility sharing the same Pareto frontier, we present. While the weak actual inefficiency is a drawback of any mathematical theorization on rational agents which constrain in a particular way their space of utility functions. For the weak actual inefficiency we state a principle of Result's Inconsistency by showing that to falsify theoretical hypotheses is rational for any agent which is informed about the preference of the other, even if the theoretical assumptions, which constrain the space of agents' utilities, are exact in the reality, i.e. the preferences of each single agent are well modeled.

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