VI. RELATED WORK
Glass and Grosz [20] developed a measure of social consciousness
called “brownie points” (BP). The agent earns BP
each time it chooses not to default a group task and loses BP
when it does default for a better outside offer. The default
of a group task may cause the agent to receive group tasks
with less value in the future, hence reducing its long term
utility. The agent counts BP as part of it overall utility beside
the monetary utility. A parameter BP weight can be adjusted
to create agents with varying levels of social consciousness.
This relates to our utility mapping function associated with
the relational MQ which can be adjusted to reflect the agent’s
different attitude in negotiation. However, the relational MQ
is agent-oriented and issue specific, so the agent can model
different attitudes towards each agent and negotiation issue.
Additionally, the mapping function can be a nonlinear function
and describe a more complicated attitude. Their work assumes
there is a central mechanism controlling the assignment of
group tasks according to agent’s rank (agent’s previous default
behavior), which is not always appropriated for an open
agent environment. Instead, in our assumption, agents are all
independent and there is no central control in the society.
Axelrod [21] has shown stable cooperative behavior can
arise when self-interested agents adopt a reciprocating attitude
toward each other. The agent cooperates with another agent
who has cooperated with it in previous interactions. The idea
of the reciprocity is related to our work if the relational
MQ is used bi-directionally between agents, agent A collect
some relational MQ from agent B and in the future the
accumulated relational MQ could be used to ask agent B
do some work for it, in this way, the relational MQ actually
works as a quantitative measure of reciprocity. Sen developed
a probabilistic reciprocity mechanism [14] in which the agent
K chooses to help agent J with certain probability p and p is
calculated based on the extra cost of this cooperation behavior
and how much effort it owes agent J because agent J has
helped it before. There are two parameters in the formula
11
for calculating p which can be adjusted so that the agent
can choose a specific cooperation level. However, this work
assumes that cooperation always leads to aggregate gains for
the group, and it was based on a known cost function - that
is, they know how much extra it will cost them to do X for
another agent. Neither of these two assumptions are necessary
in our work. Also our work deals with more complex and
realistic domains where tasks have real-time constraints and
there are potentially complex interrelationships among tasks
distributed across different agents.
Our experimental work has shown that even in a cooperative
system it may not be the best for the social welfare to have
agents be completely externally-directed. Similar result is also
shown in [22], which uses a distributed constraint satisfaction
model that is much different from the underlying model in this
work. Vidal [23] has also studied the teaming and selflessness
when using multi-agent search to solve task-oriented problems.
His study also shows the fact that neither absolute selfishness
nor absolute selflessness result in better allocations, and the
fact that the formation of small teams usually leads to better
allocations. This work explores a similar issue as in our work,
however, it is in a relatively simplified domain and there
is no complex interaction among agents. Other related work
includes the cooperative negotiation work on task allocation
[24], where the agents use the marginal utility gain and
marginal utility cost to evaluate if it worth to accept a task
contract in order to increase the global utility. However in this
work, the agent acts as in a “completely-cooperative” mode
and there is no choice on how cooperative it wants to be.
This paper is an extended version of [25]. Compared with
the conference paper, this extended paper has the following
improvements. In this paper, we introduce two new concepts
“self-directed” and “externally-directed”, which are different
from “self-interested” and “cooperative”. This paper provides
a more complete description of the MQ framework. This
paper also includes more experimental result. We performed
additional experiments using different parameters, the results
show that the best policy depends on the environmental context
such as the outside offer, so it is important to have agents to
dynamically choose the level of cooperation.
VII. CONCLUSION AND FUTURE WORK
We introduce an integrative negotiation mechanism that
enables agents to interact over a spectrum of negotiation attitudes
from completely self-directed to completely externallydirected
in a uniform reasoning framework, namely the MQ
framework. The agent can not only choose to be self-directed
or externally-directed, but also can choose how externallydirected
it wants to be. This provides the agent with the
capability to dynamically adjust its negotiation attitude in a
complex agent society. Introducing this mechanism in the
agent framework also strengthens the capability of multiagent
systems to model human societies. Multi-agent systems
are important tools for developing and analyzing models and
theories of interactivity in human societies. There are many
complicated organizational relationships in human society,
and every person plays a number of different roles and
is involved in different organizations. A multi-agent system
with this integrative negotiation mechanism is an ideal testbed
to model human society and to study negotiation and
organization theories. Experimental work shows it may not be
a good idea to always be completely externally-directed in a
situation involving an unknown agent’s assistance; in that case,
choosing to be partially externally-directed may be appropriate
for both the individual agent and also for the society.
We recognize that the experimental results are scenario
specific and they do not answer the question about how
externally-directed an agent should be in a given situation.
In [15], we presented an analytical model of the environment
that enables the agent to predict the influence of its negotiation
attitude on its own performance and also on the social welfare,
hence to select the appropriate level of cooperation to balance
its own utility achievement and the social welfare. We plan to
develop learning techniques that enable an agent to learn from
its previous interactions with other agents about how to adjust
its negotiation attitude parameter.