Page 261 - Socially Intelligent Agents Creating Relationships with Computers and Robots

244 Socially Intelligent Agents

The unbounded formulation of such an economical problem has long been
the central concern of classic game theory which has produced a number of
models of social choice. For this reason game theory models have become
strong candidates for models of social agents. Surprisingly, such apparently
simple games can be used to conceptualize a variety of synthetic, meaningful
and formal prototypical context as games. Therefore, such models can be used
to design and engineer multi-agent systems as well as analyze the behaviour of
the resulting social artifact using the logical tools of the models. However, the
underlying unbounded assumptions of classic game theory is problematic for
the design of computational systems [2].
Artificial Intelligence (AI) on the other hand has long considered models of
the relationship between knowledge, computation and the quality of solution
(henceforth referred to as the K-C-Q relationship) [7]. AI has shown that there
exists a hierarchy of tradeoffs between K, C and Q, with models that achieve
perfect optimal results (like game theory models) but at the cost of requiring
omniscience and unbounded agents, to models that sacrifice optimality of Q
for a more realistic set of requirements over K and C [12]. Different agent
architectures are then entailed from different K-C-Q relationship theories.
In the next two sections two such computational models of negotiation are
proposed, one deductive and the other agent-based simulation, that can be an-
alyzed as two different games. The aim of these models has been to attempt to
address some of the computational and knowledge problems mentioned above.
In particular, in the first model the types of problems of interest is when K is
limited because agents have at best imperfect and at worst no knowledge of the
others’ utility functions. The best an agent can do is to reason with imperfect
knowledge by forming approximations of others’ utilities. In the second model
the knowledge problem is even more extensive because agents in addition are
assumed to have an incomplete knowledge of their own utility functions.

2. A Bargaining Game
In this model there are two players ( and ) representing one consumer
and one producer of a service or a good. The goal of the two agents is to
negotiate an outcome ,where is the set of possible contracts describing
multi-dimensional goods/services such as the price of the service, the time at
which it is required, the quality of the delivered service and the penalty to be
paid for reneging on the agreement. If they reach an agreement, then they
each receive a payoff dictated by their utility function, defined as
. If the agents fail to reach any deal, they each receive a
conflict payoff . However, from the set , only a subset of outcomes are