negmas was designed mainly as a research and educational tool with special emphasis on supporting multi-strand multilateral multi-issue negotiations with complex utility functions. This section gives an introduction to the main concepts of the public interface.

In order to use the library you will need to import it as follows (assuming that you followed the instructions in the installation section of this document):

import negmas

To simplify the use of this platform, all classes and functions from all base modules are aliased in the root package (except generics and helpers). This is an example of importing just Outcome which is defined in the outcomes package

from negmas import Outcome

It is possible but not recommended to just import everything in the package using:

from negmas import *
from negmas.helpers import *
from negmas.helpers.prob import *


The package is organized into a set of modules/packages that combine together related functionality. There are base modules, protocol specific modules, advanced and helper modules.

  • Base Modules Implements basic automated negotiation functionality:

    1. outcomes This module represents issues, outcome and responses and provides basic functions and methods to operator with and on them.

    2. preferences This modules represents the base type of all preferences and different widely used utility function types including linear and nonlinear utilities and constraint-based utilities. This module also implements basic analysis tools like finding the pareto-frontier, sampling outcomes with given utilities from the outcome space, etc.

    3. negotiators This module represents basic negotiation agent implementation and provides basic interfaces to be overriden (implemented) by higher specialized modules

    4. mechanisms This module represents the most basic conceptual view of a negotiation protocol supporting both mediate and unmediated mechanisms. The term mechanism was used instead of the more common protocol to stress the fact that this mechanism need not be a standard negotiation protocol. For example auction mechanisms (like second-price auctions) can easily be implemented as a Mechanism in negmas.

    5. common Provides data structures that are used by all modules including mechanism-state, and the agent-mechanism-interface.

    6. genius Implements a specific type negotiator for the stacked alternating offers protocol called GeniusNegotiator which can run NegotiationParty based agents from the Java Genius platform.

  • Mechanism Specific Modules These modules implement the base mechanism, negotiator type(s), state, and related computational resources specific to a single (or a set of related) negotiation/auction protocols

    1. sao Implements that stacked alternating offers protocol for unmediated multiparty multi-issue negotiations. Other than providing the SAOMechanism class representing the protocol, this package provides a set of simple negotiators including the time-based AspirationNegotiator, a SimpleTitForTatNegotiator, among others.

    2. st Implements two basic single-text mediated negotiation protocols (veto and hill-climbing) and the basic negotiator types to support them.

    3. mt Implements and extension of single text mediated protocols to handle multiple proposed agreements in parallel.

    4. ga Implements a Genetic Algorithm based single text mediated negotiation protocol

  • Advanced Negotiation Modules These modules model advanced negotiation problems and techniques

    1. situated Implements world simulations within which agents with intrinsic utility functions can engage in simultaneous interconnected situated negotiations. It is the most important module for the goals of this library. The Agent and World classes described in details later belong to this module

    2. modeling This is a set of submodules implementing modeling of opponent utility, opponent strategy, opponent’s future offers and opponent’s probability of accepting offers.

    3. elicitation Implements several preference elicitation during negotiation methods.

    4. concurrent Implements mechanism types, and other computational resources to support concurrent negotiation.

  • Helper Modules These modules provide basic activities that is not directly related to the negotiation but that are relied upon by different base modules. The end user is not expected to interact directly with these modules.

    • common Provides common interfaces that are used by all other modules.

    • helpers Various helper functions and classes used throughout the library including mixins for logging.

    • inout Provides functions to load and store XML Genius domains and utility functions.

    • java [Depricated] Provides an interface to JNegMAS allowing agents and negotiators to be developed in Java.

    • tournaments Supports creating and running tournaments to compare agents and negotiators.

    • checkpoints Supports saving and reloading world simulations to/from secondary storage.

    • visualizers [Under development] Supports visualization of world simulation, negotiation sessions, negotiators, and agents.

    • generics Provides a set of types and interfaces to increase the representation flexibility of different base modules.

A (not very) brief introduction to NegMAS

This figure shows the main active components of a simulation in a NegMAS world: NegMAS world

The simulation is run using a World object which defines what happens in every simulation step, provides a BulletinBoard object containing all public information about the game, calls various callbacks defined in the Agent object representing each agent in the environment, takes care of running negotiations and keeps track of agreement signing and the resulting Contracts. The World object also controls logging, event management, serialization, visualization, etc. Refer to the World documentation for more details (you need to do that only if you are implementing new world simulations).

The designer of the game implements a World class by overriding few abstract methods in the base World class.

The logic of an agent is NegMAS is implemented in an Agent object. The designer of the simulation, should provide a base class for its specific world inherited from NegMAS’s Agent class. Refer to the Agent documentation for more details about general NegMAS agents.

So now we have the World and the Agent objects, and we already said that the agent does not directly interact with the world. How does these two types of entities interact then?

  • When the World wants to interact with the Agent, it calls some method in it. For example, to instruct the agent to initialize itself, the world calls the init() method defined by the Agent. To inform the agent that a negotiation it is involved in is concluded with success, the World calls the method on_negotiation_success() defined by the agent.

  • When the Agent wants to interact with the World, it accesses an interface object called an AgentWorldInterface or AWI for short which provides all the services available to the Agent. For example, to request a negotiation with another agent, the Agent object needs to call request_negotiation() defined in the AWI.

The world designer usually defines an AWI for its world that inherits NegMAS’s AgentWorldInterface class and provides any special services for agents interacting in this world. You can find all the services available to your agent through the AgentWorldInterface here. These methods and properties are still available for your agent in SCML. Nevertheless, in many cases, more convenient ways to access some of the information (e.g. the bulletin board) is provided in the specific AWIs implemented in the SCML package to be described now.

