max_relative_welfare_points

negmas.preferences.max_relative_welfare_points(ufuns: Sequence[UtilityFunction], frontier: Sequence[tuple[float, ...]], ranges: Sequence[tuple[float, ...]] | None = None, outcome_space: OutcomeSpace | None = None, issues: Sequence[Issue] | None = None, outcomes: Sequence[Outcome] | None = None, eps=1e-12) → tuple[tuple[tuple[float, ...], int], ...][source]

Calculates all the points with maximum relative welfare (i.e. sum of improvements above reserved value) on the Pareto frontier of a negotiation.

Parameters:

  • ufuns – A list of ufuns to use

  • frontier – a list of tuples each giving the utility values at some outcome on the frontier (usually found by pareto_frontier) to search within

  • outcome_space – The outcome-space to consider

  • issues – The issues on which the ufun is defined (outcomes may be passed instead)

  • outcomes – The outcomes on which the ufun is defined (outcomes may be passed instead)

Returns:

  • A tuple of utility values at the Nash point

  • The index of the given frontier corresponding to the Nash point

Return type:

A list of tuples (empty if cannot be calculated) each consists of

Remarks:

  • The function searches within the given frontier only.