Biblio

We analyze a dynamic oligopoly model with strategic sellers and buyers/consumers over a finite horizon. Each seller has private information described by a finite-state Markov process; the Markov processes describing the sellers' information are mutually independent. At the beginning of each time/stage t the sellers simultaneously post the prices for their good; subsequently, consumers make their buying decisions; finally, after the buyers' decisions are made, a public signal, indicating the buyers' consumption experience from each seller's good becomes available and the whole process moves to stage t + 1. The sellers' prices, the buyers' decisions and the signal indicating the buyers' consumption experience are common knowledge among buyers and sellers. This dynamic oligopoly model arises in online shopping and dynamic spectrum sharing markets. The model gives rise to a stochastic dynamic game with asymmetric information. Using ideas from the common information approach, we prove the existence of common information based equilibria. We obtain a sequential decomposition of the game and we provide a backward induction algorithm to determine common information-based equilibria that are perfect Bayesian equilibria. We illustrate our results with an example.

We formulate and analyze a general class of stochastic dynamic games with asymmetric information arising in dynamic systems. In such games, multiple strategic agents control the system dynamics and have different information about the system over time. Because of the presence of asymmetric information, each agent needs to form beliefs about other agents’ private information. Therefore, the specification of the agents’ beliefs along with their strategies is necessary to study the dynamic game. We use Perfect Bayesian equilibrium (PBE) as our solution concept. A PBE consists of a pair of strategy profile and belief system. In a PBE, every agent’s strategy should be a best response under the belief system, and the belief system depends on agents’ strategy profile when there is signaling among agents. Therefore, the circular dependence between strategy profile and belief system makes it difficult to compute PBE. Using the common information among agents, we introduce a subclass of PBE called common information based perfect Bayesian equilibria (CIB-PBE), and provide a sequential decomposition of the dynamic game. Such decomposition leads to a backward induction algorithm to compute CIB-PBE. We illustrate the sequential decomposition with an example of a multiple access broadcast game. We prove the existence of CIBPBE for a subclass of dynamic games.

We formulate and analyze dynamic games with d-step (d ≥ 1) delayed sharing information structure. The resulting game is a dynamic game of asymmetric information with hidden actions, imperfect observations, and controlled and interdependent system dynamics. We adopt common in- formation based perfect Bayesian equilibrium (CIB-PBE) as the solution concept, and provide a sequential decomposition of the dynamic game. Such a decomposition leads to a backward induction algorithm to compute CIB-PBEs. We discuss the features of our approach to the above class of games and address the existence of CIB-PBEs.