In this section we discuss the available options for determining whether or not the current course of the negotiation builds for a software agent the basis to keep negotiating in further following the above mentioned offer generation strategies, or to interrupt these strategies to avoid exploitation by the opponent or unfavorable outcomes, if this is enabled by the protocol. According to the approach for fair concession making proposed by Bartos (1977) in his ’simple model of negotiation’ one possibility to avoid exploitation is to reject making further offers – and therefore concessions in the case of continuous concession strategies. Basing on the egalitarian norm of reciprocity Bartos (1977) proposes a simple non-mathematical theory of negotiation. Essential to this theory is the rule of distributive justice according to which men view as fair, rewards that are proportional to the recipients’ contribution to society – i.e. equal rewards only for equal contribution. For negotiation, as a special form of social interaction, this means that negotiators should receive a payoff proportional to their feasible maximal payoff. The maximal utility is defined in this model as the utility reached by a negotiator when the other negotiator achieves an utility equivalent to his evaluation of the BATNA – as the participation constraint for negotiation –, which are for the two negotiators the extremities of the individually rational zone of the Pareto frontier. These points are also reference points in several normative axiomatic solution approaches for bargaining problems (Rosenthal, 1976; Roth, 1977; Thomson, 1981). This maximal payoff is also the opening offer proposed by Bartos – and used for our software agents as discussed above. After having these first offers on the table the midpoint between these offers achieved by splitting the difference – which is also proposed by Raiffa (1982) as an important strategy in negotiations, and a common wisdom for reaching agreements – acts as an expectation for the final outcome. After having determined the opening offer how large should the subsequent concessions be? For the concession after the opening offer Bartos argues that the first concession should be only small to avoid being exploited, although he states that other aspects could play an important role in determining the first concession like for instance personality, reputation, or institutional constraints. Later concessions should be fair if the opponent’s concessions were fair, otherwise the negotiator should not concede until the opponent is up to his level of concession to avoid being exploited. The negotiator should not retract a concession made as there exists a common code in negotiations, that offers once made and therefore on the table should not be withdrawn or otherwise there will be some sanctions like for the violation of any code. Rational negotiators would expect fair concessions if the opponent reciprocates their own last concession, however, due to lack of knowledge of the opponent’s payoffs we cannot measure if the opponents concession matches the own last concession. Fair in this context of concession making is operationalized as the demand that the expected final outcome – the midpoint of the two opening offers – should remain the same. Bartos finally
4.2. Automated negotiation system 95
shows that the midpoint of the initial offers in his model, for a negotiation problem where the Pareto frontier is a straight continuous line, equals the well-known and empirically supported Nash solution (Nash, 1950), which is due to its symmetry axiom considered as a fair solution. Adopting Bartos’ ’simple model of negotiation’ to our conceptual model, where software agents also have no information about the payoffs of the opponent, a concession is considered unfairly small if the total reduction of utility from the starting point of negotiation – assumed to be the worst payoff for the focal software agent as described above – to the current offer of the opponent is smaller than the reduction of utility between the opening offer of the focal software agent – its most preferred offer, as argued in the model and implemented in the opening offer of the software agents – and the current offer of the focal software agent, as this would make it necessary to change the first expectations about the final agreement, which was the midpoint of the opening offers. Denoting j as the focal agent, −j as its opponent and letting uj be the utility function
of software agent j, and oj,t the offer of agent j proposed in round t, then due to the sequential
nature of our alternating turn protocol two different reference values against which to compare the opponent’s concession made with its last offer o−j,t−1exist, the own concession determined
by the last own offer oj,t−2 or the next offer to be proposed oj,tas depicted in Figure 4.10.
Figure 4.10: Focal negotiator’s and opponent’s concessions
Using the next own offer to be proposed oj,t according to the software agent’s offer generation
strategy as reference point leads to a rather passive concession strategy formulated in (4.2). With the passive concession strategy a software agent only further negotiates if it does not exceed the opponent’s concession magnitude up to the last offer of the opponent with the own concession determined by their next offer to be sent. So this strategy could be considered rather pessimistic and offers are only made in a way to stay at or below the opponent’s concession magnitude to avoid exploitation. Only if this is the case the software agent further negotiates in making offers according to his offer generation strategy or accepting the opponent’s offers. This passive strategy can be expected to lead to better agreements for the focal negotiator, however, maybe also to fewer agreements.
negobasis= TRUE if 100 − uj(oj,t) ≤ uj(o−j,t−1) FALSE else (4.2)
By contrast if the software agent uses the last own offer oj,t−2 as the basis for comparing own
and opponent’s concession magnitudes this leads to the considerations represented in (4.3), which can be considered to be more active and optimistic. If the opponent with his last offer matched the concession magnitude the focal software agent reached with his last offer then the software
agent further negotiates in making a new offer and a concession step ’ahead’. By contrast in the passive concession strategy the own concession magnitude will always be lower or at most equal to the concession magnitude of the opponent. Though this going ahead in making concessions possibly could be exploited – actually only the one concession the agent goes ahead – it could be a good means to keep negotiations running and reach agreements where passive concession strategies fail to do so.
negobasis= TRUE if 100 − uj(oj,t−2) ≤ uj(o−j,t−1) FALSE else (4.3)
In Figure 4.10 for example the current offer of the opponent constitutes a concession magnitude larger than the concession made by the focal agent with its last offer but smaller than the concession to be made with the next offer. Therefore agent following the active concession strategy – act represented in equation (4.3) – would have a negotiation basis – as the opponent’s concessions are larger than the own made up to this point in time – while an agent following the passive concession strategy – pas represented in equation (4.2) – would have no negotiation basis as the opponent’s concessions are smaller than those to be made with the next offer. Furthermore note, that if the next offer is to be proposed – here only in the case of the active agent – the software agent will accept the last offer of the opponent, due to the acceptance criterion discussed subsequently, rather than proposing its own next offer as it affords higher utility.