Example 1. Nash arbitration with the golden section search method
Assume we have the following partial conflict game between two players:
Player II Strategies C1 C2
Player I R1 (2, 6) (5,4) R2 (10,5) (4,8)
Assume in this example we have already found the Nash equilibrium, (4.666, 5.6). We plot the points and obtain the convex polygon shown in figure 3.
Figure 3. Payoff polygon and Pareto optimal line segment
We find the Nash equilibrium is not Pareto optimal. To be Pareto optimal, the Nash equilibrium must line on the Pareto optimal line segment. For sake of illustration, we assume we have tried all other strategic moves’ methods to improve our outcomes and we move on to arbitration.
Finding the security
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Finding the Pareto optimal line segment equation
We use the end points (4, 8) and (10, 5) to obtain the equation of the Pareto Optimal line shown in figure 3 using the point-slope formula of a line: .
We find the equation as (y-8) =-3/6 (x-4) which simplifies to y= -1/2 x +10.
Nash arbitration
Now, we can return to the Nash arbitration scheme that says in particular find the values of (x, y) along the line y=-1/2 x + 10 where x > 4.6666, y > 5.6 that maximizes the product (x-4.6666) (y-5.6).
To use golden section in one dimension, we simply create a function of one variable by substituting -1/2 x + 10 for y in the function to be maximized, (x-4.6666) (-1/2 x + 10-5.6) or (x-4.6666) (-1/2 x + 4.4). We can simplify this through multiplication, if desired, to obtain -1/2 x2 + 6.73333 x -20.53333. The next crucial element is to determine the interval. The value of x must be greater than 4.6666 and less than the x coordinate of right most end of point of the Pareto optimal line, which in this case is 10.
Therefore, we will use golden section to find the value of x that maximizes the function, -1/2 x2 + 6.73333 x -20.53333, within the interval [4.6666, 10].
We have built a template, available upon request, to perform the calculations. We find the value of x that maximizes this function within the interval to be x= 6.733241. So how do we find the y coordinate? We substitute x= 6.733241 into the equation y = -1/2 x + 10 and find y =6.63338. Our Nash arbitration
The point of profit maximization for the firm in the given scenario occurs at a quantity of 8 units. At this point they have maximized their profit and as you can see to go beyond this point would cause the firm to incur economic losses.
The diagram below shows the feasible region of the intersection of two lines. This means that any point within the feasible region satisfies all constraints that we established before graphing. Feasible regions make it easier for us to determine the maximum profit and now we know all the possible combinations it’s important to know what point on the graph is going to be the most profitable.
You just won a $100 shopping spree at a store that sells only DVDs and CDs. You are trying to determine what combination of these two goods would maximize your utility. The price of CDs is $10 and DVDs are $20. Below is the total utility you receive from consuming these goods.
The negotiators in these situations should mainly on the integrative bargaining. It means that negotiator should arrange a face to face meeting for both the parties by motivating them to practice integrative barging so that they can use the conflict strategy management to innovate positive solutions rather than dysfunctional conflicts. The negotiator should focus mainly on problem solving, compromising, smoothing and finding solutions. Motivating both the parties for a face-to-face meet is done so that, they can identify the problem and resolve it by an open discussion. Each team should give up something so that they can come to an agreement. The negotiator should use smoothing technique by reducing the conflicts while stressing common interests between both the teams. By compromising and smoothing both the parties should know about their common interests and goals and should create a shared goal. Once the negotiator make them realize that they need each other for achieving their goals, integrative positions solutions will be obtained instead of dysfunctional
1. How did you plan for the negotiation? Explain how you decided on a strategy?
Our team approached this negotiation case in a very efficient way. Each of us had a very clearly job assignment. Two people took care of the calculation while the other two people were responsible for the negotiation. Thus we quickly built up a model and provided several options to our counterparts with different terms but same net value of the final bargaining agreement to our team.
It occurs in profit or non profit organizations, government sectors, dealing among nations and also in our personal situations such as salary package, house purchase, marriage, divorce and etc. The strategy to use can either be distributive or integrative depending on the situations and the outcomes that the party want out from the negotiation.
In Energetics meets Generex negotiation, I was acting as a Chief Operating Officer (COO) for Energetics Corporation and my opponent and my classmate Chace Eskam was acting as a COO of Generex Corporation. In this deal, as a COO I was supposed to sell the Wind energy division of the Energetics to Generex. Energetics Corporation was in desperate need of cash due to bankruptcy. Another hurdle was that I could not sell three different locations of Wind plants individually. My company needed cash within three months with no additional terms added to this deal. My another best alternative was to sell all the assets of Wind Energy division to generate some cash if deal with Generex fails in this negotiation. Our negotiation went on for 15-20 minutes during class time and deal was set in $247 millions. My opponent Chace was very tough in this negotiation to deal. He was very prepared with facts and numbers before he came to the table. My opponent asked me lot questions such as the depreciation of the property, equipment’s life, taxes etc. After having lot of discussion we ultimately came to the conclusion that Generex will pay Energetics $247 million right away in cash to purchase Wind Energy division from Energetics.
“Instead of approaching the problem in a competitive as distributive bargaining (claiming value only for one), the integrative negotiation the parties adopt an attitude aimed at solving the problem and seek a favorable outcome for both” (Business Blog Review, 2011).
Subject to x + y ≤ 100 (acres) 50x + 75y ≤ 6,000 (water) x ≤ 0 y ≤ 0 1 b) Sketch of
Power is never linked to price, but always to value.” Power in negotiations can be perceived or real which affects the final negotiation outcome. Generally all disputants have some power to an extent which is used to achieve a favourable outcome. It is unlikely the power balance stays consistent, power shifts throughout the negotiation process. Knowing how the power works and how to use power to achieve desirable outcome is important for successful negotiations. The notion of parity in power is vital in relationships between the disputants. The parity in negotiation is when one party perceives that the other party can oppose any form of power with dissimilar or similar form of power (Lewicki and Saunders et al., 1997). Power parity means there will be a balance in power positioning to some extent. The two different objective powers involving in the bargaining process are power depending on the lack of dependence and role power (Staff, 2013). The first power parallels to a disputants BATNA (Best alternative to a negotiated agreement). Going into a negotiation with strong BATNA means the disputant is less dependent on the other parties in achieving the desired outcome compared to having a weaker alternative. The second power is linked with the positions, titles or roles which grant power simply because of the control or authority they possess. This is often found in hierarchical organisations. Apart from the objective powers there is possibility of
For example in the Prisoner dilemma, ‘confess’ is the optimal choice for both players so it is the Nash equilibrium. Though, the combine payoff for both players to confess is lower than if both players to deny, which shows that t he Nash equilibrium can also be Pareto inefficient in a finite game. If there is some way for them to cooperate through
The fourth mistake runs in parallel with the fifth mistake is to search too hard for common ground which is neglecting BATNA. In fact, a negotiator has to try similarities with the others to have a deal. However, a negotiator has to know where he can’t go and the others alternatives. Moreover, if you try to seek too hard for similarities, you risk stopping the negotiation. Differences of interests can unbundle different elements and give each party what it values the most; many times at least cost to others.
Gain (S sunny, Temperature ) = 0.970 - (2/5) 0.0 - (2/5) 1.0 - (1/5) 0.0 = 0.570