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from left (light) to right (dark) as follows: (1) Linear weighted combination, (2)
Constrained linear weighted combination, (3) thread-based) and (4) concession-
based mechanism. The monotonic mixing mechanisms tend to shift utility from
an agent that gained advantage through its non-monotonic utility sequence to
the other agent with monotonic concession behaviour (e.g. for buyer strategy
CaS/Cal), whereas both agents may also gain significantly higher utilities in
some scenarios when using the proposed mechanisms (e.g. buyer applying the
competitive BaS/Bal mixed strategy). The results also demonstrate that both
monotonic mechanisms perform similar because of the independent treatment of
pure tactics in both methods. In general, we further observed the effect that the
difference between traditional and the monotonic mixing mechanisms increases
when the time-dependent tactics and the mixing weights are oppositional, i.e.
one agent uses conceder with small mixing weights while the other agent em-
ploys boulware tactics with large mixing weights and vice versa. For instance, if
both agents use similar strategies (both cooperative or both competitive) utili-
ties are similar for all mixing mechanisms. These observations correspond to the
results from the first experiment (cf. figure 2(a)) where oppositional concession
behaviours exposed the highest rate of non-monotonicity.
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Related Work
A large number of negotiation scenarios have been studied to provide effective
negotiation mechanisms and strategies, while, however, many focus on single
families of tactics [4], trade-off mechanisms [3] or meta-strategies [11], but do
not consider the dynamic effects in the negotiation process. For example, Fatima
et al [6] investigate scenarios of single- and multi-issue negotiation where agents
have only partial information about each other trying to find optimal strategies
that most exploit the opponent. The work focus on the effect of time, informa-
tion states and discounting factors on the outcome while comparisons are made
to equilibrium solutions but are limited to time-dependent tactics. Evaluation
results for pure, static and dynamic mixed strategies are presented in [3] with
focus on the influence of long and short term deadlines, and initial offers. Matos
et al [8] propose the application of genetic algorithms to determine most suc-
cessful mixed strategies that evolve depending on the environment and strategy
of the opponent. Both approaches demonstrate that mixed strategies perform
better than pure tactics in terms of gained utility and negotiation cycles, but do
not investigate the mechanism of their mixing with respect to the emergence of
non-monotonic behaviour. Cardoso et al [2], and Brzostowski et al [1] consider
the mixing of different tactic families to evaluate adaptive strategies based on
reinforcement learning, respectively, heuristic predictive methods or regression
analysis with respect to their negotiation outcomes only. Sierra and Ros [11] pro-
pose to let an agent make concessions through single or mixed tactics whenever a
deadlock occurs, i.e. the opponent's last offer does not improve the utility of the
offer two steps before, otherwise a trade-off tactic is used. However, utilities of
offers may also decrease when pure tactics are combined as shown in this paper.
Our work is different in that it focuses on the analysis of the mixing mechanism
