From Problems to Protocols:
Towards a Negotiation Handbook
Ivan Marsa-Maestrea!, Mark Kleinb, Catholijn M. Jonkerc, and Reyhan Aydoğanc
a Computer Engineering Department. University of Alcala, 28803 Alcala de Henares, Madrid, Spain
b Center for Collective Intelligence. Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
c Interactive Intelligence Group, Delft University of Technology, Delft, The Netherlands
Automated negotiation protocols represent a potentially powerful tool for problem solving in decision support systems
involving participants with conflicting interests. However, the effectiveness of negotiation approaches depends greatly
on the negotiation problem under consideration. Since there is no one negotiation protocol that clearly outperforms all
others in all scenarios, we need to be able to decide which protocol is most suited for each particular problem. The goal
of our work is to meet this challenge by defining a “negotiation handbook”, that is, a collection of design rules which
allow us, given a particular negotiation problem, to choose the most appropriate protocol to address it. This paper
describes our progress towards this goal, including a tool for generating a wide range of negotiation scenarios, a set of
high-level metrics for characterizing how negotiation scenarios differ, a testbed environment for evaluating protocol
performance with different scenarios, and a community repository which allows us to systematically record and analyze
protocol performance data.
Automated negotiation represents an important class of decision support system, helping self-interested decision
makers rapidly reach high-quality agreements (Robu et al., 2005) (Fenghui et al., 2009) (Sycara, 1993). It has been
studied extensively in e-commerce settings (Myerson and Satterthwaite, 1983) (Athey and Segal,2007) (Lau et al.,
2008) but can also be seen more generally as a paradigm for solving coordination and cooperation problems in
complex multi-agent systems, e.g. for task allocation, resource sharing, or cooperative planning and design (Smith,
1980) (Hemaissia et al., 2007) (Wu et al., 2009) (Sim and Shi, 2009). The protocol used during the negotiation
determines the rules of the negotiation. It determines when parties can make offers, how long offers stand, whether
or not there are deadlines, or a fixed set of rounds, and all other “rules of encounter” (Rosenschein and Zlotkin,
1994). A wide range of negotiation protocols have been explored in research to date, ranging from auctions to
iterative concession to mediated single- and multiple-text protocols, including both bilateral and multilateral variants
(Parsons et al., 2011) (Raiffa, 1982) (Fatima et al., 2009) (Lai et al., 2004) (Kraus, 2006) (Sandholm, 1998)
(Jennings et al., 2001).
A critical challenge facing negotiation research is that no protocol is the best choice for every possible negotiation
scenario. Protocols that work quickly and well for simple negotiations with a few independent issues, for example,
fare poorly when applied to complex negotiations with many interdependent issues (Klein et al., 2003). Some
protocols may be fast but produce less-than-optimal results, and others the opposite. The question then becomes,
which protocols should be used for which negotiation problems.
The research community has been unable to answer this key question, to date, because the different efforts all tend
to test their protocols using their own idiosyncratic negotiation scenarios, varying widely across dimensions that
include the number of agents, size of the contract space, degree of issue interdependency, and so on. It’s been like
comparing apples and oranges. This problem is exacerbated by the fact that there currently is no systematic
enumeration of what types of negotiation challenges exist, nor do we have standard tools for identifying the type of
any given real-world negotiation problem.
Our work aims to address this challenge directly, and enable a much more systematic and cumulative effort by the
negotiation research community. To achieve this, we have been creating the infrastructure depicted in Figure 1.
! Corresponding author: email@example.com
Figure 1. The Negotiation Handbook infrastructure.
This infrastructure consists of the following components:
● a scenario generator that creates a range of test scenarios
● scenario metrics that can be used to characterize key properties of such scenarios
● a testbed for evaluating protocols with these scenarios
● repositories that allow researchers to upload test scenarios, in addition to experimental results on how well
their protocols performed on these scenarios, for use and analysis by the larger community
Researchers can use standard test scenarios already existing in the repository, or upload their own for use by others.
Researchers can also use the testbed to evaluate their protocols, or do their own evaluation and simply upload the
results to the experiment repository. The experiment repository can then be data-mined by any interested party to
find correlations between scenario properties and protocol performance. As this process continues, the research
community can converge upon a negotiation handbook, suited for use by negotiation practitioners, that specifies
design rules concerning which protocols to use for which kinds of problems.
We describe, in the remainder of this paper, the progress we have made towards achieving these goals. We begin by
defining what we mean by a negotiation scenario (section 2), describe the algorithms we are developing to generate
test scenarios (section 3), review the metrics we have developed to capture key properties of such scenarios (section
4), and describe the protocol testbed (section 5) and repository elements (section 6) that are used to gather empirical
data about the relationships between scenario properties and protocol performance. We conclude with a review of
the unique contributions of this work and possible directions for future work.
2. What is a Negotiation Scenario?
A negotiation scenario should specify everything we need to know about a negotiation problem in order to pick the
right protocol for the job. These elements include:
• The domain i.e., the range of contracts being negotiated over, which is defined by the set of issues being
negotiated over as well as the valid values for each issue. The domain for a purchase negotiation, for
example, would probably include price (whose values are positive real numbers) and delivery date (whose
values are dates). A contract specifies a single valid value for every issue in the domain, and an agreement
is generally the contract that all negotiating parties agree upon. Key properties of a domain include the
types of the issues (e.g., continuous vs. discrete) as well as the size of a domain (i.e., the number of possible
• The number and characteristics of the players involved in the negotiation, including:
o Agent preferences, which specify how highly an agent values any particular set of issue values.
Key factors here include the types of the agents preferences (e.g., ordinal vs. cardinal, fixed vs.
mutable), reservation values (i.e., the threshold, possibly time-sensitive, for deciding whether or
not to accept an agreement), as well as the preferential dependencies (i.e., whether the agent’s
preferences for one issue are influenced by the choices made for other issues). An agent’s
preferences may also include such factors as retaining goodwill with some other agents because
they will likely negotiate again in the future.
o Agent decision-making style, such as the agent’s risk attitude (i.e., its willingness to risk poor
outcomes in the pursuit of better ones) (Eckel & Grossman, 2008), cognitive style (i.e., whether it
bases its decision on economic rationality, emotion, or other factors) (Patton & Balakrishnan,
2010), cognitive capability (i.e., whether agents have sufficient computational capability to pick
the best negotiation moves in the time available), truthfulness (i.e., whether agents choose to
report their preferences in a truthful vs. a manipulative way) (Ellingsen et al. 2009), and
characteristic strategies (e.g., some agents may adopt a Boulware strategy, wherein they concede
as slowly as possible towards the other agents’ proposals, until the negotiation deadline comes
close). An agent’s strategy, of course, will be deeply influenced by the protocol being used.
