# Using Game Theory to determine the optimal product launch time in a competitive scenario.

Game theory is the analysis of strategies dealing with competitive situations where the outcome of a participant’s choice depends heavily on the actions of the other participants.

In this post, I will analyze the optimal time for a company to launch its (new) product in a competitive scenario.

**The story: **Imagine two competitors, company A (cA) and company B (cB), readying similar new products that address the same consumer need/want. The two companies are on the verge of launching their respective products. Each company is aware of the other’s product and the implications that the competitor’s launch will have on that of its own.

If you launch too early, you’ll miss the market. Launch too late and the competition will eat you.

**Factors to Consider:**

(a) If a company — the ‘first-mover’ — launches its product before the other, its product will have a higher probability of attracting customers and building early market share in that category through brand recall.

(b) The company launching first may do so ‘prematurely’, i.e., before the product offering is fully ready, and so risks misreading the market or being overtaken by the competitor, that now has an opportunity to offer a more refined offering based on market feedback. In fact, poor market response to the first-mover’s launch may adversely affect its brand in the longer-term and offer the second-mover an opportunity to defer its launch plans around the new product entirely.

The consultant Jack Trout has found that American families, on average, repeatedly buy the same 150 items, which constitute as much as 85% of their household needs; it’s hard to get something new on the radar.

Therefore, it is vital for a company to launch a new offering at the optimal time in order to maximize its chances for market success. Companies may use game theory to ascertain whether they ought to be a first-mover in launching a new product in such a situation, and exactly what time to choose for the product launch. I walk through this process below.

The adjoining graph shows the probabilities of ‘market success’ for the two companies on launching their product at day ‘d’. The x-axis on the graph depicts the ‘number of days before full-readiness’, starting from 0 (fully ready for launch) and moving higher (under-prepared for launch). Thus, the probability of success for both companies on day 0 is 1. In this graph, when I refer to day *n,* it means the *nth* day before full-readiness (d=0).

**Assumptions:**

(a) Only one company can do a product launch in a day

(b) Success Probabilities of cA and cB are known to both the companies

**The problem: **Clearly, cA has a higher probability of success than cB after day 0. cA will find it rationally possible that cB will launch a day prematurely (d=1) to gain the first mover’s advantage. cB, working this through itself, will assume that cA will choose to launch a day prior to that (d=2) to preempt cB from launching and garnering more market share — and so on and so forth. Now as we can see, this is more complicated than it first seemed.

#### Walk through till optimal launch day:

On the nth day before launch*, *if cA knows that, on the next day (i.e., n-1 days before launch), cB will **not launch**, then cA will decide that they, too, should *defer their launch date,* as they will be able to enhance their offering and will stand a better chance of market success the day after next (n-2 days before launch).

On the other hand, on day *n, *if cA knows that cB **will launch** the product the next day, then cA’s action will depend on the probability of its own market success on that day **and **the probability of *market failure *of cB the following day. Specifically, cA should proceed with the product launch in this case if its probability of market success is more than or equal to the probability of cB’s market failure on the next day.

=> PcA(n) ≥ 1-PcB(n-1)

=> PcA(n) + PcB(n-1) ≥ 1 ….(i)

Therefore, till the probability of cA succeeding on that day and the probability of cB succeeding on next day is ≥ 1, cA should not launch. This applies for cB as well.

For example, if on the *nth* day cA is thinking of launching. If cA knows that cB is not going to launch tomorrow, then they should not launch. However, if cA knows that cB is going to launch tomorrow, but if inequality (i) does not hold then cA should still not launch. This is known as the *dominant strategy *(i.e., “cA **should not launch”** is the company’s ** dominant strategy** at this point).

This continues every day (assuming that only one company can launch in a day) till the inequality (i) is true. Therefore, till the inequality is not true, the dominance argument says that, no matter what happens, the companies should not launch. Let the day when the inequality holds be **d***.

#### Backward induction:

Now at d*, if cA knows that cB will not launch tomorrow then cA should also *not launch*. On the other hand, if cA knows that cB will launch next then cA *should launch *(because inequality (i) is satisfied).

From this point (day) forward, the companies need to use backward induction. Backward induction is the process of reasoning backwards in time, starting from the very end of the problem or situation.

For example, let’s say, at d=0 cB is contemplating whether or not to launch. Here, cB will launch (as P*cB is 1*). At d=1, cA knows that in the next day cB will launch and succeed for sure and therefore cA will choose to launch.

At d=2, cB knows that the next day cA will launch, cB will launch if and only if P*cB*(2)* ≥ *1-P*cA*(1)* **(ii)** — *this depends on the quality of the product and other factors which may or may not lead to market success for the company. If inequality (ii) is false, then cB will not launch on day 2, and cA will launch the next day and succeed. However, if inequality (ii) is true, then cB will launch on day 2.

At d=3, cA will launch if P*cA(3) ≥ 1-PcB(2) is true.* Otherwise, PcB launches first at d=2.

Therefore, backward induction takes us to d*, where it was cA’s turn to decide to launch. Generalising the previously mentioned inequalities we get:

PcA(d*) ≥ 1-PcB(d*-1)

From this we can deduce that the cA should launch at d* if the above inequality holds. As, I previously mentioned, d* is the point at which this inequality **DOES** hold, therefore, whichever company is thinking about launching on day d* **SHOULD** launch. This is the optimal launch day.

Therefore, the perfect time for cA or cB to effect their respective product launch depends not only on their individual probabilities of market success but also on the sum of their combined probabilities of market success.

#### Why do some companies launch prematurely:

From the above examples, we can see that the time of a product launch is a key factor in determining market success of that offering. One of the reasons that companies sometimes launch products prematurely (i.e., before they are fully market-ready) is due to an **‘overconfidence bias’.**

The overconfidence bias is a well-established bias, which leads someone to over-rate his/her abilities. This may lead the company to overestimate their product’s need and value to the market.

individuals are more prone to overestimate outcomes to which they are highly committed (Weinstein, 1980)

**Citations:**

Hall, J. S. (2014, July 31). Why Most Product Launches Fail. Retrieved March 10, 2017, from https://hbr.org/2011/04/why-most-product-launches-fail

Using Game Theory to Time the Perfect Product Launch. (n.d.). Retrieved March 10, 2017, from https://blogs.cornell.edu/info2040/2014/09/14/using-game-theory-to-time-the-perfect-product-launch/

Bonatti, A. (n.d.). Game Theory for Strategic Advantage. Retrieved from https://ocw.mit.edu/courses/sloan-school-of-management/15-025-game-theory-for-strategic-advantage-spring-2015/lecture-notes/MIT15_025S15_Lec_7.pdf

Nichol, P. B. (2017, February 21). The innovation duel: game theory and product launch timing. Retrieved from https://leadersneedpancakes.com/innovation-duel-game-theory-timing/

Polak, B. (2013, October 30). Retrieved from https://www.youtube.com/watch?v=M3oWYHYoBvk

Weinstein, N. D., ‘Unrealistic optimism about future life events’, Journal of Personality and Social Psychology, Vol. 39, 1980, pp. 806–20. Retrived from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.535.9244&rep=rep1&type=pdf