Analysis of dynamic game played with inaccurate demand beliefs

Abstract This paper studies the impact of inaccurate demand beliefs on dynamic quantity-setting market games. The conventional assumption that players share a uniform and accurate demand model in game is relaxed by a more realistic model—players individually make their subjective demand estimation possibly with errors. A dynamic game with such subjective demand belief for two heterogeneous players is built. Based on this model, the impact of demand belief errors on the game’s equilibriums and their stability is investigated. The results shows that the stability region is not only determined by the parameters of the system configuration and the bidding adjustment-as pointed out in conventional model, but also by the player’s imperfect knowledge about the market. Thus new dynamic behaviors and instability may arise given an original error-free system (where all players are assumed to have perfect and uniform knowledge about the market). It is suggested that in order to avoid possible system instability, the design of players’s adjustment speed, and the possible demand belief errors from different players must be taken into account. Moreover, this paper points out that the various behavior patterns of players have different influence on the stability regions and corresponding dynamic characteristics of system equilibriums. The changes of players’s profits and customer surplus induced by inaccurate beliefs are also studied. The stability analyses, dynamics behaviors, and system performance in steady state are validated with a set of numerical experiments.