Now that we know how worlds and agents work and interact, we can look at how negotiation is managed in NegMAS. Note that you can create negotiations that do not belong to any world

A negotiation is controlled by a Mechanism object which implements the negotiation protocol (e.g. the alternating offers protocol). NegMAS provides several mediated and unmediated negotiation protocols (as well as auction mechanisms). The specific Mechanism that is used in SCML is the SAOMechanism which implements the bargaining protocol.

Negotiation strategies are implemented in a Negotiator object which usually inherits some base negotiator-class corresponding to the mechanism(s) it supports.

The interaction between Mechanism and Negotiator objects mirrors the interaction between World and Agent objects. Mechanism objects call methods in Negotiator objects directly but Negotiator objects can only access services provided by the Mechanism object through a NegotiatorMechanismInterface (AMI). You can find more details about the general NegMAS NMI here.

Each specific Mechanism defines a corresponding specific AgentMechanismInterface class (in the same way that World classes define their own AWI).

To negotiate effectively, negotiators employ a UtilityFunction (or any other form of Preferences objects) to represent their preferences over different possible Outcomes of the negotiation (where an outcome is a full assignment of values to all negotiated Issues). NegMAS provides an extensive set of preferences types, utility functions, and issue types. Please refer to this overview and tutorials for more details. NegMAS also provides some basic SAONegotiators for the SAOMechanism (Check the class diagram here). Moreover, you can access almost all Genius agents using NegMAS’s GeniusNegotiator including all finalists and winners of all past ANAC competitions.

Now we understand how agents interact with worlds through AWIs and negotiators interact with mechanisms through AMIs. We know that the general simulation is controlled by the world while each negotiation is controlled by a mechanism within that world. We need now to connect these two triplets of objects

As the figure above shows: Negotiator objects can be created and controlled by Agent objects for the purpose of negotiating with other Agent objects. The standard flow of operations is something like this:

  1. Agent A uses its AWI to request_negotiation() with Agent B passing a Negotiator to be used in this negotiation. Usually Agent A will also create a UtilityFunction and attach it to the Negotiator it just created (by setting its ufun attribute).

  2. The World calls Agent B’s respond_to_negotiation_request() asking it to provide its own Negotiator to negotiate with Agent A’s Negotiator. It can also just reject the negotiation request by returning no negotiators.

  3. The World will then create a Mechanism and ask both Negotiators to join it. If all goes well, the negotiation starts (at a time defined by the simulation rules) and runs until either an agreement or disagreement is reached.

  4. The World class will then inform Agents A and B about the results of the negotiation using their on_negotiation_success and on_negotiation_failure callbacks.

  5. Successful negotiations lead to Agreements but are still not binding in general until signed by all agents involved (A and B in this case). Agent’s ’sign_all_contracts is used for this.

  6. Signed agreements become Contracts and are executed (as specified in the simulation rules) by the World.

When negotiations are independent, these are all the objects needed. Nevertheless, in many cases, negotiations are inter-dependent. This means that what is good in one negotiation depends on other concurrently running negotiations (or on expectations of future negotiations). NegMAS provides two ways to support this case shown in the following figure:



  1. Let Negotiators use UtilityFunctions that depend on some common state. That is what is happening in the left two negotiations.

  2. Have multiple Negotiators be controlled by a single Controller object with its own utility function that depends on what is happening on all the negotiations controlled.

The Negotiators connected to a controller lost their autonomy and just pass control to their owning Controller.

This concludes our introduction to NegMAS and different objects you need to know about to develop your agent.

Outcomes, Issues and Outcome Spaces

Negotiations are conducted between multiple agents with the goal of achieving an agreement (usually called a contract) on one of several possible outcomes. Each outcome is in general an assignment of some value to a set of issues. Each issue is a variable that can take one of a – probably infinite – set of values from some predefined domain.

The classes and functions supporting management of issues, outcome-spaces and outcomes are implemented in the outcomes module.

Issues are represented in negmas using the Issue class. An issue is defined by a set of values and a name.

NegMAS supports a variety of Issue types.

  • Using a set of strings:

# an issue with randomly assigned name
issue1 = make_issue(values=["to be", "not to be"])
# an issue with given name:
issue2 = make_issue(values=["to be", "not to be"], name="The Problem")
issueQKqgvpMi: ['to be', 'not to be']
The Problem: ['to be', 'not to be']
  • Using a single integer to give an issue which takes any value from 0 to the given integer minus 1:

issue3 = make_issue(values=10, name="number of items")
number of items: (0, 9)
  • Using a tuple with a lower and upper real-valued boundaries to give an issue with an infinite number of possibilities (all real numbers in between)

issue4 = make_issue(values=(0.0, 1.0), name="cost")
cost: (0.0, 1.0)

The Issue class provides some useful functions. For example you can find the cardinality of any issue using:

[issue2.cardinality, issue3.cardinality, issue4.cardinality]
[2, 10, inf]

It is also possible to check the type of the issue and whether it is discrete or continuous:

[issue2.type, issue2.is_discrete(), issue2.is_continuous()]
['categorical', True, False]

It is possible to check the total cardinality for a set of issues:

    num_outcomes([issue1, issue2, issue3, issue4]),  # expected inf
    num_outcomes([issue1, issue2, issue3]),
]  # expected 40 = 2 * 2 * 10
[inf, 40]

You can pick random valid or invalid values for the issue:

    [issue1.rand_valid(), issue1.rand_invalid()],
    [issue3.rand_valid(), issue3.rand_invalid()],
    [issue4.rand_valid(), issue4.rand_invalid()],
[['to be', '20231127H095259847823jJTGt6qBto be20231127H095259847844XtRgNy0I'],
 [6, 10],
 [0.6118970848141451, 1.928063278403899]]

You can also list all valid values for an issue using all or sample from them using value_generator. Notice that all and value_generator return generators so both are memory efficient.

except ValueError as e:
('to be', 'not to be')
('to be', 'not to be')
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Cannot enumerate all values of a continuous issue


Now that we know how to define issues, defining outcomes from a negotiation is even simpler. An outcome can be any python mapping or iterable with a known length. That includes dictionaries, lists, tuples among many other.

