# Bargaining power

Bargaining power

Bargaining power ( Engl. Bargaining power ) is a term used in various negotiation theories , is made up of the terms of negotiations and power , and describes the relative bargaining power between individuals or organizations during a balance of interests. Bargaining power is generally used to describe the dominance in a negotiation over the other side. In economic theory, the balance of interests is basically reduced to monetary values, which are divided according to bargaining power.

## Bargaining power as an instrument

The bargaining power is instrumentalized in a negotiation in order to reach an agreement (distribution of monetary values). The instrument of bargaining power is the ability to influence the other party in your own favor in order to generate a profit. The respective strength of the bargaining power is measured by the specific relationship to the party involved. The more one side can enforce its own demands in a negotiation, the greater it is. With equal bargaining power between the parties, the result is balanced. According to this classification, bargaining power can finally be quantified as a unit of measurement (ratio) in order to describe the relative advantage or relative strength.

Overall, it becomes clear that bargaining power is particularly important in business life (concretization in trade through market power ), politics , sociology and game theory . In addition, the bargaining power in automated negotiations is becoming increasingly important, since a large part of goods is now traded electronically (such as Amazon or Alibaba ).

## Limitation of bargaining power

A limitation of one's own negotiating position through one's own interventions takes place mainly under sociological (ethical and moral) aspects, for example allowing older or needy people to take precedence. Self-limitation makes sense in a strategic sense if the benefit is maximized indirectly through the direct limitation. This is the case, for example, if the insurance company waives an increase in the insurance premium after a car accident in order to retain the customer in the long term (see also moral hazard ).

Various strategic moves can be used to actively restrict the opponents (e.g. the bargaining power of suppliers, customers ) . B. Promises or the conscious influencing of the influencing factors can be exploited.

The determination of one's own bargaining power (from outside) by third parties takes place e.g. B. takes place within the framework of state intervention in the form of antitrust law by preventing company mergers, as this could lead to a dominant position (market power). The state thus regulates bargaining power from a social (fairness, protection) and economic ( welfare ) point of view.

## Factors influencing bargaining strength

Personal influencing variables of a participant in the context of a negotiation include social status , image and existing reputation . The negotiator's "word" is automatically given more weight. Furthermore, a negotiation can be influenced by strategic moves or manipulation. An example of this is the creation of information asymmetry between the parties in order to put the negotiating partner in a worse position through an information disadvantage. Furthermore, the existence of alternative options influences the bargaining power so that one is not necessarily bound by the offer of the other party. During a negotiation, this is reflected, for example, in the different costs of waiting. The opposite case of alternatives are dependency relationships between the negotiating participants, the relationship of which is described via the lock-in effect and switching costs . Finally, the patience of the negotiating parties should be mentioned as an influencing factor. The more impatiently one side can wait for an agreement, the sooner these concessions will be made, which will make the opposing party better off.

Economic factors influencing bargaining power are the type and volume of demand of a market participant . The more he asks a provider for products or services , the greater his bargaining power and vice versa. Large buyers therefore have high bargaining power , who can help determine the market price or enjoy volume discounts or special tariffs . Customers without bargaining power have the status of volume adjusters as market behavior , while major customers can sometimes act as option fixers.

## Bargaining power in game theory

### Basics

#### conditions

The concept of bargaining power fits into the structure of cooperative game theory . For application in game theory, all negotiation situations must contain the following features:

• The total disbursement through an agreement of the parties should be at least equal to or greater than the sum of the individual disbursements, otherwise there is no benefit.
• The negotiation is not a zero-sum game , because without disbursements to be distributed, the influencing variable bargaining power has no effect in the negotiation process.

#### Natural bargaining power

A natural negotiating power already exists before the start of negotiations and is therefore to be equated with a system-related power (from a structural or context-related point of view). One party's negotiating position can naturally be higher than that of another. Such a relationship exists e.g. B. between superiors and subordinates or between state and people. An existing handicap can also (negatively) influence negotiating power in advance.

#### Established bargaining power

Deliberately created better positions in a negotiation serve to improve a given position in your own favor. Several instruments ( strategic moves ) can be used for this purpose : threats , promises or warnings . In the same way, creating a handicap in the opposing party - for example by reducing its reputation - can strengthen one's own position. This also includes your own worse position, provided that the other side is negatively influenced to a greater extent and you are thus in a better position (e.g. through self-commitment ).

