Bargaining Behavior and Outcomes on Game Show “Divided”
This article summarizes data analysis done on the game show Divided, an interesting high-stakes situation for viewing a real life scenario of a more complex ultimatum game. The first part of this game has three contestants collaborate to answer trivia questions and accumulate prize money. The second part of the game is the subject of bargaining analysis; the total prize money jackpot is divided into three set values, typically A=60%, B=30% and C=10% (there are other similar subdivisions cited but I will refer to this most common one for simplicity), and the contestants first each make an individual claim as to which share they think they should get. Then, if they do not immediately agree on who should get which share, they have 100 seconds to discuss and come to a unanimous decision, and as time counts down, the jackpot also decreases until the time is up and the jackpot value is 0. According to this article, the majority (72%) of teams agree while the timer counts down, and with this, the ‘efficiency’ or bargaining is about 50%, meaning that on average, half of the original jackpot value is awarded and split between the contestants. The article partly focuses on claiming that demographics do not significantly affect competitive behavior or favorable outcomes, except for that younger contestants tend to get larger shares. The most important factor in contestants’ share claims, according to this article, is the contestants’ individual contributions to the communal jackpot, which this study rigorously defined, but basically they quantified that those who more often argued for the correct answer were better contributors and therefore claimed a larger share and ended up with a larger prize. The article also made many other intriguing conclusions, such as that making ‘hardball announcements’ (declaring that one will not back down from their initial claim) is not beneficial because it makes the bargaining process more difficult and is more likely to result in a 0 payoff outcome.
This game was clearly designed to create a high-stake, high-stress bargaining process that would be likely to cause controversy between contestants and be entertaining for viewers to watch. Since all three players must get one of the three set shares, this situation cannot be described in the typical network exchange framework because that usually depends on two people making a deal and evaluating outside options, and only one deal is to be made. In this situation, three people must make a deal between themselves, where they all know each other (have edges between all nodes) and they all have the same outside options. This results in a triangle, which we know to be unstable; if you look at the possible share values, 0.60, 0.30, and 0.10, every outcome is unstable because each pair of values adds up to less than 1. Additionally, there is no opportunity for Nash Bargaining Equilibrium, obviously because this implies that a final deal is made between only two people and there are three people here. But even ignoring this fact and assuming there can be a deal between two people, the surplus is never equally shared, since both nodes have the same outside option, and would thus require equal shares, and we know this is never the case in the game. Since the typical representation of power in a network cannot apply the same here, since all contestants know each other, it could potentially be useful to evaluate relative power using the contestants’ contribution values. Perhaps a contestant who contributed more would have ‘stronger’ ties to the other nodes, and would allot power in a relatively similar way to our current model. This would give a better prediction for the split of shares, and, as validated by the article, would especially facilitate share agreement and maximize payoff if contestants had access to quantitative contribution data.