First Mover Fails in A Stackelberg Competition, Why?

There is an old Chinese saying, “the first crab eater makes the fortune”. Of course “crab eater” here is a euphemism to say the pioneers of an industry make better payoffs. The old Chinese wisdom is generally true. Although in some games it is better to be a second mover, in many games, such as Stackelberg competitions, the first mover invariably has an advantage of gaining higher payoffs by being the trailblazer of that area. Unfortunately, the trailblazer sometimes flounders even in a Stackelberg competition with a strong first mover advantage. Why? I garnered some ideas from a game we played in my recent business strategy class.

The game is called 21 desks and the rules are simple. There are two teams (team 1 and team 2), and 21 desks in the classroom. Each team takes turns to take out one, two or three chair(s). Whichever team has the last one, two or three chair(s) wins the game. The game is a classic Stackelberg competition – the first mover chooses a desired quantity, the second mover follows with a response, but the first mover invariably wins the game because of the first mover advantage. Regardless of how the second mover responds, the first mover has a strategy that leads to the victory of the game. In the language of game theory, it is best response (BR). Luckily, my team (team 1) played the first move, but unfortunately, we lost the game despite having the advantage.

What is the first mover advantage of this game, and what should be the BR of the first mover? Let us solve the game. The total number of chairs is 21, each team takes out one to three chair(s) each time. If team 1 brings the number of chairs down to four, five, or six before team 2 chooses their number, then team 1 wins, vice versa. We can quantify the best response as below:

Let x = number of chairs team 1 takes out, y = number of chairs team 2 takes out. The winning strategy is 4 ≤ x + y ≤ 6. Using backward deduction, the lowest number of chairs that team 1 can win the game is 4, we can say the BR for team 1 is x + y = 4. No matter how many chairs team 2 takes out, the best response of team 1 is to take out 4 - y chairs. Easily enough, the numbers that player could win this game are 4, 8, 12, 16, and 20. Whichever team can bring the chairs to any of these numbers, and respond with x + y = 4 onwards, will win the game. With a total number of 21 chairs, of course the first mover, in this case, is my team has the advantage to first bring down the number to 20. Notwithstanding the number of chairs team 2 takes out, as long as my team best responds with 4 – y chairs, we would have invariably won the game.

Regrettably, it was not the case, and it is not uncommon that organizations fail despite the first mover advantage in real life. Why? A few reasons I garnered.

Lack of perceptual acuity – when leaders of organizations lack the ability to foresee the future changing business climate, companies fail. Nokia, as an example, the company forfeited dominance in the mobile industry because the company failed to adapt the rise of smartphones.

Business myopia – Businesses tend to maximize their short-term profit and ignore the importance of R&D that is necessary to thrive in the long-term. TeliaSonera, the Swedish telecommunication multinational that first provided 4G networks, lost in the 5G race as a pioneer. Its R&D expenses in 2022 was roughly US$ 90 million, less than 4% of Huawei’s R&D expenses in 2022 of US$ 23.33 billion.

Innovation paradox – Companies that are profiting greatly from their current technologies are sometimes less willing to innovate. Take hard drives as an example. IBM first developed the hard drive as an external storage solution. However, like the flamboyant flowers in spring that bloom briefly, it was soon replaced by cloud storage. Profit from hard drive? Exterminated.

Corporate incompetence – when people who are incompetent to identify the best strategies and unfortunately are the decision makers, the organization is doomed to fail. For instance, the team I was in for the 21-desk game. Take the team as a small corporation, some people were eager to be the decision makers but neither have come up with the right strategy, nor have the ability to listen, even with the first mover advantage, the team lost. In real life, when organizations promote the wrong people, which can inevitably lead to disastrous outcomes.