• The context of other negotiations. An agent, for example, can use knowledge of previous similar
negotiations to predict the other agents’ preferences and styles (e.g. it can predict that buyers always want
to maximize price), which can in turn inform its own decision-making during a negotiation. Furthermore,
there might be other negotiations going on at the same time for related topics, and the progress in the
negotiations could mutually influence each other.
These elements define a large space, and many dimensions of this space are as yet incompletely understood. The set
of possible agent strategies, for example, is large, and possibly unbounded. Accordingly we have chosen to focus, in
our initial efforts, on characterizing the two most basic elements of any negotiation: the domain being negotiated
over, and the preferences of the agents doing the negotiation. Since we have already discussed how to represent a
negotiation domain, we focus in the discussion below on how to represent agent preferences.
There are many different ways to represent agent preferences. Perhaps the simplest is the ordinal graph, which
consists of nodes (each representing one possible agreement) connected by links that indicate that the source
contract is preferred, by the agent, to the target contract. Ordinal graphs are fully expressive (they can capture any
internally consistent set of preferences), and can handle cases where only partial preference information is available
(i.e. where some preference orders are not yet known), but they capture only ordinal preferences, providing no
information on how much one contract is preferred over another. Ordinal graphs also scale poorly; capturing the
preferences for a domain with 10 issues, 10 values per issue, would require a graph with 10 billion nodes.
If we wish to capture cardinal preferences (i.e. where we can specify how much an agent prefers one contract over
another), we move into the realm of utility functions. A utility function is defined, for each agent j, as
It assigns, to each possible agreement in the domain D = ∏ i = 1,...,n di, a real number representing the utility that
agreement yields for agent j. Note that cardinal preferences subsume ordinal preferences, since we can always derive
the preference order of two contracts by comparing their cardinal utility values.
The simplest form of cardinal utility function, and the one most widely used in the negotiation literature, is the
additive utility function (Raiffa, 1982) (Brafman and Domshlak, 2009). In such functions, an agent’s utility for a
contract is calculated as the weighted sum of the agent’s utility for each issue Xi:
Additive utility functions provide a compact preference representation, but they are unable to capture the important
phenomenon of preferential dependency, i.e., where the utility of the choice for one issue is dependent upon the
choices made for other issues. Preferential dependencies are ubiquitous in real-life negotiations. When we negotiate
over the stereo system we are going to purchase, for example, the utility of any particular issue value choice (e.g.
which tuner we select) depends fundamentally on the choices made for other issues (e.g. whether we selected
speakers that are compatible with that tuner). Utility functions without preferential dependencies always have a
simple linear structure, with a single optimum, while utility functions with preferential dependencies can have a
much more complex, nonlinear, structure, with multiple optima.
There is a range of utility function representations suited for dealing with preferential dependencies. Auction
preference languages (Boutilier and Hoos, 2001) (Cramton et al., 2006) capture preferential dependencies in the
context of allocation negotiations (i.e. where there are only binary issues, each representing whether an agent
acquires a particular good or not). The preference language expression:
for example, expresses the idea that the agent assigns a value of 50 to acquiring either goods a and b, or good c, and
it assigns a premium of 5 to the latter.
Utility graphs (Robu et al., 2005) capture allocation preferences as a set of nodes (each representing the issue of
whether or not a given good was purchased) in addition to a set of links between these nodes that capture the
(positive or negative) complementarities between the goods. In the utility graph in Figure 2, for example, there are
four goods as well as three dependency relationships.
Figure 2. An example utility graph, adopted from (Robu et al., 2005).
The utility of a given contract, to an agent, is given by the sum of the values for goods acquired, plus the sum of the
values for the complementarity links whose source and target goods were both acquired. In this graph, for example,
the contract [I1, I2, I3] (i.e. where the agent acquires the goods I1 I2 and I3) has the utility 5 + 3 + 4 + -3 +2 = 11.
Utility graphs only capture binary preference dependencies (i.e. dependencies between pairs, but not higher-order
tuples, of issues).
While allocation negotiations are of course very common, especially in e-commerce contexts, there are many real-
world negotiations with N-ary issues that concern more than just whether the agent acquires a given good, or not.
When engineers are negotiating over the design of a car, for example, many of the issues (e.g. What kind of engine
should we have? What kind of transmission? How many passengers should we make room for?) will have more than
two possible values.
CP-nets (Boutilier et al., 2004) capture preferential dependencies for N-ary issues using directed graphs in which
each node represents the agent’s preference for an issue, and each link captures the impact one issue choice has on
the preferences for another. In the CP-net example in Figure 3a, for example, there are three issues involved in a
vacation negotiation: season, location, and duration. The agent prefers Spring over Summer, Spain over Belgium,
and has preferences for duration that depend on the selected season and location:
I1 (5) I2 (3)
Figure 3a. An example of a CP-net.
CP-nets can be used with N-ary issues (i.e. where an issue can have more than just two possible values), and can be
used when we do not fully know an agent’s preferences, but they capture only ordinal, as opposed to cardinal, utility
information. Cardinal utilities can only be estimated, in this representation, by applying heuristics such as those
described in (Aydogan et al., 2011).
UCP-nets (Boutilier et al., 2001) address this challenge by including utility values, rather than simply preference
orderings, with each node in the network. In the UCP-net in Figure 3b, for example, the utility for the agreement
[Spring, Spain, 2 weeks] is 5 + 5 + .1 = 10.1:
Figure 3b. An example of a UCP-net.
K-additive utility functions (Grabisch, 1997) are a generalization of additive utility functions, where the utility of a
contract for an agent is the sum of the agent’s value for each issue choice plus the values due to the preferential
dependencies between two (or more) issues. The following example:
U(j) = U(<i1>,j) + U(<i2>,j) + U(<i1,i2>,j)
calculates the utility for agent j of a contract as the sum of the values of the choices for issues i1 and i2, plus the
value due to the dependency (synergistic or antagonistic) between those two issues. This approach can be applied to
preferential dependencies between any number of issues.
