Game Theory for Negotiators

Game theory is “the study of mathematical models of conflicts and cooperation between intelligent rational decision-makers” (Myerson, 1991). It helps to explain how people interact in key decision-making processes under certain rules. In a strategic game, two or more participants have to make choices of action, which may lead to gain or lose, depending on what others choose to do. Also, in many situations, uncertainty can be also involved because no participant knows for sure what the other participants are going to decide. Originally, game theory focused on zero-sum games, in which one participant’s gains result in losses for the other participants. Extensively, non-zero-sum games that need cooperation are also addressed (Scott, 2003). Nowadays, game theory is widely applied to military, politics, entrepreneur management and business negotiation.

        In business, negotiation is playing a decisive role in many aspects such as product design, bargaining activities, marketing decisions and so on. In almost every kind of business, people need to negotiate deals, identify what their trading partners and competitors are likely to do next, and to position themselves accordingly (Scott, 2003). For many strategic situations where competitive or individual behaviors can be modeled, game theory is an efficient tool to simplify the complicated and uncertain elements in the negotiation process (Osak, 2010). Therefore, a good understanding of game theory is necessary when business negotiators are shaping their strategies.

        In game theory, one of the well-known non-cooperative games is the Prisoner's Dilemma (PD) Game. This game demonstrates that why two completely “rational” individuals might not cooperate, even if cooperation can lead them to best outcome. PD game reflects the following scenario: Two prisoners are arrested and interrogated separately. Each must decide to confess (defect) or not (cooperate). If they cooperate, which means no person defect, then both will be sentenced to only 1 year in jail. If they both defect, then both will be sentenced to jail for 2 years. If one confesses and the other does not, then the confessor will be released immediately but the other will be sentenced to 3 years in jail. Because betraying a partner offers a greater reward than cooperating with him, the only possible action for both prisoners is to confessing (Milovsky, 2013, p.1). The dilemma here is that the “rationality” to maximize individual’s gains in fact created a worse outcome.

       Business practices in many situations are faced with the similar dilemma. Lacking of complete information about the other competitors’ or business partners’ intentions, agreements between two parties are unlikely if each party has an incentive to defect in order to maximize their own gains (Alfredson & Cungu, 2008, p.12). For example, let’s assume that the wine market in a small town is dominated by only two wine producers A and B. Without knowing each other’s action, two wine producers may simultaneously adopt low price strategy to fight for a maximum individual profit. Even though each company could have higher profits without any price promotion. If there is only one round negotiation and the goal for two parties is to capture all gains, then negotiators usually will hold back information and choose to not cooperate. This can help to explain why negotiators often have non-cooperative behaviors in one-shot deal.

       However, in real life, business negotiations often consist of many rounds and those deals are often long-term oriented. In these cases, defecting will not be the “dominant strategy” for negotiators anymore. Taking the classic PD game again as an example: If the original one-shot game became a repeated one or the prisoners will interact with each other again in the future, the outcome can be changed in a significant way. Assume that after the first-round game, and the prisoner either are freed or are released from jail they will commit another crime and the game will be played again. In this situation, in the first round the prisoner may think that they should not confess because if they do not their partner will not punish him by confessing in the second game (Levine, 2001). In 1980s, political scientist Robert Axelrod (1984) conducted a repeated version of the PD game. In this game, the total number of rounds N is random and unknown to the players. Axelrod discovered that players have an incentive to cooperate when they know they may meet again. Because repetition increases possibility of being rewarded or punished in the future for current action, the players in repeated game learned to see the advantages of long-term cooperation over short-term defection (Levine, 2001). Similarly, negotiators should understand that in a long-term business relationship, altruistic strategies are more likely to help companies to achieve better outcome than greedy strategies (Axelrod, 1984).

       But how can a negotiator to make his counterpart act in a cooperative way? What if his counterpart defects in some round? The repeated PD game can better help negotiators to adopt proper strategy in business negotiations. Using a computer tournament, Axelrod founded that the Tit for Tat (TFT) strategy is the best approach to help the players to achieve the optimal outcome. In this strategy, it involves cooperating on the initial round and then mirroring whatever the other player did in the next round. In a long-term business relationship, TFT can be a very effective strategy for negotiators to maximize their total benefit since negotiators can signal their intentions with words and actions. Since each party knows as long as they cooperate, their counterparts will cooperate as well. According to Axelrod, there are four key elements work together make TFT a good strategy:  (1) It was cooperative, but (2) willing to retaliate. (3) If after retaliation the opponent started to cooperate, then Tit-for-Tat was forgiving. (4) Finally, it communicated by its actions a clear and consistent message. In this way, TFT has the best chance of eliciting not only long-term cooperation, but short-term cooperation as well. Let’s go back to the example of the price competition between two wine producers Following the TFT strategy, the business negotiator of wine producer A should:  

1. Open negotiation in a cooperative way: Express the willingness of cooperation and set a high price  
2. Retaliate only after bargaining partner has responded to his cooperative action with a competitive one: If producer B set a low price in one round, A should set a low price to punish B in the next round.
3. Be willing to forgive after one act of retaliation: If B gave up the low price strategy and go back to the high price, A should forgive B and also go back to the high price.
4. Be clear and consistent on his behavior: A should clearly tell B in advance that he will stick to high price as long as B does, but will adopt the low price strategy if B betrayed him. Furthermore, A’s action should be consistent to his promise.  

        From a different angle, looking at the differences between negotiations process and PD game can provide business negotiators with more advantages to break negotiator’s dilemma:

        Firstly, before business negotiations, negotiators usually have time to prepare or have opportunities to have pre-interactions with their opponents. During this period, negotiators should prepare well and identify their goal clearly. If negotiators want to create value and look for a long-term business relationship, they should focus on the mutual interest with their other opponents instead of purely maximizing their own interest.