Here is how to define an outcome for the last three issues mentioned above:

valid_outcome = {"The Problem": "to be", "number of items": 5, "cost": 0.15}
invalid_outcome = {"The Problem": "to be", "number of items": 10, "cost": 0.15}

Notice that the invalid_outcome is assigning a value of 10 to the number of items issue which is not an acceptable value (cost ranges between 0 and 9).

Because outcomes can be represented with many built-in collection classes, the only common ancestor of all outcome objects is the object class. Nevertheless, the outcomes module provide a type-alias Outcome that can be used for static type checking if needed. The outcomes module also provides some functions for dealing with outcome objects in relation to Issues. These are some examples:

    outcome_is_valid(valid_outcome, [issue2, issue3, issue4]),  # valid giving True
    outcome_is_valid(invalid_outcome, [issue2, issue3, issue4]),  # invalid giving False
[True, False]

It is not necessary for an outcome to assign a value for all issues to be considered valid. For example the following outcomes are all valid for the last three issues given above:

    outcome_is_valid({"The Problem": "to be"}, [issue2, issue3, issue4]),
        {"The Problem": "to be", "number of items": 5}, [issue2, issue3, issue4]
[False, False]

You can check the validity of outcomes defined as tuples or lists the same way.

    outcome_is_valid(["to be", 4, 0.5], [issue2, issue3, issue4]),
    outcome_is_valid(("to be", 4, 1.5), [issue2, issue3, issue4]),
[True, False]

It is also important for some applications to check if an outcome is complete in the sense that it assigns a valid value to every issue in the given set of issues. This can be done using the outcome_is_complete function:

    outcome_is_complete(valid_outcome, [issue2, issue3, issue4]),  # complete -> True
        invalid_outcome, [issue2, issue3, issue4]
    ),  # invalid -> incomplete -> False
        {"The Problem": "to be"}, [issue2, issue3, issue4]
    ),  # incomplete -> False
[True, False, False]

Outcome Ranges and constraints

Sometimes, it is important to represent not only a single outcome but a range of outcomes. This can be represented using an OutcomeRange. Again, an outcome range can be almost any mapping or iterable in python including dictionaries, lists, tuples, etc with the only exception that the values stored in it can be not only be int, str, float but also tuples of two of any of them representing a range or a list of values. This is easier shown:

range1 = {
    "The Problem": ["to be", "not to be"],
    "number of items": 5,
    "cost": (0.1, 0.2),

range1 represents the following range of outcomes:

  • The Problem: accepts both to be and not to be

  • number of items: accepts only the value 5

  • cost: accepts any real number between 0.1 and 0.2 up to representation error

It is easy to check whether a specific outcome is within a given range:

outcome1 = {"The Problem": "to be", "number of items": 5, "cost": 0.15}
outcome2 = {"The Problem": "to be", "number of items": 10, "cost": 0.15}
    outcome_in_range(outcome1, range1),  # True
    outcome_in_range(outcome2, range1),  # False
[True, False]

In general outcome ranges constraint outcomes depending on the type of the constraint:

  • tuple The outcome must fall within the range specified by the first and second elements. Only valid for values that can be compared using __lt__ (e.g. int, float, str).

  • single value The outcome must equal this given value.

  • list of values The outcome must be within the list.

  • list of tuples The outcome must fall within one of the ranges specified by the tuples.

Outcome Spaces

An outcome-space is a set of outcomes which can be enumerated, sampled, etc.

NegMAS supports a special kind of outcome-spaces called CartesianOutcomeSpace which represents the Cartesian product of a set of issues and can be created using make_os function:

myos = make_os([issue1, issue2, issue3, issue4])
<class 'negmas.outcomes.outcome_space.CartesianOutcomeSpace'>

A special case of CartesianOutcomeSpace is a DiscreteCartesianOutcomeSpace (see the examle above) which represent a Cartesian outcome-space with discrete issues (i.e. no issues are continuous).

OutcomeSpace provide convenient methods for gettin information about the outcome-space or manipulating it. Some of the most important examples are:

  • is_numeric, is_integer, is_float Checks if all components of all outcomes are numeric, integer or float.

  • is_discrete, is_finite, is_continuous Check if the outcome space itself is discrete, finite or continuous.

  • cardinality returns the number of outcomes in the outcome-space.

  • cardinality_if_discretized returns the number of outcomes in the outcome-space if we discretize it.

  • to_discrete, to_largest_discrete create an discrete outcome-space that ranges over the input outcome-space.

  • sample returns outcomes from the outcome-space.

  • enumerate_or_sample sample from continuous outcome-spaces and enumerate all outcomes of discrete outcome-spaces.

DiscreteOutcomeSpace is a special case of OutcomeSpace representing a finite outcome space and adds some operations including:

  • to_single_issue generates a single-issue outcome-space with the same number of outcomes as the given outcome-space

  • limit_cardinality generates a discrete outcome-space that approximates the input outcome-space using at most some predefined number of outcomes.

Utilities and Preferences

Agents engage in negotiations to maximize their utility. That is the central dogma in negotiation research. negmas allows the user to define their own utility functions based on a set of predefined base classes that can be found in the utilities module.

