In negotiations about prices and salaries, it is best to act first to set a reference point. The other party must then negotiate starting from your reference point. This is straight forward in bilateral negotiations, but what happens if a negotiation involves three parties?
The statutes of the World Federation Fifa, for example, stipulate the order of negotiations for player transfers. If a player has more than 6 months left on their contract with the current club (CC), the interested club (IC) must announce its interest in a player to the CC. The CC must then agree to the negotiations before the IC can negotiate with the player. Before concluding the contract, the player must undergo a medical examination and receive clearance from the IC.
In simplified terms, the IC negotiates first with the CC and then with the player. The decision tree in Figure 1 illustrates the official process, assuming that the player is medically fit.
IN REALITY HOWEVER, THE FIFA STATUTES ARE BYPASSED BY NOT TALKING DIRECTLY WITH THE PLAYER BUT WITH THE PLAYER’S ADVISERS LONG BEFORE THE OFFICIAL NEGOTIATIONS WITH THE CURRENT CLUB.
The unofficial process switches the order of the negotiation, leaving the CC last, as shown in Figure 2.
It looks as if reversing the order is just a small change in the process and therefore does not have a significant impact on the outcome of the negotiation. However, a game theoretical analysis shows that the effect on the bargaining power of each party, and hence the payout, significantly changes with the order of the negotiation.
To demonstrate this clearly, let’s use an example with the following assumptions:
The interested club (IC)
- … is willing to pay the player a maximum of €10 million per year for a 5-year contract
- … is willing to pay the CC a maximum transfer fee of €100 million
- … is therefore prepared to pay a maximum value of €150 million
- … currently earns €5 million per year at the CC
- … has a contract for the next 5 years
- … in addition to a high income, prefers to play for a club that supports him
The current club (CC)
- … pays the player a salary of €5 million per year for a 5-year contract
- … sees the total value of the player as €100 million
- … know that minus the salary, the player is worth €75 million to them
All 3 parties naturally want to maximise their own benefit. This means that the IC wants to pay as little salary and transfer fee as possible, while the player wants to receive as much salary and support as possible. The CC also wants to maximise its benefits from both the player and transfer fee.
Using these assumptions, the transfer can be solved by means of backwards induction using both the official and unofficial process.
SCENARIO 1: THE OFFICIAL PROCES
Backwards induction means starting the analysis with the last decision node and working towards the start. In this case, the last decision node is the player’s decision to accept the transfer.
The decision the player makes depends on the benefit of the decision to him:
- If the player agrees to the transfer, he receives his future salary from the IC and the security of the full support of the IC, since they will want to promote their new player.
- If the player refuses the transfer, he will continue to receive his salary from the CC (€ 5 million per year) but runs the risk of receiving less support from the club.
- In the previous decision node, the CC signaled that they would prefer the transfer fee compared to keeping the player. The current salary of the player is known and therefore the player is better switching to the IC if the salary is at least € 5 million per year (or more than € 25 million in 5 years).
Since the decision of the last decision node is now known, the CC can compare the options at its decision node:
- If the CC rejects the transfer, they keep a player who, at least theoretically, does not know about a transfer offer. The CC therefore keeps a motivated player, which is why they only agree to a transfer if the transfer fee exceeds the player’s benefit to the CC.
- Since the clubs do not know about the value of the player’s benefit to the other club, the value of the transfer fee will end up between € 100 million (the maximum transfer fee of CC) and € 75 million (the current value of the player for the CC). The expected value, assuming an equal distribution, of the transfer fee is € 87.5 million.
SCENARIO 2: THE UNOFFICIAL PROCESS
Using the unofficial process, the last decision node is again analysed by means of backwards induction. In this scenario, the CC is the decision maker at the last decision node.
- If the CC agrees to the transfer, the player changes club and the CC receives a transfer fee.
- If the CC declines the transfer, then the player stays with the CC under the current contract.
The decision of the CC depends on the benefit of the decision to them:
- If the transfer is approved, the CC receives the transfer fee, but loses the player.
- If the transfer is rejected, the CC keeps an unmotivated player who had already agreed to a transfer. The IC knows about the reduced benefits of an unmotivated player and can therefore be tougher in the negotiation of the transfer fee. The expected transfer fee will be between € 75 and € 87.5 million and thus less than the transfer fee in scenario 1.
Now that the possible outcome of the last decision node is known, the player can evaluate the options of his decision node:
- If he decides against the transfer, the player will stay at the CC and receive his current salary (€ 25 million over the next 5 years).
Similar to scenario 1, an information asymmetry exists between the CC and IC. The IC does not know if the CC is interested in a transfer and how much the player values his current club in addition to his current salary. Thus, the bargaining power between the IC and the player is balanced.
Assuming equal distribution, the negotiation of the future salary of the player will end in the middle of the current salary (€ 25 million in 5 years) and the maximum salary of the CC (€ 50 million in 5 years), equating to € 37.5 million.
The expected payouts in the case of a successful transfer in both scenarios are shown in Figure 3:
Figure 3 clearly shows the advantage of negotiating earlier in a multi-stage, multi-party negotiation. In scenario 1, where the CC negotiates earlier, they receive a higher payout. Whereas in scenario 2, where the player negotiates earlier, they receive a higher payout.
The party that can negotiate first has the advantage of having a stronger bargaining position through information asymmetry. As soon as the first party finds an agreement with the IC, it signals its own valuation of the third party to the IC, which thereby gains an information advantage in the negotiation. This benefit is reflected in the reduced payout to the third party.
WAITING TOO LONG IN NEGOTIATIONS CAN BE A DISADVANTAGE.
By considering the possible decision paths, game theorists can analyse which factors have a critical influence on the bargaining position of the participating negotiation partners and how these factors can be influenced for their own benefit.
In this example, the parties negotiating earlier have an information advantage over the later party. This advantage can also be found in the Stackelberg Duopoloy or the First-Mover-Advantage when entering a new market. For the IC this means that it is best to negotiate first with the party with less bargaining power. The gained information advantage can then be used in the negotiation with the stronger party.