Informational Cascades With Nonmyopic Agents

• 成果类型: Article
• 署名作者: Bistritz, Ilai; Heydaribeni, Nasimeh; Anastasopoulos, Achilleas
• 署名单位: Stanford University; University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3165483
• 发表日期: 2022
• 页码: 4451-4466
• 关键词: Bayesian learning; dynamic games; Informational cascades; perfect Bayesian equilibrium

摘要

We consider an environment where players need to decide whether to buy a certain product (or adopt a technology) or not. The product is either good or bad, but its true value is unknown to the players. Instead, each player has her own private information on its quality. Each player can observe the previous actions of other players and estimate the quality of the product. A classic result in the literature shows that in similar settings, informational cascades occur, where learning stops for the whole network and players repeat the actions of their predecessors. In contrast to this literature, in this paper, players get more than one opportunity to act. In each turn, a player is chosen uniformly at random from all the players and can decide to buy the product and leave the market or wait. Her utility is the total expected discounted reward, and thus, myopic strategies may not constitute equilibria. We provide a characterization of perfect Bayesian equilibria (PBEs) with forward-looking strategies through a fixed-point equation of dimensionality that grows only quadratically with the number of players. Using this tractable fixed-point equation, we show the existence of a PBE and characterize PBEs with threshold strategies. Based on this characterization, we study informational cascades in two regimes. First, we show that for a discount factor delta strictly smaller than 1, informational cascades happen with high probability as the number of players N increases. Furthermore, only a small portion of the total information in the system is revealed before a cascade occurs. Second, and more surprisingly, we show that for a fixed N, and for a sufficiently large delta < 1, when the product is bad, there exists an equilibrium where an informational cascade can happen only after at least half of the players revealed their private information, and consequently, the probability for a bad cascade where all the players buy the product vanishes exponentially with N. Finally, when delta = 1 and the product is bad, there exists an equilibrium where informational cascades do not happen at all.