The weighted hypercube approach (Ito et al., 2008) represents a utility function as a collection of hypercubes that
each assigns a numeric weight to a sub-volume of the domain of possible contracts:
utility_function := (ufun <weighted_hypercube>*)
weighted_hypercube := (hypercube <weight> + <bound>*)
bound := (<issue> <min value> <max value>)
The utility for a given contract is then calculated as the sum of the weights for the hypercubes that include that
contract, which means the contract is within all the bounds the hypercube imposes to the different issues. Imagine
Location Spain > BelgiumSpring > Summer
Spring - Spain
Spring - Belgium
Summer - Spain
2 weeks > 1 week
1 week > 2 weeks
1 week > 2 weeks
2 weeks > 1 week
Spring - Spain
Spring - Belgium
Summer - Spain
1 week 2 weeks
we have a scenario with three issues, each of which can have a value between 1 and 20. Imagine, further, that the
utility function for an agent consists of the following weighted hypercubes:
(issue1 from 2 to 4)
(issue2 from 3 to 6) (issue3 from 12 to 17)
(issue1 from 1 to 5) (issue2 from 7 to 10) (issue3 from 10 to 12)
The contract [issue1 = 5, issue2 = 4, issue3 = 11] is included in the second and third hypercubes, so the utility of that
contract is 12 + 7 = 19. This representation is capable of representing any imaginable utility function with a discrete
domain; at worse, we simply need to create unit-volume hypervolumes for every contract in the domain.
We can summarize these different utility representations using the following table:
Additive utility functions
Auction preference languages
The most expressive utility representations are the three (in the lower right cell) which support N-ary issues, N-ary
dependencies, and cardinal utilities. These three representations are equivalent in terms of expressiveness, since they
are theoretically capable of representing any well-defined utility function for discrete issue domains.
We adopted, in our work, an extended version of the weighted hypercube representation, wherein the hypervolume
weights can be a constant, linear, or sine function of the issue values:
scenario := (scenario :name <string>
domain := (<def>*)
def := (issue <string> real from <number> to <number>) |
(issue <string> integer from <number> to <number>) |
(issue <string> one-of <string>*)
agent := (agent :name <string> :ufun ufun)
ufun : = ( <hypervolume>* )
hypervolume := (cube (<bound>*) <weight>) |
(plane (<bound>*) (<weight>*) <bias>) |
(sine (<bound>*) <height>) |
bound := (limit <string> from <number> to <number>) |
(limit <string> one-of <symbol>*)
This representation can capture any imaginable utility function for both discrete and continuous domains, since we
know that any waveform can be represented with arbitrary accuracy (using the Fourier transform) as the sum of sine
waves (Bracewell, 2000). Figure 4 presents two examples of utility functions (for a two-issue contract domain) that
can be generated using a weighted hypervolume approach.
Figure 4: Examples of utility functions expressed using weighted hypervolumes.
The utility functions have high regions where many high-weight hypervolumes reside, and lower regions where
there are few and/or low-weight hypervolumes.
3. Scenario Generation
How can we acquire the scenarios we need to test different negotiation protocols? One obvious approach is to
simply collect the scenarios that have been used in previous negotiation research and store them in our scenario
repository for general use (we describe how this can be done in section 6: “Repositories”). A key limitation with this
approach, however, is that there is a vast number of possible negotiation scenarios, and previous research has
necessarily only covered a tiny fraction of this space, predominantly scenarios without preferential dependencies.
We need, therefore, a way to cover the scenario space more comprehensively. This is the purpose of the scenario
generator. It allow users to generate negotiation scenarios by systematically varying a compact set of high-level
parameters, including (1) the negotiation domain, including the issues and possible issue values, (2) a scenario
utility histogram (see below), which defines the distribution of contracts in utility space, and (3) several structural
parameters that specify the topography (e.g. ruggedness) of each agent’s utility function. Our scenario generator
then creates, using a stochastic process, utility functions (sets of weighted hypervolumes) for each agent that satisfy
the user’s specifications. We describe this process in the sections below.
3.1. Specifying Scenario Utility Histograms
Utility histograms are a generalization of utility diagrams. The latter provide a simple way to visualize the possible
agreements between negotiating agents. In such diagrams, there is one axis for every negotiating agent, and one
point per possible agreement. The position of a point represents the utility of an agreement for each agent. In the
(two-agent) utility diagram in Figure 5a, for example, the y axis represents the utility of an agreement to agent A,
and the x axis represents the utility of an agreement to agent B. The Pareto front represents agreements that cannot
be improved upon for one agent without sacrificing utility for other agents. The optimality of any proposed
agreement can be assessed by measuring its distance from the Pareto front.
Figure 5a. An example of a scenario utility diagram.
The problem of scenario utility diagrams is that they do not capture the multiplicity of agreements. That is, if we
have, for instance, one thousand contracts which give the same utility values for the agents, they would be
represented in the diagram as a single point. This multiplicity, however, may be highly significant in negotiation.
For instance, the scenario utility diagram in Figure 5a may correspond to a negotiation scenario where 80% of the
contracts are within the Pareto front, or to an scenario where only 1% of the contracts are, both scenarios being quite
different in terms of potential impact on protocol performance. Taking this into account, we generalized scenario
utility diagrams into scenario utility histograms where each point in the diagram is assigned a number, representing
either the number of contracts in the domain which yield the corresponding utility values to the agents or the ratio of
contracts relative to the volume of the domain. The former can be used only with discrete domains, while the latter
can be used with both discrete and continuous domains. Figure 5b shows a utility histogram for two agents. For a
number of agents 𝑛!>2, we can represent the utility histogram as a set of 𝑛!+1-dimensional vectors, where the
first 𝑛! dimensions represent the utility values 𝑢! for every agent 𝑖, and the last dimension represents the number or
volume 𝑣 of contracts corresponding to these utility values. We can also use a functional notation 𝐻𝑢=𝑣 to refer
to the different points in the histogram.
Figure 5b. An example of a scenario utility histogram.
