Abstract. We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic information about the state process and the other controller's past actions and observations. This leads to a dynamic game of asymmetric information among the controllers. Building on our earlier work on finite games with asymmetric information, we devise an algorithm to compute a Nash equilibrium by using the common information among the controllers. We call such equilibria common information based Markov perfect equilibria of the game, which can be viewed as a refinement of Nash equilibrium in games with asymmetric information. If the players' cost functions are quadratic, then we show that under certain conditions a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. We also show through an example that there could be other Nash equilibria in a game of asymmetric information, not corresponding to common information based Markov perfect equilibria.1. Introduction. A game models a scenario where multiple strategic controllers (or players) optimize their objective functionals, which depend not only on the self actions but also on the actions of other controllers. In stochastic static games, players observe the realization of some random state of nature, possibly through separate noisy channels, and use such observations to independently determine their actions so that the expected values of their individual cost (or utility) functions are optimized. In a stochastic dynamic game, on the other hand, the players act at multiple time steps, based on observation or measurement of some dynamic process which itself is driven by past actions as well as random quantities, which could again be called random states of nature. What information each player acquires at each stage of the game determines what is called the information structure of the underlying game. If all the players acquire the same information at each time step, then the dynamic game is said to be a game of symmetric information. However, in many real scenarios, the players do not have access to the same information about the underlying state processes and other players' observations and past actions. Such games are known as games with asymmetric information. For example, several problems in economic interactions [1][2][3], attacks on cyber-physical systems [4], auctions, cryptography, etc. can be modeled as games of asymmetric information among strategic players.Games with symmetric and/or perfect information have been well studied in the literature; see, for example, [5][6][7][8][9]. In these games, the players have the same beliefs on the states of the game, future observations and future expected costs or payoffs. However, in games with asymmetric information, the players need not have the same beliefs on th...