Electronic Negotiation and Behavioral Elements

Abstract

Systems based on information and communication technologies have facilitated the support or automation (partial/complete) of many a task and process, including negotiation. Electronic Negotiation Systems (ENSs), whose genesis and evolution can be traced to software systems of the 1970s, have grown significantly since the advent of the Internet, in terms of both scope and numbers. Yet, given the complexity of negotiation, there is a need for incorporating behavioral elements into ENSs. This chapter, which concerns a two-party negotiation setting, outlines the behavioral negotiation literature and describes the evolution of ENSs, thus contextualizing the problem of incorporating behavior into negotiation systems. We propose a framework to approach this problem, entailing a characterization of user-preferences, and in turn, the resulting negotiation strategy. We use relevant exemplars from the literature to illustrate how the trade-off between the fidelity and tractability of such characterizations can determine the level of automation afforded by an ENS. Research opportunities arising from endowing ENSs with behavioral features are identified.

Appendices

Appendix A: Negotiation Strategy

Researchers on electronic negotiations (Step 1 of section “Integration Exemplars”) have identified a number of strategies that govern the offers made in a negotiation, including for example, time-dependent, resource-dependent, and tit-for-tat. Faratin et al. (1998) gives function forms of these strategies that provide the offer that must be made in a given round.

Drawing upon previous research (e.g., Faratin et al. 1998; Mok and Sundarraj 2005; Sundarraj and Mok 2012), we illustrate below the time-dependent strategy. Here, the offers³ are generated by considering the following parameters: the starting offer; the reservation offer; the maximum time allowed for the negotiation; and the rate at which concessions are made as the negotiator proceeds from the starting offer to the reservation offer. Based on these parameters, a mathematical of the offer at time t is given by:

$$ P(t)={P}_{\mathrm{min}}+{e}^{{\left(1-\frac{t}{T_{\mathrm{max}}}\right)}^{\beta}\ln (K)}\left({P}_{\mathrm{max}}-{P}_{\mathrm{min}}\right)\quad\mathrm{if}\ \mathrm{utility}\ \mathrm{is}\ \mathrm{decreasing} $$

(1)

$$ P(t)={P}_{\mathrm{min}}+\left(1-{e}^{{\left(1-\frac{t}{T_{\mathrm{max}}}\right)}^{\beta}\ln (K)}\right)\left({P}_{\mathrm{max}}-{P}_{\mathrm{min}}\right)\quad\mathrm{if}\ \mathrm{utility}\ \mathrm{is}\ \mathrm{increasing}, $$

(2)

where

t	Is time (number of turns) in the interval [0,Tmax]
Pt	Is the value of the negotiating issue proposed at time t
Pmin	Is the minimum value of the negotiation issue
Pmax	Is the maximum value of the negotiation issue
K	Is a constant that determines the value of the first offer negotiating issue in the first offer
Tmax	Is the time limit (maximum number of turns) proposed by an agent
β	Is a constant (concession rate) determining the degree of convexity

The five parameters, P_min, P_max, T_max, β, and k, uniquely determine the function’s range and can yield a rich set of offers. For example, even if P_min, P_max, T_max and k are kept constant, a change in β can yield significant changes in the offer prices. This is illustrated in Fig. 4, wherein the offer-differential for the first five turns is less than 20 for β = 0.1 and more than 200 for β = 7.5. Such offer-differentials significantly impact the negotiation process and outcome.

Fig. 4

Illustrating an offer-generation strategy

The above characterization is in terms of single negotiation-issue (e.g., price), although it can be applied to multi-issue negotiations as well (involving other factors such as lead time etc.). With multiple issues, under the important condition that the negotiation issues are separable, different decision-functions can be used to the different issues, with the various negotiation parameter-values applicable to one issue being different from those for another (e.g., maximum/minimum values applicable to lead time are likely to be different from those for price).

Appendix B: Eliciting Time Preferences

Preferences have to be elicited both for the type of negotiation strategy that the user wants to employ, as well as aspects pertaining to the behavioral element. Here, we will focus on the latter for the case of time-preference (Step 2 of section “Integration Exemplars”); more details are available in Krishnaswamy et al. (2016).

The varying impatience levels described in section “Integration 2” indicate that preferential independence does not hold in the case of time-preference models. In both increasing and decreasing impatience types, changing the value of time can result in a change in price. That is the delivery time has an effect on price. In order to incorporate this (instead of a linear additive utility model), the utility U(p, d) of a price-delivery-time combination (p, d) is given by (Loewenstein and Prelec 1992; Bleichrodt et al. 2009):

$$ U\left(p,d\right)=\left(\frac{p^{max}-p\ }{p^{max}-{p}^{min}}\right)\ \phi (d), $$

(3)

where ϕ(d) is the discounting function.

A number of normative models have been proposed to capture the functional form of ϕ(d). Samuelson (1937) assumed that several factors that devalue utility with respect to time may be amalgamated, and proposed the exponential discounting model (4). Exponential discounting model has capabilities to represent only stationary time preference (i.e., constant impatience), where the ratio ϕ(d)/ϕ(d + 1) is constant with time. Stationary Time Preference (Constant Impatience):

$$ \phi (d)={e}^{- rd},r>0 $$

(4)

where r is the rate of discounting.

Experiments have, however, shown that impatience behaviors have anomalies and can be decreasing or increasing with time (Loewenstein and Prelec 1992; Attema et al. 2010). Loewenstein and Prelec (1992) proposed the generalized hyperbolic function to model some of the anomalies.

$$ \phi (d)={\left(1+\alpha d\right)}^{-\beta /\alpha },\alpha, \beta >0 $$

(5)

where α, β are constants.

