Bargaining
Why Studying Business Strategy? | Business Strategies | Bargaining | Notes
What is Bargaining Game?
Hobbes refer the State to state of nature. There is a choice between a state of nature in which a was of all againsts all and a peaceful society where the peace is enforced vy a State which acts in the interest of all. Hobbes's state of nature clearly see the advantages of creating State. Hoever, there are issues to be resolved. The people must agree to the rights which the State will defend and share the common interest in peace. They still need to decide what rights are selected and how people resolve conflicts of interst. This is where bargaining problem arises.
The bargaining problem arises in any situation in which two or more agents are able to produce some benefit through cooperating with one another. If they fail to agree, they do not get the potential benefit and both lose. For instance, there is a gain to both a union and an employer from reaching an agreement on more flexible hours so that production can respond more quickly. The question is how the surplus is to be distributed between a union and an employer.
No alternatives
Suppose there is a hotel in a summer resort. The season lasts 101 days. Each day the hotel operates and it makes a profit of $1,000. At the beginning of the season, the employees' union confronts the management over wages. The union presents its demand. The management either accepts this, or reject it and returns the next day with a counteroffer. The hotel can open only after an agreement is reached.
First suppose bargaining has gone so long that the hotel can open for only the last day of the season. When it comes to the union's turn to present its demand, the management should accept anything becuase it is better than nothing. So the union gets the whole $1,000.
Now look at the day before the last, when it is the management's turn to make an offer, they know that the union can alwyas reject this. So they let the process go on to the last day, and get $1,000. Therefore the management cannot offer any less. Likewise, the union cannot do any better than get $1,000 on the last day, so the management does not need offer any more. Therefore, each side gets $500 a day. Now move back one more day. By the same logic, the union will offer the management $1,000 and ask for $2,000, which gives the union $667 per day and the management $333.
Each time the union makes offer, it has advantage, because they have ability to make the last all-or-nothing offer. The two sides' positions are identical: $505 versus $495. There were no alternating offfer, etc. When the time between offers is short and the bargaining horizon is long, split the total down the middle is the best choice. Since the two sides look ahead to predict the same outcome, there is no reason why they fail to agree and jointly lose $1,000 a day.
This is well explained by a Nash bargaining solution. Strategies are represented in the Nash bargaining game by a pair (x, y). x and y are selected from the interval [0, z], where z is the total good. If x + y is equal to or less than z, the first player receives x and the second y. Otherwise both get 0. There are many Nash equilibria in the Nash bargaining game. Any x and y such that x + y = z is a Nash equilibrium. If either player increases their demand, both players receive nothing. If either reduces their demand they will receive less than if had they demanded x or y. There is also a Nash equilibrium where both players demand the entire good. Here both players receive nothing, but neither player can increase their return by unilaterally changing their strategy.
With alternatives
Although both sides may lose an equal amount of profits, one party may have other alternatives that help partially recapture this loss. Suppose that the members of the union can earn $300 a day from somewhere else, while negotiations whith the hotel management go on. Now each time the management offers, it must offer the union not only what the union could get a day, but also at least $300. The situation chages in the union's favor.
The management could also operates the hotel using other work forces, but those workers could be less efficient or must be paid more, or guests do not like to see union's strike, the management's profit could be only $700 a day. If the union members have no outside income passibilities, there will be immediate settlement with the union without a strike. But the management will prefer to use other work forces, becuase it will give $700 to the management, while the union gets only $300.
Damages to the both sides
A strategic bargainer observes a better outside opportunity and a better share in a bargain, so he will look for strategic moves that improve his outside opportunities. Suppose the union members could earn $300 a day outside, while the management could make a profit of $500 a day using other labor. Then only $200 remains free to be bargained. So both sides split $200: the management gets $600 and the union gets $400. Now suppose the union members give up $100 a day of outside income to join their picketing, and this reduces the management's profit by $200 a day. Then the bargaining gives the union a starting point of $200($300-$100) and the management $300($500-$200). The two starting points add up to $500, and the remaining $500 of daily profit from operation of the hotel is split equally between them. The union gets $450 and the management gets $550. The union's threat of hurting both has earned it an extra $50.
Strikes
Although the firm and the union may want the agreement to succeed, theymay have different ideas. The two parties do not always look froward and see the same end. They may not have the same information or share the same perspective. What is more, a side with a low waiting cost begins to show it can hold out longer, becuase lower costs make higher risks acceptable. And this is where the negotiations will end that leads to the beginning of a strike.
