We propose the full information minority game (FIMG) in which agents perfectly recognize their impact on the market. For reflecting the impact of agents, we introduce an actual total action and an actual payoff which depend on the agent’s strategies. Unlike the perpetual fluctuating dynamics of the standard minority game, the dynamics of the FIMG settles into one of four steady states after a transient time. We classify steady states of the FIMG and analyze their characteristics. In most cases, the total payoff is maximized, and the total action settles into a periodic state. For measuring the degree of cooperation on the FIMG, we calculate a fraction of total payoff maximization and a mean relaxation time for the dynamics to settle into a steady state whose total payoff is maximized.