The above hyperbolic discounting function is not robust to model increasing impatience of any degree (Bleichrodt et al. 2009). Bleichrodt et al. (2009) proposed a function shown in (6) that can model both increasing (δ < 0) and decreasing impatience (0 < δ < 1):

$$ \phi (d)={ke}^{-{rd}^{1-\delta }},\, r>0,\, \delta <1,\, k>0 $$

(6)

where r, δ, k are constants. While (6) can be more robust, irrespective of the functional form, ϕ(d) has to be obtained. The broad steps entailed in this are as follows:

• Step B1: Elicitation of user preferences by administering a time-preference elicitation (TPE) task

• Step B2: Calculation of indifference points from the user choices

• Step B3: Calculation of discount factors and plotting of discounting curve

• Step B4: Parameter estimation using curve fitting function and calculation of discount function φ(d)

The TPE task presents the user with a set of questions between a “larger-sooner cost” and a “smaller-later cost” (note: the same can be readily adapted to rewards as well). The user answers the questions based on the outcomes and time delay. The questions are presented in a way that the user exhibits indifference between the available choices at a point of the task, known as the indifference point. The indifference points are normalized to get the utility points from which, for example, curve fitting can be used to obtain the parameters of the discount function. There are two approaches to Steps B1 and B2 above: choice and matching-based (Attema and Brouwer 2013) methods.

A simple choice method is titration-based choice. Here, the participants make a choice between two options: delayed smaller price and immediate larger price. Such option questions are then systematically posed for a range of amount-delay combinations. In a simple version of the procedure, for example, for a given delay, a series of option-questions are posed by varying (i.e., titrating) the amounts, and then the indifference point is noted for this delay. This step is then repeated for various delay-values.

Example 1: Choice Based Method

Consider a user who has to choose between delivery tomorrow for $100 or a free delivery in 3 days. If the user chooses free delivery in 3 days, then the paid delivery price is decreased by some percentage, say, to $88, and a similar question is posed. If the user now chooses delivery tomorrow for $88, then indifference point is $94 (average of 88 and 100). On the other hand, if, in response to the original question, the user chooses delivery tomorrow for $100, then the paid delivery price is increased by some percentage, say, to $108, and then similar questions are posed until the indifference point is obtained. Then, the whole procedure is repeated for a different delay.

The titration choice method tends to cover a range of amount-delay combinations and that can tend to reduce decision-biases on the part of the participant. It is, however, time consuming, so there are other methods, including other choice-based methods and the matching approaches given next.

Matching task involves matching pairs of alternatives to indifference. Of the various types of matching methods, time-trade-off (TTO) method is an example (Attema et al. 2010). In the matching methods, the user has to fill in one of the attributes of one pair which makes it indifferent to other pair. This procedure gives information on the discount function without requiring assumptions about the shape of the discount function or the validity of the DU model. The TTO method entails a sequence t₀, t₁…, t_n of time points such that there exist two outcomes β and γ with (t₀: β) ∼ (t₁: γ) (∼ is symbol for indifference), (t₁: β) ∼ (t₂: γ), …….(t_n-1: β) ∼ (t_n: γ); that is, each delay between two consecutive time points exactly offsets the same outcome improvement, and therefore makes both tuples indifferent.

Example 2: Matching Task Time-Trade-off Method

Figure 5 illustrates this approach. As given in the top box, the user is asked how many days he/she is willing to wait for a lower delivery price of $50. Assume that the response is 3 days. This implies that, the user is indifferent between paying delivery price of INR 150 on day 0 to paying delivery price of INR 50 on day 3. This response is chained in the next question (box 2), and the procedure continues.

Fig. 5

Example for TTO task

Appendix C: Integration of Time Preference

Once the time-preference is characterized, it can be used to alter (Step 3 of section “Integration Exemplars”) the negotiation strategy (see also Krishnaswamy et al. 2016). Step (a) uses a strategy to determine the concession that must be offered, giving bounds on the utility value that must be respected during offer generation (note: besides concessions, section 2 lists other negotiation principles as well). Step (b) gives the mechanism for generating multiple trade-off offers.

• a) The buyer fixes the utility U_t(p, d)for the current round t (t ∈{1, 2, …Tmax}) based on the concession level u_t. U_t(p, d) is given by:

$$ {U}_t\left(p,d\right)={U}_{t-1}\left(p,d\right)-{u}_t $$

(7)

where the initial U₀ = 1.0 and u_t is determined by using a concession tactic (Appendix A gives more details of one concession tactic to obtain round-utility).

• b) The ENS can then create an offer-tuple by choosing p-d values to satisfy (8) (round index t is dropped below):

$$ U\left(p,d\right)=\left(\frac{p^{max}-\, p\ }{p^{max}-{p}^{min}}\right)\phi (d) $$

(8)

That is, by choosing price from [p^min, p^max], we can determine the delivery time with (9); alternatively, for delivery time in [d^min, d^max] the price can be computed using (10):

$$ p=\left[{p}^{max}-\frac{U\left(p,d\right)\ \left[{p}^{max}-{p}^{min}\right]}{\phi (d)}\right], $$

(9)

$$ d=-\left(\frac{1}{r}\right)\mathit{\ln}{\left(\left[\frac{U\left(p,d\right)\ \left[{p}^{max}-{p}^{min}\right]}{\left({p}^{max}-p\right)k}\right]\right)}^{\frac{1}{1-\delta }} $$

(10)

where ϕ(d) is a suitably chosen discounting function. This way the ENS can exploit price-time trade-offs and propose multiple offers, thereby reducing impasse and improving the possibility of integrative offers. If the seller accepts the offer or the negotiation deadline is reached, go to step (d).

• c) The seller proposes a set of counter-offer(s). If the buyer accepts the offer or the negotiation deadline is reached, go to step (d); else go to Step (a).

• d) Stop.