Specifying scenarios in terms of their utility histograms has two great advantages. One advantage is that it represents
an excellent way, as we shall see, of manipulating important properties of the scenario. We can specify, for example,
whether the negotiation is highly competitive (the Pareto front is flat or even concave) or not, what proportion of the
contracts are close to the Pareto front (making a good contract easier to find), and so on. The other advantage of this
approach is that the Pareto fronts for our scenarios are known up-front, making it easy to get an exact value for the
optimality of the agreements negotiated for that scenario. Negotiation researchers typically start by defining utility
functions for the individual agents, and then estimating the Pareto fronts using an optimization approach such as
genetic algorithms. If the contract space is large, and there are preferential dependencies (which as we’ve noted
create multi-optima utility functions) then the Pareto front estimate may be quite inaccurate. Our approach obviates
this whole problem by deriving the agent utilities from the Pareto front itself, as opposed to the other way around.
Agent 1 Utility
Agent 2 Utility
Agent 1 Utility
Agent 2 Utility
Our scenario generator provides a simple way for users to specify scenario utility histograms, based on a small set of
high-level parameters. The user first defines the Pareto front shape as a set of weighted hyper-spheres, each which
we can define as follows:
where na is the number of negotiating agents, ui is the utility obtained by agent i and
i is a weighting parameter
which allows to control the shape of the Pareto front. In particular, as seen in Figure 6 (a) to (c), giving the same
weights to all agent (that is, ∝𝒊=∝𝒋∀𝒊,𝒋) allows to control the concavity or convexity of the Pareto front, and thus
the competitiveness of the scenario (see Section 4). Note that we can theoretically model all ranges of
competitiveness, including the zero-sum game (∝𝒊=𝟎.𝟓∀𝒊).
(a) ∝!=0.5∀𝑖 (b) ∝!=1∀𝑖
(c) ∝!=0.25∀𝑖 (d) ∝!=2;∝!=0.25
Figure 6: Pareto fronts generated as 2-dimension weighted hyper-spheres.
In a similar way, as shown in Figure 6 (d), giving different weights to different agents allows us to adjust the
symmetry of the Pareto front, thus varying the symmetry of the scenario. In particular, the different weights given to
the utilities of the agents may be seen as modeling their bargaining power, as suggested in (Ley, 2006). More
complex Pareto fronts may be obtained by aggregating different weighted hyper-spheres, though in these cases the
absence of non-dominant points in the resulting front cannot be assured, so residual points need to be removed after
generation. Figure 7 shows an example of such a Pareto front. The figures show continuous Pareto Fronts, though
our generator uses discrete utility histograms for scenario generation. To discretize the Pareto fronts, the points have
been generated uniformly throughout the hyper-sphere, using a generalization of the method in (Lai et al., 2004)
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
Figure 7: A complex Pareto front generated using two weighted hyper-spheres.
Once we have generated the Pareto fronts, we need to generate the rest of the points in the scenario utility histogram.
To do this, we apply different probability distributions to a generalization of the Marsaglia algorithm (Marsaglia,
1972). Figure 8 shows the results of using a uniform and two normal distributions (one centered at the origin and the
other at the Pareto front). We can see that varying the distribution used allows us, for instance, to study the effect of
different utility or social welfare centroids on the negotiations, or the impact of having a high or low density of
points near the Pareto front.
Figure 8: Scenario utility histograms for the same Pareto front, using probability distributions that are (a) uniform, (b) favor
points away from the Pareto front, and (c) favor points near the Pareto front.
3.2. Specifying Agent Utility Functions
Once the utility histogram has been defined for a scenario, our scenario generator can then define the utility function
for the individual agents. Our algorithm does so using shared hypervolumes. The idea is to include similar
hypervolumes (that is, hypervolumes involving the same contracts but with different shapes) in the utility functions
of the different agents, adjusting the parameters of the hypervolumes so that they generate appropriate points within
the scenario utility histogram. For instance, if we want to generate utility functions for a trivial scenario utility
histogram 𝐻𝑢 for two agents, where the histogram value is 𝑣 for 𝑢=𝑎,𝑏 and 0 otherwise, we could achieve
this by generating two utility functions which share a hypercube of volume v, with weight a for the first agent and
weight b for the second. Figure 9 shows another simple example for two agents and two integer issues whose values
may take values ranging from 1 to 10. In this case, the utility histogram (shown in Figure 9a) includes four points, as
• Two pareto-dominant points: 𝐻1,0.6=16 and 𝐻0.5,1=18.
• A non-dominant, nonzero utility point: 𝐻0,25,0.5=29.
• A point representing the rest of the contracts, which yield zero utility for both agents: 𝐻0,0=37.
The generation algorithm must find a set of hypervolumes which satisfy the volume values imposed by the diagram.
In our example, this can be achieved using the three hypervolumes shown in Figure 9b and 9c. Hypervolumes C1
and C2 create an intersection 𝐶1𝐶2!of 3 by 6 (18 contracts), while the union 𝐶1𝐶2 encompasses 63 contracts,
leaving 37 contracts unassigned (that is, with zero utility). Finally 𝐶3 has 4 by 4 (16) contracts, and the area within
𝐶1𝐶2 which is not inside 𝐶1𝐶2 or inside 𝐶3 encompasses a total of 29 contracts. Once the hypervolumes have
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
been found, the algorithm assigns the appropriate weights to the hypervolumes in the utility function of every agent
so that the utility values in the histogram are satisfied. In our example, this is achieved with the weights shown in
Figure 9b and Figure 9c. The resulting utility functions are shown together in Figure 9d.
(a) Utility histogram (b) Agent 2 weighted hypervolumes
(c) Agent 1 weighted hypervolumes (d) Resulting Utility Functions
Figure 9: Example of scenario generation from utility histograms.
Of course, as the number of points in the utility diagram increase, the complexity of the generation process also
increases, since we have to take into account the effect of the intersection between shared hypervolumes. A first
approximation to avoid this problem is to divide the utility space in non-overlapping regions and to assign shared
hypervolumes (one for each agent) to each region, with the utility values needed to match the points in the scenario
utility diagram. The problem here is that, depending on the shape of the hypervolumes we are using, the resulting
scenario utility histogram may differ from the original (e.g. a bell-shaped hypervolume adds more points to the
histogram apart from the one corresponding to its peak value). A solution to this problem may be to feed this first
approximation of the scenario utility histogram to a nonlinear optimizer which tries to minimize the approximation
error. However, the computational cost of running that kind of optimizer for large cardinality contract spaces makes
it unfeasible. Other alternatives are to use hypervolumes that do not introduce approximation error (i.e.
hypervolumes with a constant weight), or simply accept that there will be some approximation error. As long as the
hypervolumes do not overlap, the approximation error will never affect the shape of the Pareto front.
