We investigate the formation of the price of an asset negotiated in an order book. In particular, we propose a game-theoretic model in many-person games and infinite games, considering costs stemming from limited liquidity. We derive closed-form formulas for the price in terms of the realized order flow. We also identify appropriate conditions that ensure the convergence of the price we find in the finite population game to that of its mean-field counterpart. We numerically assess our results using high-frequency data from ten stocks listed in the NASDAQ stock exchange.