#### Negotiation horizon

For an infinitely long game theory negotiation process, the bargaining power no longer has any influence on the negotiation and the subsequent distribution of the payouts. Furthermore, the assumption does not take into account a possible departure of a party (e.g. through illness or death). As a consequence, an infinite number of negotiation rounds can only lead to the result of an equal distribution of the payouts.

The use of a finite time horizon leads to the consideration of a fixed end point from which conclusions can be drawn. In game theory, the finite process is expanded to include the principle of foresight and inference. This principle basically ensures that an agreement is reached at the beginning of the negotiation. In sequential games in particular, the so-called "all-or-nothing offer" occurs, the negotiating influence of which decreases as the negotiation horizon increases.

### Application in game theory

#### Easy negotiation without bargaining power

A simple negotiation is a dispute with equal bargaining power between the parties - i.e. without any advantage for either side. This situation is also described as a "pure negotiation game", since only the results of cooperation or non-cooperation occur.

The following example should illustrate the respective positions and the procedure during the negotiation:

 The owner of an old gold mine has a number of workers. Since the mine is very old and therefore almost completely dismantled, his miners fear the threat of job loss and want more wages as a precaution. Furthermore, it can be assumed that the mine can only be operated for 199 days before it collapses and that gold worth 10,000 euros will be mined on each day of commissioning. With each passing day, the total amount to be distributed for the owner and the wages of the miners decrease. The negotiation takes place in such a way that the miners make an offer early before they start work, which the mine owner can accept or reject. A counter offer by the owner is made the next morning.

To understand the explanations, it is first necessary to consider the extreme points - what happens on the last day of the negotiation. The miners can submit an offer for the last time on the last day. For the sake of simplicity, it can be assumed that the mine owner will accept any offer made by his workers. Thus they can collect the total amount of the last day (10,000 euros).

On the penultimate day - the day on which the owner can make a counter offer for the last time - he can see on the last day (extreme point) by simply closing the back that the miners would reject any amount of money below 10,000 euros, as this amount is safe for them . Accordingly, on the penultimate day, the gold mine owner will distribute the proceeds (20,000 euros) so that his workers receive half - a share of 10,000 euros (5,000 euros per working day). Because both parties have equal bargaining power, the owner will never offer more than half of the total amount to his miners.

The negotiated solution for the following sample calculations is determined by the following function:

${\ displaystyle income_ {j} = {\ frac {V- \ sum _ {i = 1} ^ {n} Alt_ {i}} {n}} + Alt_ {j}}$
V = the amount of money to be distributed
n = number of negotiating parties, ${\ displaystyle \ mathrm {n \ in \ mathbb {N}}}$
${\ displaystyle Alt_ {j}}$ = Alternative income of the negotiating party j

The following table outlines the entire negotiation:

Proportion of miners Mine owner's share
Remaining
days
Offer
through
Total
in euros
Per day
in euros
Total
in euros
Per day
in euros
1 Miners 10,000 10,000 0 0
2 owner 10,000 5,000 10,000 5,000
3 Miners 20,000 6,667 10,000 3,333
4th owner 20,000 5,000 20,000 5,000
5 Miners 30,000 6,000 20,000 4,000
... ... ... ... ... ...
198 owner 990,000 5,000 990,000 5,000
199 Miners 995.995 5,005 994.005 4,995

It is clear from the table that the benefit of the miners' last offer decreases with the number of remaining negotiation rounds (remaining days). Since both parties can look ahead to the table above, owners as well as miners come to an agreement on the first day. Both sides will split the amount in half , as each party loses 5,000 euros with every day that has passed.

 Result for miners: 5,000 euros

#### Negotiation with unilateral bargaining power

With unilateral bargaining power, one party has an advantage in the negotiation. Favoring factors were listed under the section Influencing factors. Applied to the above example, the miners could e.g. B. the alternative to temporarily pursue another job, where they earn a total of 3,000 euros during the negotiation phase. The costs of waiting are therefore lower for the miners. Accordingly, the mine owner must take into account the wages for the mine work and the alternative wages in his counter offer.

The owner calculates:

 1.) 10,000 - 3,000 = 7,000 (remaining amount to be distributed) 2.) 7,000 / 2 = 3,500 (Owner's share, miners' basic wage) 3.) 3,500 + 3,000 = 6,500 (Offer to miners)

This gives the miners greater bargaining power, which ultimately puts them in a better position. As a consequence, an agreement is also reached on the first day of the negotiation, as both sides can again look ahead to the following overview:

Proportion of miners

Mine owner's share

remaining
days
Offer
through
total
in euros
per day
in euros
total
in euros
per day
in euros
1 Miners 10,000 10,000 0 0
2 owner 13,000 6,500 7,000 3,500
3 Miners 23,000 7,667 7,000 2,333
4th owner 26,000 6,500 14,000 3,500
5 Miners 36,000 7,200 14,000 2,800
... ... ... ... ... ...
198 owner 1,287,000 6,500 693,000 3,500
199 Miners 1,294,495 6,505 695.505 3,495

The alternative means that the costs of waiting for the miners are lower and their bargaining power with the owner improves.