A second downside of the non-overlapping hypervolumes approach is that the utility function representation is not
very compact, since it will have at least one hypervolume per point in the utility histogram. In some cases, this can
be solved by using compression techniques to convert from non-overlapping hypervolumes to overlapping ones (this
works relatively well with hypercubes). However, since the purpose of the generator is not to allow for compact
utility representation, but to provide a consistent comparison of negotiation scenarios, we believe succinctness of the
0 0.2 0.4 0.6 0.8 1
Agent 1 Utility
Agent 2 Utility
0 2 4 6 8 10
0 2 4 6 8 10
representation is not an issue at this point. Furthermore, the use of shared, non-overlapping hypervolumes has some
advantages for the computation of scenario and utility function metrics, so this is the approach we finally adopted.
This simplified algorithm works as follows:
1. For each utility histogram point 𝐻𝑢=𝑣, where 𝑢=𝑢!𝑖=1…𝑛! and at least one 𝑢! is nonzero, we
partition the associated volume 𝑣 into a set of region volumes 𝑣
! such that 𝑣
!!=𝑣, according to the
desired structural properties (see Section 4). For instance, if we want utility functions with low correlation
length, the partition will involve small region volumes.
2. We map each region volume 𝑣
! to a particular hypercube region in the contract space which has the
appropriate volume and does not overlap any previously allocated region. In this way, we guarantee our
hypervolumes do not intersect. Again, the shape of the hypercube may be altered to satisfy desired
structural properties. For instance, if we want asymmetric epistatic interactions, the hypercubes should be
wider in some dimensions than in others.
3. We include the generated hypercube in the utility function of each agent 𝑖, assigning to it a weight equal to
the corresponding utility value associated to that agent in 𝑢, 𝑢!.
4. The algorithm progresses until all volume has been allocated.
An important property of this scenario generation strategy is that the shape and parameters of the shared
hypervolumes may be varied so that additional properties of the generated functions are satisfied. Figure 10 shows
an example for two agents and weighted hypercubes, where we have generated two scenarios with identical utility
histograms and different correlation lengths. The type of hypervolumes or the aggregation operators used may be
adjusted as well, but in these cases we have to take into account the effect that changes may have on the resulting
scenario utility histogram.
(a) ψ0.7 = 5.9
(b) scenario utility histogram
(c) ψ0.7 = 1.7
Figure 10: Utility functions from the same utility histogram but with different correlation lengths.
4. Metrics Calculation
In this section we discuss the metrics we have developed to capture the “key properties” of negotiation scenarios, i.e.
those that help predict which protocol(s) will work best for which scenarios. Our metrics are divided into three
categories: (1) structural metrics, which capture properties of the individual agents’ utility functions, (2) relational
metrics, which capture how the negotiating agents’ utilities relate to each other, and (3) contextual metrics, which
capture properties of the context in which the negotiations occurs. We describe these metrics in the sections below.
4.1. Structural Metrics
Our structural metrics attempt to capture how difficult it is to find high-utility contracts in a given agent’s utility
function. Many such metrics have been defined in such fields as artificial intelligence, operations research, and
evolutionary computing (Vassilev et al., 2003).
Perhaps the simplest metric is based on the skew of agent’s individual utility histograms. Consider two histograms
in Figure 11, giving the number of contracts at each utility value within a given agent’s utility function.
Figure 11. Agent utility histograms with differing skews.
The utility function whose histogram is shown on the left is probably harder to optimize because most of its
contracts have a relatively low utility, while the one of the right is probably easier to optimize.
Another metric is modality variance, which measures the variance in the heights of the local optima in the utility
function. In Figure 12, for example, the modality variance is low in the utility function on the left, and higher in the
utility function on the right:
Figure 12. Agent utility functions with different modality variances.
The intuition behind this metric is that, if the modality variance is zero, an agent can simply hill-climb from any
random point to find an optimal contract, since every local optimum is also globally optimal. As the modality
variance increases, agents are increasingly likely to get stuck in poor local optima.
Our ruggedness metric assesses how “bumpy” a utility function is, and therefore how many local optima a search
algorithm is likely to encounter when looking for the global optimum. Ruggedness can be assessed using fitness
distance correlation (FDC) (Tomassini et al., 2005) (Jones and Forrest, 1995), which measures the correlation
between the utility of a contract and it’s Euclidean distance, in the contract space, from the global optimum. If there
is a strong correlation between distance and utility, this implies a smooth utility function. If the correlation is weak,
this implies a rugged utility function with many “bumps” along the way. Consider the examples in Figure 13:
(a) FDC =-1.0
(b) FDC = -0.61
Figure 13. Agent utility functions with different FDC values.
The top charts in the figure show two different utility functions in a single-issue contract domain, and the bottom
charts show utility as a function of a contracts’ distance from the globally optimal contract. The left utility function
is smooth, and shows a strong correlation between utility and distance (a high FDC). The right utility function is
more rugged, and has a correspondingly lower FDC value. The lower the FDC (in absolute value), the more local
optima exist and the more difficult it will probably be to find the global optimum. A related metric is the correlation
length (AKA correlation distance) which is defined as the minimum contract space distance which makes the utility
correlation between contracts pairs fall below a given threshold (usually 0.5) (Lopez-Carmona et al., 2011) (Marsa-
Maestre et al., 2012).
Our information content metric takes a different tack, assessing the information content of the utility space based on
the intuition that the higher the information content of a utility function, the more difficult it will be to perform a
search in that utility space. The extreme cases would be a totally flat utility space (minimum information content, a
single sample gives information about all the space) and a totally random utility space (maximum information
content). Finding an optimal contract in a random utility space would of course be much harder, because you can’t
use slope information to guide your search at all. Information content can be assessed by measuring high-frequency
components of the utility functions, for instance by using a n-dimensional Fast Fourier Transform (FFT) (Bracewell,
2000). For solution spaces which are too large to allow for comprehensive sampling, we can use random walk
entropy measurements, where a random walk is performed throughout the utility space, and the entropy of the
utilities of the contracts in the walk is measured.
