Strengths of the Weakest-Link
The "Weakest Link" is a game show full of paradox. To increase the probability of winning, contestants should eliminate the strongest players. Yet, if it is anticipated that the best player is to be eliminated, participants do not answer questions correctly and nothing is gained. We solve a game that illustrates the Weakest Link tradeoffs and show that two equilibria coexist: an equilibrium in which players remain silent and a more entertaining equilibrium in which they give good answers whenever they can. We study the first wave of the Weakest Link show broadcast in France. Contestants vote against the weakest player and answer truthfully to the questions. They exhibit, however, myopic behavior as they do not use all the available information. The selection of one equilibrium or the other relies on how players coordinate in voting subgames. Three arguments are provided to explain observed behavior: Pareto domination, risk domination, and the "mise en scène" of the show.
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