Utility Values

In most applications, utility values can be represented by real numbers. Nevertheless, some applications need a more complicated representation. For example, during utility elicitation (the process of learning about the utility function of the human being represented by the agent) or opponent modeling (the process of learning about the utility function of an opponent), the need may arise to represent a probability distribution over utilities.

negmas allows all functions that receive a utility value to receive a utility distribution. This is achieved through the use of two basic type definitions:

  • Distribution That is a probability distribution class capable of representing probabilistic variables having both continuous and discrete distributions and applying basic operations on them (addition, subtraction and multiplication). Currently we use scipy.stats for modeling these distributions but this is an implementation detail that should not be relied upon as it is likely that the probabilistic framework will be changed in the future to enhance the flexibility of the package and its integration with other probabilistic modeling packages (e.g. PyMC3). A concrete implementation of Distribution provided by NegMAS is ScipyDistribution. A special case if the Real distribution which represents a delta distribution \(\delta(v)\) at a given real value \(v\) (i.e. \(p(x)=1\) for \(x=v\) and \(0\) otherwise) which acts both as a Distribution and a float.

  • Value This is the input and output type used whenever a utility value is to be represented in the whole package. It is defined as a union of a real value and a Distribution (float | Distribution). This way, it is possible to pass utility distributions to most functions expecting (or returning) a utility value including utility functions.

This means that both of the following are valid utility values

u1 = Real(1.0)
u2 = UniformDistribution()  # standard normal distribution
U(0.0, 1.0)


Rational entities in NegMAS (including Agents, Negotiators, and Controllers) can have Preferences which define how much they prefer an Outcome over another. Several types of preferences are supported in NegMAS and they all must implement the BasePref protocol.

Ordinal and Cardinal Preferences

The most general Preferences type in NegMAS is Ordinal Preferences which can only represent partial ordering of outcomes in the outcome-space throgh the is_not_worse() method. An entity with this kind of preferences can compare two outcomes but it gets one bit of information out of this comparison (which is better for the entity) and has no way to know how much is the difference

CarindalProb Preferences, on the other hand, implement difference_prob() which return a Distribution indicating how much is the difference between two outcomes. A crisp version (CardinalCrisp) moreover implements difference() which returns a float indicating exactly the difference in value for the entity between two outcomes.

Every CadrinalCrisp object is a CardinalProb which is also an Ordinal object.

Crisp and Prob Preferences

NegMAS usually implements two versions of each Preferences type (other than Ordinal) that represent a probabilistic version (ending with Prob) returing Distributions when queried, and a crisp version (ending with Crisp) returning a float. This simplifies the development of agents and negotiators working with probability distributions.

Stationary and Non-Stationary Preferences

Stationary Preferences are those that do not change during the lifetime of their owner, while non-stationary Preferences are allowed to change. The entity having non-stationary preferences usually faces a harder problem achieving its goals as it needs to take into account this possible change. Entities interacting with other entities with non-stationary Preferences are also in reatively harder situation comapred with those dealing with entities with stationary Preferences.

Stationary Preference type names start with Stationary (e.g. StationaryCardinalProb) while non-stationary types start with NonStationary (e.g. NonStationaryCardinalProb).

Utility Functions

Utility functions are entities that take an Outcome and return its Value. There are many types of utility functions defined in the literature. In this package, the base of all utiliy functions is the BaseUtilityFunction class which is defined in the preferences.ufun module. It behaves like a standard python Callable which can be called with a single Outcome object (i.e. a dictionary, list, tuple etc representing an outcome) and returns a Value. This allows utility functions to return a distribution instead of a single utility value. Special cases are UtilityFunction which is the base class of all crisp ufuns (returning a float when called) and ProbUtilityFunction which is the base class of all probabilistic ufuns (returning a Distribution when called).

Utility functions in negmas have a helper property called type which returns the type of the utility function and a helper function eu for returning the expected utility of a given outcome which is guaranteed to return a real number (float) even if the utiliy function itself is returning a utility distribution.

To implement a specific utility function, you need to override the single eval function provided in the UtilityFunction/ProbUtilityFunction abstract base class. This is a simple example:

COST = 0

class ConstUtilityFunction(UtilityFunction):
    def eval(self, offer):
            return 3.0 * offer[COST]
        except KeyError:  # No value was given to the cost
            return None

    def xml(self):
        return "<ufun const=True value=3.0></ufun>"

f = ConstUtilityFunction()

Note that we used StationaryUtilityFunction as the base class to inform users of the ConstUtilityFunction class that it represents a stationary ufun which means that it is OK to cache results of calls to the ufun for example.

General Utility functions can store internal state and use it to return different values for the same outcome over time allowing for dynamic change or evolution of them during negotiations. For example this silly utility function responds to the mood of the user:

class MoodyUtilityFunction(UtilityFunction):
    def __init__(self, mood="good", stationary=False):
        self.mood = mood
        self._stationary = stationary

    def to_stationary(self):
        return MoodyUtilityFunction(mood=self.mood, stationary=True)

    def eval(self, offer):
        if self.mood not in ("good", "bad"):
            raise ValueError(f"Cannot calculate utility for {offer}")
        return float(offer[COST]) if self.mood == "good" else 0.1 * offer[COST]

    def set_mood(self, mood):
        if self._stationary:
        self.mood = mood

    def xml(self):

offer = (10,)

f = MoodyUtilityFunction()
# I am in a good mode now
print(f"Utility in good mood of {offer} is {f(offer)}")
print(f"Utility in bad mood of {offer} is {f(offer)}")
    y = f(offer)
except ValueError as e:
    print(f"Utility in good mood of {offer} is undecidable: {e}")
Utility in good mood of (10,) is 10.0
Utility in bad mood of (10,) is 1.0
Utility in good mood of (10,) is undecidable: Cannot calculate utility for (10,)

Notice that (as the last example shows) utility functions can return None to indicate that the utility value cannot be inferred for this outcome/offer.