Other metrics assess how effective optimizers are at locating global maximums in the utility functions. One example
is the hill-climbing success ratio, which measures how often a hill-climbing optimizer can find optimal contracts
within an agent’s utility function. The minimum annealing temperature metric is a variant that assesses the
minimum starting temperature needed for simulated annealing-based optimizer (Kirkpatrick et al., 1983) to achieve
a given success ratio. The higher the temperature needed, the more rugged and challenging the utility function.
A final metric assesses the degree of preferential interdependency. Utility functions with preferential dependencies
create multi-optimum topographies that are typically much harder to optimize than those involving independent
issues (Klein et al., 2003). Preferential dependency can be assessed using an information-theoretic measure known
as epistasis (Ventresca and Ombuki-Berman, 2007), originally developed in the context of genetic biology. It is
defined as follows::
where I(i;U) and I(j;U) are the amount of information that each issue i and j reveals about the value of the utility
function U, and I(i,j;U) is the amount of information both issues reveal about the value of U. An alternative
0" 5" 10" 15" 20"
0" 5" 10" 15" 20"
technique to assess interdependency relationships between issues is to perform a Walsh analysis of the utility
function (Heckendorn and Whitley, 1999).
Structural measures can be less meaningful in anisotropic utility functions where there are significant local
variations in geography (e.g. where the utility function is smooth in some regions, and rugged in others) (Stadler and
Gruner, 1993) (Greenwood and Hu, 1998). In this situation, we can calculate these measures separately for different
regions of the space, using local optimum for example to delineate the centroids for the different regions.
4.2. Relational Metrics
We have also defined a set of metrics that assess relationships between the utility functions of the agents involved in
a negotiation. Relational metrics capture important properties that are not obvious from examining any one agent’s
utility function. We may have, for instance, scenarios where agents have highly rugged utility functions that make it
difficult for them to determine their own high utility regions, but where once these regions have been found
agreements are fairly straightforward, because high utility regions for the different agents coincide. On the other
hand, we may have scenarios where the agents have smooth easy-to-optimize utility functions, but where mutually
acceptable regions are nevertheless hard to find.
It should be noted that relational metrics will be especially critical in domains with strong preferential dependencies.
When there are no preferential dependencies, utility diagrams have simple symmetric structures, with convex Pareto
fronts, and differ mainly in whether the agent utility functions are have strongly negative (zero-sum) correlations,
strongly positively (win-win) correlations, or something in between (see Figure 14).
Figure 14. Typical utility diagrams for zero-sum, win-win, and uncorrelated scenarios with no preferential dependencies.
In this context, many of our relational metrics will do little to distinguish between negotiation scenarios. This picture
changes completely, however, when we consider “nonlinear” utility functions with strong preferential dependencies.
As we can see (figure 15), when preferential dependencies are introduced, the utility diagrams can become much
more complex and diverse, with non-symmetric structures and concave Pareto fronts, and capturing key dimensions
of variation between such scenarios requires a richer set of metrics.
Agent 1 Utility
Agent 2 Ut
Agent 1 Utility
Agent 2 Utility
ent 1 Utilit
Agent 2 Utility
Figure 15. Utility diagrams for scenarios with strong preferential dependencies1.
Our goodness metrics assesses the proportion of high-utility agreements in the contract domain. This includes the
ratio of high-social-welfare contracts (which measures what fraction of the contracts have top-quartile social
welfare), the ratio of mutually-acceptable contracts (which measures what fraction of the contracts lie above the
reservation values for the agents) and the ratio of Pareto-efficient contracts (which measures what fraction of the
contracts are within a distance 𝜖 of the pareto front). A scenario where these ratios are small will probably be more
challenging for a negotiation protocol.
Our symmetry metric assesses the symmetry of the utility histogram across the equal utility line. Some scenarios
may be inherently asymmetric, in the sense that there may be few or no contracts that offer equally high utility
values for all the negotiating agents. Scenarios with a low symmetry metric will be more challenging if we want our
protocol to find a fair agreement, where fairness can be defined for example as in (Fujita et al., 2010). We compute
symmetry by adding up, for every agent, the distances of possible contracts from the equal utility line. The standard
deviation of these sums gives an idea of how much an scenario favors some agents against others.
Our competitiveness metric captures the extent to which a scenario is win-win, or win-lose, for the agents involved.
We calculate this by finding the average fairness for contracts that have high social welfare (and thus are more apt to
include the final agreement). Intuitively, a scenario where most such contracts are highly unfair is more competitive
than those where most such contracts are fair. A scenario with a highly convex Pareto front (where the highest social
welfare contracts are very unfair) is, by this definition, more competitive than one with a highly concave Pareto
front (where the highest social welfare contracts are good for all the agents involved).
Our correlation metric measures the correlation between the utility functions for different agents. Scenarios with
high correlation values will presumably be easier for a protocol seeking win-win agreements.
Our locality metric measures the correlation between the distance of contracts in the solution and utility spaces,
which is likely to have a strong impact on the suitability of similarity-based protocols.
Our basin metrics, finally, checks for the presence and size of basins of mutual gain (regions in the contract space
where agents may find dominant directions for increasing mutual gain), which favors hill-climbing protocols.
Our relational metrics involve calculating some function of the utility values for all the contracts in the contract
space. This can be computationally impractical, of course, if the contract domain is too large. In this case, we can
calculate these values for a representative (e.g. random) sample of the contracts in the domain. It is also
straightforward to calculate these metrics from the utility histogram for a scenario, so we can get exact metrics
values for scenarios created by our scenario generator.
4.3. Contextual Metrics
This set of metrics is used to assess the potential impact of a negotiation scenario’s context. We have focused, in our
work so far, on metrics to assess predictability, i.e. how well agents can anticipate what will happen in their current
negotiation based on the context of previous, similar, negotiations. The notion of negotiation predictability was first
introduced in (Hindriks et al., 2007) and later extended in (Hindriks et al., 2011). Predictability is important because
it helps negotiating agents make offers that will be appreciated by the opponent, as well as develop strategies that
bring the highest utility to the negotiator. For the first we introduce the notion of preference profile predictability
and for the latter we introduce bidding strategy predictability.
