Boundedly Rational Agents in Sequential Posted Pricing

We consider the well-studied sequential posted pricing scenarios. In these scenarios, an auctioneer typically learns the value distributions of all agents as prior information and then offers a take-it-or-leave-it price to each sequentially coming agent. If the value distributions are correctly learned, the dominant strategy of each agent is telling the truth. However, an agent could manipulate her value distribution to exploit the auctioneer. We study the behavior of sophisticated agents predicted by two prominent bounded rationality models: the level-fc and the cognitive hierarchy models. We begin with analyzing the structure of the optimal reported distributions and then provide algorithms to compute the optimal distributions for each model. In the continuous scenarios, we show that both models are ill-defined by some examples. Moreover, we evaluate both models in discrete scenarios with different numbers of agents, different minimum units of the values, and different risk tolerances. The empirical results and a brief discussion about the Bayesian Nash equilibrium of the experimental scenarios show that both the level-fc model and the equilibrium suggest the highest possible prices. In contrast, the cognitive hierarchy model suggests low prices. The level-fc model and the equilibrium somehow explain the “winner’s curse” in online markets. The models and the equilibrium fail to explain that the same item could have different prices in different shops. To explain the different-price phenomenon, we suggest trying other bounded rationality models for agents and/or considering the auctioneers with bounded rationality. © Shanghai Jiao Tong University 2023.