Consider the following three-stage duopoly game. There are two firms in the market: Firm 1 and Firm 2. In the first stage, a first-price auction is conducted to determine the order of moves. The firm with the highest bid (first mover) pays a cost equivalent to its bid and chooses its action in the second stage. After observing this action, the other firm (second mover) chooses its action in the third stage. When there is a tie in the first stage (both firms submit the same bid), a coin is tossed to determine the winner, and only the winner pays its bid. Each firm has the following three possible actions: small (expansion), medium (expansion) and large (expansion), and the payoffs they obtain in the market (not the final payoffs yet) are shown below: The second mover Small Medium 16, 12 Medium 18, 8 19, 7 13, 10 14, 11 14, 12 Large 9, 9 10, 13 12, 10 Small The first mover Large The final payoff is equivalent to the payoff obtained in the market minus the cost (if any) paid in auction. In the unique subgame perfect Nash equilibrium (SPNE) of this three-stage duopoly game, both firms will bid $ in the first-stage auction.