 Result for miners: 5,000 euros → 6,500 euros

#### Negotiation with multilateral bargaining power

If both or all parties involved have different levels of negotiating strength, one speaks of a negotiation with multilateral negotiating power. Each side can therefore have different degrees of influence on the outcome of the negotiation. Transferred to the example, mine owners and miners can use bargaining power in order to improve their position. The miners had looked for an alternative job during the negotiations. If the mine owner is also looking for short-time workers for the negotiation phase, who at least produce gold for 5,000 euros from the mine, his position will also improve.

The owner recalculates his offer:

 1.) 10,000 - (3,000 + 5,000) = 2,000 (remaining amount to be distributed) 2.) 2,000 / 2 = 1,000 (Basic share of the owner, basic wage of the miners) 3.) 5,000 + 1,000 = 6,000 (Owner's share) 4.) 3,000 + 1,000 = 4,000 (Offer to miners)

Because the mine owner also has an alternative, the bargaining power changes in favor of the owner.

 Result for miners: 6,500 euros → 4,000 euros

Taking into account the relative attractiveness of the respective alternatives, the miners can improve if a strategic move harms the mine owner to a greater extent. In addition, a miner could not pursue alternative work - whereby the alternative wage would decrease from 3,000 to 2,800 euros - and warn all short-time workers of the poor working conditions in front of the mine and then only a few short-time workers could start work - with only gold for 3,400 euros per day is promoted.

After this strategic move, the owner recalculates his offer:

 1.) 10,000 - (2,800 + 3,400) = 3,800 (remaining amount to be distributed) 2.) 3,800 / 2 = 1,900 (Basic share of the owner, basic wage of the miners) 3.) 3,400 + 1,900 = 5,300 (Owner's share) 4.) 2,800 + 1,900 = 4,700 (Offer to miners)

Because the miners are relatively less badly off than the owner by their actions, the bargaining power changes in favor of the miners (since the marginal utility increases).

 Result for miners: 4,000 euros → 4,700 euros

## supporting documents

1. See Dixit / Skeath, Games of Strategy, p. 571.
2. ^
3. Cf. Dixit / Nalebuff, Game Theory for Beginners, page 278.
4. See Holler / Illing, Introduction to Game Theory, page 243.
5. See Martin, Bargaining Power, page 4 ff.
6. Cf. Buettner / Kirn, Bargaining Power in Electronic Negotiations, page 92 ff.
7. See Holler / Illing, Introduction to Game Theory, page 190 f.
8. ^ A b Avinash K. Dixit / Susan Skeath, Games of Strategy , 1995, p. 575 ff.
9. Avinash K. Dixit / Susan Skeath, Games of Strategy , 1995, pp. 587 ff.
10. Avinash K. Dixit / Barry J. Nalebuff, Game Theory for Beginners , 1997, p. 281 f.
11. Manfred J. Holler / Gerhard Illing, Introduction to Game Theory , 2005, p. 258 ff.
12. Avinash K. Dixit / Barry J. Nalebuff, Game Theory for Beginners , 1997, p. 291 f.
13. See Holler / Illing, Introduction to Game Theory, page 187.
14. Cf. Dixit / Skeath, Games of Strategy, page 566 f.
15. See Dixit / Skeath, Games of Strategy, p. 586.
16. Vg. Dixit / Nalebuff, game theory for beginners, page 281 f.
17. Cf. Dixit / Nalebuff, game theory for beginners, page 282 ff.
18. Cf. Dixit / Nalebuff, Game Theory for Beginners, pages 278, 280.
19. See Osborne / Rubinstein, Bargaining and Markets, page 54.
20. See Holler / Illing, Introduction to Game Theory, page 226 f.
21. ^ Based on Dixit / Nalebuff, Game Theory for Beginners, page 280.
22. ^ Based on Dixit / Nalebuff, Game Theory for Beginners, page 281.
23. ^ Based on Dixit / Nalebuff, Game Theory for Beginners, page 282.
24. Cf. Dixit / Nalebuff, Game Theory for Beginners, page 283.
25. ^ Based on Dixit / Nalebuff, Game Theory for Beginners, page 283.