Preferences Protcols

The preferences module provide a set of other python protocols that guarantee that a given Preferences object has some predefined properties. This can be used by developers to adjust the behavior of any entity based on the specific features of its preferences or to limit the applicability of some strategy to a given Preferences type.

Here are some examples of these protocols all applying to utility functions (see next section) (note that protocol here is used in the Pythonic sense of a duck-typed interface):




The utility function can be scaled by some factor


The utility function can be scaled in some part of the outcome-space


The utility function can be shifted by some constant value


The utility function can be by some constant value in some part of the outcome-space


The utility function can be normalized to fall in some given range


The utility function defines some outcome as the default outcome in case of disagreement


The utility function defines some distribution as the distribution from which a value is chosen in case of disagreement


The utility function defines some value as the default value for the agent in case of agreement in case of disagreement


The utility function defines some value as the default value for the agent in case of agreement in case of disagreement


The utility function is a mathematical function (linear or otherwise) of a set of single-issue functions.

The package provides a set of predefined utility functions representing most widely used types. The following subsections describe them briefly.

Linear Additive Utility Functions

The LinearAdditiveUtilityFunction class represents a function that linearly aggregate utilities assigned to issues in the given outcome which can be defined mathematically as follows:

\[U(o) = \sum_{i=0}^{\left|o\right|}{w_i\times g_i(o_i)}\]

where \(o\) is an outcome, \(w\) is a real-valued weight vector, \(\left|o\right|\) is the number of issues, \(o_i\) if the value assigned in outcome \(o\) to issue \(i\), and \(g\) is a vector of functions each mapping one issue of the outcome to some real-valued number (utility of this issue).

Notice that despite the name, this type of utiliy functions can represent nonlinear relation between issue values and utility values. The linearity is in how these possibly nonlinear mappings are being combind to generate a utility value for the outcome.

Note that a utility function needs to know the outcome-space over which is it defined. There are three ways to pass this to the UtilityFunction constructor:

  1. issues=… pass a list of issues (usually made using make_issue)

  2. outcome_space=… pass an OutcomeSpace type (usualy made using make_os)

  3. outcomes=… pass a list of outcomes.

The following three ufuns are exactly equivalent:

issues = [make_issue(2, "i1"), make_issue(2, "i2")]
u1 = LinearAdditiveUtilityFunction(
    issues=issues, values=[lambda x: x, lambda x: x, lambda x: x]
u2 = LinearAdditiveUtilityFunction(
    outcome_space=make_os(issues=issues), values=[lambda x: x, lambda x: x, lambda x: x]
u3 = LinearAdditiveUtilityFunction(
    outcomes=[(0, 0), (0, 1), (1, 0), (1, 1)],
    values=[lambda x: x, lambda x: x, lambda x: x],

For example, the following utility function represents the utility of buyer who wants low cost, many items, and prefers delivery:

issues = [
    make_issue((0, 10), "price"),
    make_issue((1, 10), "number of items"),
    make_issue(["delivered", "not delivered"], "delivery"),
buyer_utility = LinearAdditiveUtilityFunction(
        "price": lambda x: -x,
        "number of items": lambda x: 0.5 * x,
        "delivery": {"delivered": 1.0, "not delivered": 0.0},

Given this definition of utility, we can easily calculate the utility of different options:

print(buyer_utility((1.0, 3, "not delivered")))

Now what happens if we offer to deliver the items:

print(buyer_utility((1.0, 3, "delivered")))

And if delivery was accompanied with an increase in price

print(buyer_utility((1.8, 3, "delivered")))

It is clear that this buyer will still accept that increase of price from '1.0' to '1.8’ if it is accompanied with the delivery option.

As explained before, you can use dict2outcome to make ufun calls more readable:

        {"price": 1.8, "number of items": 3, "delivery": "delivered"},

Nonlinear Aggregation Utility Functions

A direct generalization of the linear agggregation utility functions is provided by the NonLinearAggregationUtilityFunction which represents the following function:

\[U(o) = f\left(\left\{{g_i(o_i)}\right\}\right)\]

where \(g\) is a vector of functions defined as before and \(f\) is a mapping from a vector of real-values to a single real value.

For example, a seller’s utility can be defined as:

seller_utility = NonLinearAggregationUtilityFunction(
    (lambda x: x, lambda x: 0.5 * x, {"delivered": 1.0, "not delivered": 0.0}),
    f=lambda x: x[0] / x[1] - 0.5 * x[2],

This utility will go up with the price and down with the number of items as expected but not linearly.

We can now evaluate different options similar to the case for the buyer:

print(seller_utility((1.0, 3, "not delivered")))
print(seller_utility((1.0, 3, "delivered")))
print(seller_utility((1.8, 3, "delivered")))

Hyper Rectangle Utility Functions

In many cases, it is not possible to define a utility mapping for every issue independently. We provide the utility function HyperVolumeUtilityFunction to handle this situation by allowing for representation of a set of nonlinear functions defined on arbitrary hyper-volumes of the space of outcomes.

The simplest example is a nonlinear-function that is defined over the whole space but that nonlinearly combines several issues to calculate the utility.

