Repeated Bargaining with Long-Run and Short-Run Players
In class so far, our discussion of trading has been limited to a single trade between two parties. In Gambling Reputation: Repeated Bargaining With Outside Options, the authors Jihong Lee and Qingmin Liu extend our classroom discussion by considering repeated bargaining. Specifically, they address the bargaining relationship between long-run players (such as large firms) and short-term players (such as customers or employees). The short-term players are similar to the players we discussed in class; their objective is to maximize payoff from a single encounter. In contrast, the goal of the long-term players is to maximize payoff over time at the expense of occasional smaller payoffs for single encounters along the way. These players aim to accomplish their goal by establishing a reputation for the company or firm; building a long-term reputation requires the firms to sometimes take “inefficient random outside options” that result in smaller payoffs for the single encounter at hand. The outcomes of a single trade encounter are similar to what we learned in class. If a deal is reached, a trade between the two partners is conducted. If not, “the players invoke an uncertain outside option (e.g. through a court verdict), which is inefficient due to a deadweight cost.”
The authors posit that a reputation equilibrium maintains two threshold levels of reputation: 0 < p* < p** < 1. A reputation above the p** value indicates that “the long-run player extracts the full benefits of reputation.” In other words, the long-run players have achieved their goal of establishing a high reputation and are now reaping the rewards. A reputation between the two thresholds, p* and p**, indicates that a long-run player is still trying to achieve their ideal reputation. At this point, a long-run player will reject any equilibrium demand from a short-run player. Instead, the long-run player will take the uncertain outside option which ends up having either a positive or negative influence on the player’s reputation. The strategy of long-run players in this situation is to use the randomness of these outside options to eventually reach the p** threshold and be able to maximize benefits. However, due to this randomness, it is possible for the long-run player’s reputation to drop below p*. At a reputation below p*, a long-run player only uses the outside option occasionally, reducing the “negative reputational effect of an adverse signal.”
In class, we learned about a relatively simplified version of bargaining scenarios. While this is valuable in understanding the topic, it is important to realize that in the real world, there are many factors and variations that might change how different players act. The situation with the long-run and short-run players proposed in this paper is just one of many such variations.