4.3.1 Preference profile predictability
A preference profile reflects which issues are important to the negotiator, which values per issue are preferred over
other values, whether or not there are dependencies between issues, and as a whole provides a (partial) ranking over
all possible agreements. Being able to (partly) predict the preference profile of the other negotiators makes it easier
to make an offer that the other party can accept, and increases the possibility of reaching a good negotiation outcome
more quickly (Zeng and Sycara, 1997) (Faratin et al., 2000). The general question we help to answer is, given a
1 In both cases, the utility functions were generated as the sum of a bell-shaped weighted hypervolumes.
negotiation domain and the negotiators, to what extent is the preference profile of a negotiator predictable? This
question can be broken down into several sub-questions (Hindriks et al., 2007) that we can define as follows:
• Role predictability. Role predictability refers to the existence of typical negotiation roles. For example, in
many domains (e.g., markets) there are sellers versus buyers, in job contract negotiations there are
applicants and hiring managers. With a role comes information about the preference profile of the agent
playing that role. For example, if the negotiation domain is about selling something, then there is typically
an issue price, and it is predictable that sellers prefer higher prices, and buyer prefer lower ones.
• Issue predictability. An issue is called predictable if we can predict negotiators’ preference profile (or some
global properties thereof) for an issue. For example, in a negotiation for a supercomputer, the issue of the
number of Teraflops and the issue of the number of Petabytes are predictable: the buyer would prefer more
of both. When negotiating with friends about an upcoming holiday, typical issues are location, duration,
start date, way of travelling, and price. Of these issues only price is predictable without knowing anything
more about the people involved.
• Issue weight predictability. Issue weight predictability refers to predicting the importance of an issue in a
negotiation, in absolute or relative terms. (Jonker and Robu, 2004) showed that knowing what the most
important issue is to the opponent can produce significant improvements in the outcome of the negotiation.
• Dependency predictability. This refers to the question of whether it is reasonable to expect that a
negotiating agent will have a dependency between some issues. For example, in a negotiation about a car,
the price depends on most other issues, such as the age, the motor, size, and which accessories will be put
in the car. Although a buyer would always prefer low price, he can adjust his reservation value for the price
with respect to those issues. He may be willing to pay more for a new model while he would be reluctant to
pay the same amount for an old model. Thus, predicting such interdependencies may help a negotiating
agent generate appropriate offers. The same can be said for predicting preferential dependencies.
• Domain predictability. This refers to how many predictable issues there are in a given negotiation, and how
much we can predict about the importance of those issues. Domain predictability is important in research
into bidding strategies (Baarslag et al., 2010) (Hindriks et al., 2011).
Preference profile predictability, or one of the related notions of predictability can be established in various ways.
Domains can be studied using conceptual analysis. For a negotiation on computing power, a conceptual analysis will
reveal that the number of computing nodes and memory nodes has an effect on the electricity consumption and the
cooling required for the nodes (which in turn requires additional electricity). Similarly, conceptual analysis of
negotiations on a purchase reveals that role predictability (buyer-seller), issue predictability (price is preferred to be
higher by the seller and lower by the buyer), and issue weight predictability (price is typically an important issue).
Conceptual analysis can also reveal issue predictability for issues that are in arbitrary domains not predictable. For
example, someone buying clothes for a wildlife observation tour will prefer colours that fit in with nature. So
understanding the underlying concerns of the negotiation helps. In other cases observing your opponent during the
negotiation, or just knowing your opponent better might help. For example, the colours the other negotiator picked
for e.g., clothing or home decoration, might make the issue of colour predictable.
Statistical analysis and data mining are techniques that can be applied on a set of preferences of a multitude of
people for a comparable issue or domain to extract a preference profile prediction (or part thereof). For example,
although colour is in general not predictable, an analysis of the car domain shows that in 2007 (see
http://www.cars.com), white was the most popular colour in North America, making up 19% of all vehicles. Silver,
black, red and grey rounded out the top five.
Various machine learning techniques are used for opponent modelling, for example, to gain more information on the
zone of agreement (Zeng and Sycara, 1997) or on the shape of the evaluation functions per issue (Hindriks et al.,
The grounds for drawing a conclusion about preference profile predictability can be economic rationality, surveys
over a large enough set of people, or an emergent pattern in a set of preference profiles for that issue or for that
domain, or in the subsequent bids made by the opponent.
4.3.2 Strategy predictability
Being able to predict the behavior of the other party enables anticipation on that behavior, see e.g., (Ji and Leung,
2010). The results of the Automated Negotiating Agent Competition (ANAC), see (Baarslag et al., 2010), show
which bidding strategies perform best against which other bidding strategy. This knowledge will probably soon be
used to create negotiation strategies that will adapt to the current strategy used by the opponent.
An opponent’s strategy is called predictable, if on the basis of earlier encounters or a personality/experience profile,
the opponents strategy can be characterized in terms of some global style, such as the negotiation styles of (Shell,
2006) (Thompson, 2011), or a known conflict-handling style, as the one shown in Figure 16 (Kilmann and Thomas,
1977) (Pruitt, 1986).
Figure 16 – The Thomas-Kilmann Conflict Mode Instrument
5. Protocol Testbed
The purpose of the protocol testbed is to allow researchers to assess how well their protocols work in different
negotiation scenarios. Our testbed is called GENIUS (General Environment for Negotiation with Intelligent multi-
purpose Usage Simulation) (Lin et al., 2012) (Baarslag et al., 2012). A user begins by specifying the experiment
they want to run, selecting the scenario (domain and utility functions), protocol, and negotiating agents (Figure 17):
Figure 17: GENIUS: negotiation simulation setup interface
Once the setup is complete, GENIUS can simulate the negotiation, deriving such statistics as the current utility
values for each agent, the product of the agent utilities, and so on (figure 18):
Figure 18.. Overview of a negotiation as it progresses over multiple rounds
The experiment results for different combinations of scenarios and protocols can then be compared with each other.
GENIUS has focused, to date, on bilateral alternating offer protocols and linear additive utility functions, and in this
form has been used to support the Automated Negotiating Agents Competitions (http://mmi.tudelft.nl/anac).