For example the previous NonLinearUtilityFunction for the seller can be represented as follows:

seller_utility = HyperRectangleUtilityFunction(
        lambda x: 2.0 * x["price"] / x["number of items"]
        - 0.5 * int(x["delivery"] == "delivered")
print(seller_utility({"price": 1.0, "number of items": 3, "delivery": "not delivered"}))
print(seller_utility({"price": 1.0, "number of items": 3, "delivery": "delivered"}))
print(seller_utility({"price": 1.8, "number of items": 3, "delivery": "delivered"}))

This function recovered exactly the same values as the NonlinearUtilityFuction defined earlier by defining a single hyper-volume with the special value of None which applies the function to the whole space and then defining a single nonlinear function over the whole space to implement the required utiltiy mapping.

HyperVolumeUtilityFunction was designed to a more complex situation in which you can have multiple nonlinear functions defined over different parts of the space of possible outcomes.

Here is an example in which we combine one global utility function and two different local ones:

f = HyperRectangleUtilityFunction(
        {0: (1.0, 2.0), 1: (1.0, 2.0)},
        {0: (1.4, 2.0), 2: (2.0, 3.0)},
    utilities=[5.0, 2.0, lambda x: 2 * x[2] + x[0]],
    weights=[1, 0.5, 2.5],

There are three nonlinear functions in this example:

  • A global function which gives a utility of 5.0 everywhere

  • A local function which gives a utility of 2.0 to any outcome for which the first issue (issue 0) has a value between 1.0 and2.0and the second issue (issue1) has a value between1.0and2.0which is represented as:{0: (1.0, 2.0), 1: (1.0, 2.0)}``

  • A second local function which gives a utility that depends on both the third and first issues (lambda x: 2 * x[2] + x[0]) on the range {0: (1.4, 2.0), 2: (2.0, 3.0)}.

You can also have weights for combining these functions linearly. The default is just to sum all values from these functions to calculate the final utility.

Here are some examples: * An outcome that falls in the range of all constraints:

f([1.5, 1.5, 2.5])
  • An outcome that falls in the range of the global and first local constraints only:

f([1.5, 1.5, 1.0])
  • An outcome that misses a value for some of the issues:

print(f([1.5, 1.5]))

Notice that in this case, no utility is calculated because we do not know if the outcome falls within the range of the second local function or not. To allow such cases, the initializer of HyperVolumeUtilityFunction allows you to ignore such cases:

g = HyperRectangleUtilityFunction(
        {0: (1.0, 2.0), 1: (1.0, 2.0)},
        {0: (1.4, 2.0), 2: (2.0, 3.0)},
    utilities=[5.0, 2.0, lambda x: 2 * x[2] + x[0]],
print(g([1.5, 1.5]))

Nonlinear Hyper Rectangle Utility Functions

HyperVolumeUtilityFunction should be able to handle most complex multi-issue utility evaluations but we provide a more general class called NoneLinearHyperVolumeUtilityFunction which replaces the simple weighted summation of local/global functions implemented in HyperVolumeUtilityFunction with a more general nonlinar mapping.

The relation between NoneLinearHyperVolumeUtilityFunction and HyperVolumeUtilityFunction is exactly the same as that between NonLinearAdditiveUtilityFunction and LinearAdditiveUtilityFunction

Other utility function types

There are several other built-in utility function types in the utilities module. Operations for utility function serialization to and from xml as sell as normalization, finding pareto-frontier, generation of ufuns, etc are also available. Please check the documentation of the utilities module for more details

print(list(_ for _ in negmas.preferences.__all__ if _.endswith("Function")))

Utility Helpers and Analysis Tools

NegMAS provides a set of functions that help with common tasks required while developing negotiation agents. These are some examples:

  • pareto_frontier Finds the pareto-frontier of a set of utility functions.

  • make_discounted_ufun Takes a utility function and returns one that is discounted (linearly and/or exponentially).

  • normalize Normalizes a utility function within a given range.

  • outcome_with_utility Finds an outcome with a utility within some range.

  • minmax Finds the range of values of a utility function and outcomes with highest and lowest utilities.


When negotiations are run, agents are allowed to respond to given offers for the final contract. An offer is simply an outcome (either complete or incomplete depending on the protocol but it is always valid). Negotiators can then respond with one of the values defined by the Response enumeration in the outcomes module. Currently these are:

  • ACCEPT_OFFER Accepts the offer.

  • REJECT_OFFER Rejects the offer.

  • END_NEGOTIATION This implies rejection of the offer and further more indicates that the agent is not willing to continue with the negotiation. The protocol is free to handle this situation. It may just end the negotiation with no agreement, may just remove the agent from the negotiation and keep it running with the remaining agents (if that makes sense) or just gives the agent a second chance by treating it as just a REJECT_OFFER case. In most case the first response (just end the negotiation) is expected.

  • NO_RESPONSE Making no response at all. This is usually not allowed by negotiation protocols and will be considered a protocol violation in most cases. Nevertheless, negotiation protocols are free to handle this response when it arise in any way.

  • WAIT Used to make the negotiation wait for a slow running process in one of the negotiators. This should never be returned from user code. It is used by some builtin controllers in the system to synchronize responses (e.g. SAOSyncController )

Rational Entities

A Rational entity in NegMAS is an object that has an associated UtilityFunction. There are three types of Rational entities defined in the library:

  • Negotiator represents a negotiation agent that can interact with Mechanism objects (representing negotiation protocols) using a dedicated AgentMechanismInterface the defines public information of the mechanism. A negotiator is tied to a single negotiation.

  • Agent represents a more complex entity than a negotiation agent. It does not interact directly with negotiation protocols (i.e. it does not have an AgentMechanismInterface) and is needed when there is a need to adjust behavior in multiple negotiations and/or when there is a need to interact with a simulation or the real world (represented in negmas by a World object) through an AgentWorldInterface.

  • Controller A mid-level entity between Negotiator and Agent. It can control multiple negotiator objects at the same time but it cannot interact with mechanisms or worlds directly. Usually controllers are created by agents to manage a set of interrelated negotiations through dedicated negotiators in each of them.


Negotiations are conducted by negotiators. We reserve the term Agent to more complex entities that can interact with a simulation or the real world and spawn Negotiator objects as needed (see the situated module documentation). The base Negotiator is implemented in the negotiators module. The design of this module tried to achieve maximum flexibility by relying mostly on Mixins instead of inheritance for adding functionality as will be described later.

To build your negotiator, you need to inherit from a Negotiator suitable for the negotiation mechanism your negotiator is compatible with, implement its abstract functions.

Negotiators related to a specific negotiation mechanism are implemented in that mechanism’s module. For example, negotiators designed for the Stacked Alternating Offers Mechanism are found in the sao module.

The Base Negotiator

The base class of all negotiators is Negotiator. Negotiators define callbacks that are called by Mechanisms to implement the negotiation protocol.

The base Negotiator class defines basic functionality including the ability to access the Mechanism settings in the form of an AgentMechanismInterface accessible through the ami attribute of the Negotiator.

Genius Negotiator

There is a special type of negotiators called GeniusNegotiator implemented in the genius module that is capable of interacting with negotiation sessions running in the genius platform (JVM). Please refer to the documentation of genius module for more information.


A Controller is an object that can control multiple negotiators either by taking full or partial control from the Negotiators. By default, controllers will just resend all requests received to the corresponding negotiator. This means that if you do not override any methods in the controller, all negotiation related actions will still be handled by the Negotiator. To allow controllers to actually manage negotiations, a subclass of Controller needs to implement these actions without calling the base class’s implementation.

A special kind of negotiator called ControlledNegotiator is designed to work with controllers that take full responsibility of the negotiation. These negotiators act just as a relay station passing all requests from the mechanism object to the controller and all responses back.


Self interested entities in NegMAS can be represented by either Negotiators or Agents. Use negotiators when a single negotiation session is involved, otherwise use an agent. Agents can own both negotiators and controllers (that manage negotiators) and can act in the World (simulated or real).

Putting Everything together

Other than Rational objects, NegMAS defines two types of entities that orchestrate the interactions between Rational objects:

  • Mechanisms represent interaction protocols which can be negotiation protocols or auctions. A Mechanism object connects a set of Negotiators and implements the interaction protocol.

  • Worlds represent either the real world or (usually) a simulation that connects Agents together. Agents can find each other using the world’s BulletinBoard (or other mechanisms defined by the world simulation), they can act in the world, receive state from it and – most importantly for our current purposes – request/run negotiations involving other agents (through dedicated Controller and/or Negotiator objects).

A picture is worth a thousand words. The following figure shows how all the classes we mentioned so far fit together

The most important points to notice about this figure are the following:

  • Almost all entities are NamedObjects which means they have a user assigned name used for debugging, printing, and logging, and a system assigned id used when programatically accessing the object. For example, agents request negotiations with other agents from the world using the partner’s id not name.

  • Controller objects can access neither worlds nor mechanisms directly and they depend on agents to create them and on negotiators to negotiate for them.

  • A UtilityFunction in negmas is an active entity, it is not just a mathematical function but it can have state, access the mechanism state or settings (through its own AgentMechanismInterface) and can change its returned value for the same output during the negotiation. Ufuns need not be dyanmic in this sense but they can be.

Mechanisms (Negotiations)

The base Mechanism class is implemented in the mechanisms module.

All protocols in the package inherit from the Mechanism class and provide the following basic functionalities:

  • checking capabilities of agents against requirements of the protocol

  • allowing agents to be join and leave the negotiation under the control of the underlying protocol. For example the protocol may allow or disallow agents from entering the negotiation once it started, it may allow or disallow modifying the issues being negotiated, may allow only a predefined maximum and minimum number of agents to engage in the negotiation. All of this is controlled through parameters to the protocol initializer.

  • provide the basic flow of protocols so that new protocols can be implemented by just overriding a single __call__() function.

  • provide basic callbacks that can be extended by new protocols.

    Protocols must extend any callback (i.e. call the super() version) instead of overriding them as they may do some actions to ensure correct processing.

The simplest way to use a protocol is to just run one of the already provided protocols. This is an example of a full negotiation session:

p = SAOMechanism(outcomes=6, n_steps=10)
p.add(LimitedOutcomesNegotiator(name="seller", acceptable_outcomes=[(2,), (3,), (5,)]))
p.add(LimitedOutcomesNegotiator(name="buyer", acceptable_outcomes=[(1,), (4,), (3,)]))
state = p.run()

You can create a new protocol by overriding a single function in the Mechanism class.

The built-in SAOMechanism calls negotiators sequentially. Let’s implement a simplified similar protocol that asks all negotiators to respond to every offer in parallel.

from concurrent.futures import ThreadPoolExecutor
from attr import define

class ParallelResponseMechanism(Mechanism):
    def __init__(self, *args, initial_state=None, **kwargs):
            initial_state=SAOState() if not initial_state else initial_state,
        self.state.current_offer = None
        self.current_offerer = -1

    def __call__(self, state):
        n_agents = len(self.negotiators)
        nxt = (self.current_offerer + 1) % n_agents
        current = self.negotiators[nxt]
        offer = None
        self.state.current_offer = (
            current.propose(self.state) if offer is None else offer

        def get_response(negotiator, state=self.state):
            return negotiator.respond(state, self.current_offerer)

        with ThreadPoolExecutor(4) as executor:
            responses = executor.map(
                get_response, [_ for _ in self.negotiators if _.id != current.id]
        self.current_offerer = nxt
        if all(_ == ResponseType.ACCEPT_OFFER for _ in responses):
            state.agreement = self.state.current_offer
        if any(_ == ResponseType.END_NEGOTIATION for _ in responses):
            state.broken = True
        return MechanismStepResult(state=state)

We needed only to override the __call__ method which defines one round of the negotiation. The protocol goes as follows:

  1. Ask the next negotiator to propose.

  2. Get the response of all negotiators (using the thread-pool)

  3. If all negotiators accept the current offer, return it as the agreement

  4. Otherwise, if any negotiators responded with END_NEGOTIATION, break the negotiation

  5. Otherwise, change the next negotiator and return.

Note that we did not need to take care of timeouts because they are handled by the base Mechanism class. Nor did we need to handle adding agents to the negotiation, removing them (for dynamic protocols), checking for errors, etc.