The final component of the Negotiation Handbook are the repositories for scenarios as well as for experimental data
concerning the performance of different protocols in these scenarios. At present we have two, complimentary,
systems that serve this function. GENIUS, as noted above, includes repositories for scenarios and experiment data,
but has focused to date on linear utility functions. The second system, a web-based tool called Negowiki, has focused
on capturing scenarios and experimental results for nonlinear cases. Negowiki supports:
• Downloading negotiation scenario. Users can search the Negowiki scenario repository for scenarios with
desired properties and download them in an XML format that instantiates the weighted hypervolume
formalism described in section 2. The repository currently includes a range of scenarios drawn from the
research literature, including (Faratin et al., 2000) (Klein et al., 2003) (Ito et al., 2008) (Lopez-Carmona et
al., 2011). Users can search for scenarios based on their properties (figure 19):
Figure 19. The Negowiki scenario selection interface.
Every scenario includes a description of the rationale behind it, as well as the values for the scenario
metrics as described in section 4 (figure 20):
Figure 20. An example of a Negowiki scenario description.
Users can also download function libraries (currently available in Matlab and Common Lisp) that calculate
the utility of a given contract for a given scenario, making it straightforward for a research group to use the
scenarios in their protocol evaluation experiments.
• Uploading negotiation scenario for analysis. Users can upload their scenarios to the Negowiki repository
using the scenario formalism described in section 2. When uploaded, the website computes and displays the
metrics values for that scenario. Users can archive these scenarios into the repository so they are available
for use by other researchers.
• Uploading negotiation results data for analysis. If users perform experiments with protocols from the
literature or with their own protocols using any of the Negowiki scenarios, they can upload their
negotiation results into Negowiki for analysis. When uploaded, the website computes a range of negotiation
outcome metrics (such as individual agent utility, social welfare, fairness, distance from the Pareto front)
and shows them to the user. The Negowiki team has devoted substantial effort to ensuring that the site
calculates accurate outcome metrics for negotiation experiment results. It is important to note that
calculating some outcome measures can be very different in nonlinear scenarios. Traditional solution
concepts such as the Nash product, for example, can become very misleading in such contexts (Fujita et al.,
2010). Users can archive their experimental results in the repository to make them available to the
community, and can search this repository for insights into which best protocols are best for solving the
negotiation problem at hand, as well as for inspiration on how to design better protocols.
For more information about Negowiki, go to http://negowiki.mit.edu/.
7. Contributions and Future Work
One of the key challenges in automated negotiation research is that it has been difficult to come up with a systematic
picture of which negotiation protocols work best for which problems, due to the diverging scenarios considered by
the different research groups. In this paper we have described an infrastructure that aims to fill this gap. This
• A tool for generating negotiation scenarios, based on the aggregation of hypervolumes to generate utility
functions, and on the use of shared hypervolumes and nonlinear regression to generate negotiation
scenarios from utility histograms. To our knowledge, despite it’s obvious advantages, no authors have
previously tried to generate negotiation scenarios from utility diagrams.
• A set of metrics to measure high-level scenario parameters, taking into account both the structural
properties of the agent utility functions, the relationships between the utility functions of the different
agents, and the context in which the negotiation occurs.
• A testbed that allows researchers to evaluate how well their protocols work on different scenarios.
• Community repositories that allow the research community to share scenarios and experiment results and
thereby carry on a much more cumulative and systematic exploration of the critical question of which
protocols work best for which negotiation problems.
While our approach has been designed to be as general as possible, it does face one inherent limitation. Our scenario
representation will not work for domains where it is impractical to capture the entire utility function up front.
Imagine, for example, that agents are negotiating over the placement of pieces on a chess board. There is an
astronomical number of possible “contracts” (i.e. chess board configurations). It would require an enormous amount
of time to calculate the utility values for every possible contract, and an impractically large number of hypervolumes
to capture this information. To handle this case, we would need to adopt a scenario representation which represents
the algorithms used to calculate the utility functions (so contract utilities can be calculated as needed) rather than the
utility functions themselves. This is a possible direction for future work.
Our more immediate efforts will involve extending our infrastructure. This will include work on:
• Scenario generation: we plan to extend the scenario generator to allow more comprehensive control over
other potentially important scenario properties, such as epistasis, fractal statistics in the utility functions
(Da Cruz, 1999), and so on.
• Metrics: our current set of scenario metrics, while promising, are preliminary and will no doubt have to
refined and extended as we develop a better understanding of which scenario properties most deeply impact
the performance of different protocols.
• Testbed: currently, the GENIUS testbed environment only supports linear additive utility functions and
bilateral protocols. We are extending the GENIUS testbed to support our weighted-hypervolume scenario
representation and to enable multilateral negotiations.
• Repositories: We will continue to populate the scenario repository with examples from the research
literature and from our scenario generator. A critical part of this will be developing a scenario taxonomy,
i.e. a systematic enumeration of all the important distinct classes of negotiation scenarios, so we can try to
assure that the scenario repository has a comprehensive collection of test cases.
• Experiments: we will perform comprehensive comparisons of negotiation performance for different
protocol and scenario combinations. We are creating a taxonomic representation of known negotiation
protocols, based on ideas developed in the Process Handbook project (Klein et al. 2006)., which will allow
us to systematically explore the space of protocol variants by a recombination process. Since the space of
possible scenarios and protocols is very large, so we will need to develop heuristics for focusing our search
on scenario-protocol pairs that are apt to be important for real-world challenges.
• Data mining: we will explore the experiment data repositories generated by these experiments to develop
keener insights into the determinants and patterns of protocol performance.
• Community development: we will work to enable a vibrant community process, building on the
infrastructure we have developed, wherein researchers share scenarios, protocols, and experiment results,
all in the service of creating a Negotiation Handbook that can substantially impact how well humanity is
able to solve its complex and critical negotiation challenges.
This work has been supported by: the ITEA-2 project 2008005, ”Do-it-Yourself Smart Experiences”; the Spanish
Ministry of Education and Science grants TIN2008-06739-C04-04 (project T2C2) and JC-2010-035 (mobility
grant); the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of
the Ministry of Economic Affairs; the Pocket Negotiator project with grant number VICI-project 08075; the US
National Science Foundation; the New Governance Models for Next Generation Infrastructures project, NGI grant
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