The __call__ method receives the current mechanism state and an optional action. If the action is passed, then it is expected that the corresponding negotiator will not be called and the action will be just used instead of calling the corresponding negotiator.

Agents can now engage in interactions with this protocol as easily as any built-in protocol:

p = ParallelResponseMechanism(outcomes=6, n_steps=10)
p.add(LimitedOutcomesNegotiator(name="seller", acceptable_outcomes=[(2,), (3,), (5,)]))
p.add(LimitedOutcomesNegotiator(name="buyer", acceptable_outcomes=[(1,), (4,), (3,)]))
state = p.run()

The negotiation ran with the expected results

Our mechanism keeps a history in the form of a list of MechanismState objects (on per round). Let’s check it:

import pandas as pd

pd.DataFrame([_.asdict() for _ in p.history])
running waiting started step time relative_time broken timedout agreement results ... error_details threads last_thread current_offer current_proposer current_proposer_agent n_acceptances new_offers new_offerer_agents last_negotiator
0 False False True 0 0.0 0.0 False False (3,) None ... {} (3,) None None 0 <class 'list'> <class 'list'> None

1 rows × 22 columns

We can see that the negotiation did not time-out, and that the final agreement was (3,) but that is hardly useful. It will be much better if we can also see the offers exchanged and who offered them.

To do that we need to augment the mechanism state. NegMAS defines an easy way to do that by defining a new MechanismState type and filling it in the mechanism:

from attrs import define

class MyState(MechanismState):
    current_offer: Outcome | None = None
    current_offerer: str = "none"

class NewParallelResponseMechanism(ParallelResponseMechanism):
    def __init__(self, *args, **kwargs):
        kwargs["initial_state"] = MyState()
        super().__init__(*args, **kwargs)

That is all. We just needed to define our new state type, set the state_factory of the mechanism to it and define how to fill it in the extra_state method. Now it is possible to use this mechanism as we did previously

p = NewParallelResponseMechanism(outcomes=6, n_steps=10)
p.add(LimitedOutcomesNegotiator(name="seller", acceptable_outcomes=[(2,), (3,), (5,)]))
p.add(LimitedOutcomesNegotiator(name="buyer", acceptable_outcomes=[(1,), (4,), (3,)]))
print(f"Agreement: {p.state.agreement}")
Agreement: (3,)

We can now check the history again (showing few of the attributes only) to confirm that the current offer and its source are stored.

def show_history(p):
    """Returns a Pandas Dataframe with the negotiation history"""
    return pd.DataFrame(
            for _ in p.history

step agreement relative_time timedout broken current_offer current_offerer
0 0 (3,) 0.0 False False (3,) none

Let’s see what happens if agreement is impossible (no intersection of acceptable outcomes in our case):

p = NewParallelResponseMechanism(outcomes=6, n_steps=6)
p.add(LimitedOutcomesNegotiator(name="seller", acceptable_outcomes=[(2,), (0,), (5,)]))
p.add(LimitedOutcomesNegotiator(name="buyer", acceptable_outcomes=[(1,), (4,), (3,)]))
print(f"Agreement: {p.state.agreement}")
Agreement: None
step agreement relative_time timedout broken current_offer current_offerer
0 0 None 0.000000 False False (5,) none
1 1 None 0.285714 False False (4,) none
2 2 None 0.428571 False False (2,) none
3 3 None 0.571429 False False (4,) none
4 4 None 0.714286 False False (0,) none
5 5 None 0.857143 False False (1,) none

As expected, the negotiation timed out. Let’s try to make it possible for the agents to agree by providing a common outcome that they may agree upon:

p = NewParallelResponseMechanism(outcomes=6, n_steps=6)
p.add(LimitedOutcomesNegotiator(name="seller", acceptable_outcomes=[(3,), (0,), (5,)]))
p.add(LimitedOutcomesNegotiator(name="buyer", acceptable_outcomes=[(1,), (4,), (3,)]))
print(f"Agreement: {p.state.agreement}")
Agreement: (3,)
step agreement relative_time timedout broken current_offer current_offerer
0 0 None 0.000000 False False (0,) none
1 1 None 0.285714 False False (1,) none
2 2 None 0.428571 False False (0,) none
3 3 None 0.571429 False False (4,) none
4 4 (3,) 0.714286 False False (3,) none

We got an agreement again as expected.

Worlds (Simulations)

A world in NegMAS is what connects all agents together. It has a simulation_step that is used to run a simulation (or update the state from the real world) and manages creation and destruction of AgentWorldInterfaces (AWI) and connecting them to Agents.

Agents can join and leave worlds using the join and leave methods and can interact with it through their AWIs.

To create a new world type, you need to override a single method (simulation_step) in the base World class to define your simulation. Most likely you will also need to define a base Agent inherited class that is capable of interacting with this world and a corresponding AgentWorldInterface.

You can see an example of a world simulation in the tutorials.