EC936: GAME OF STRATEGY (MBA SUMMER SCHOOL)
TOPIC: GAME THEORY ANALISYS ON PRICE WAR BETWEEN ED-TECH
ORGANIZATION’S
NAME: SHAKTI RASTOGI
REGISTERATION NUMBER: 202190559
COURSE: MBA (Full Time – Lochan21)
1. Introduction
In this assignment, we are trying to analyse cut-throat competition among two online Ed-Tech players. It is
one of the unexploited industries. As education begin the importance, price war among different firms in
this industry is cut-throat. Through, this article my attempt is to use the science of game theory to discuss
about competition and analyse the possibility of price coordination. We want the organizations to come out
of price war and move the focus of competition to technology and innovation. Firm should be rational about
marketing strategies, must avoid destruction caused due to market competition, and should avoid loss of
customer because of high prices.
In this article we limit ourselves to two-players: VEDANTU & UNACADEMY. In this we will try to understand
the strategic interaction between both the players. Being the education giants in India, unacademy started
providing online content at a lower cost, so it’s up to vedantu either to lower the prices or keep selling the
product at the same cost. They will act as players, and we have considered their payoffs in terms of units
being sold by both the firms when we have high price and low price. This game is popularly known as Price
war game. It is an infinitely repeated version of prisoner’s dilemma, and we are pre assuming that in
prisoner’s dilemma, we get Nash equilibrium when both firms defect, and we will try to analyse what
happens when it is repeated infinitely and how both the organizations can cooperate with each other.
2. BUILDING THE GAME THEORY
As stated previously “prisoner’s dilemma “can easily indicate the ongoing price war between firms. finite
time coordination game between 2 players which gives either Cooperative- collective rationality or noncooperative- individual rationality. From the matrix we can observe that both players can get better payoffs
when they cooperate, but they end up defecting each other because of human selfishness or fear of betrayal,
they follow the path of non-cooperation. We can say each prisoner gets higher pay off by defecting each
other.
In price war, assuming that these two are two oligopolistic firms in the market and sell homogeneous product
like online content, classes. Both firms are trying to acquire majority stake in online learning industry to earn
monopoly and greater profits. In the meanwhile, the game process meets the following two characteristics
as:
1) Complete Information: pricing behaviour of the players is public, and consumers along with
competitors can easily get the other information’s associated to prices.
2) Repeated games: it is an endless repeated game. Price keeps on changing depending on volume &
variation because of which prices will vary time to time, it becomes a repeated endless game.
Now, to understand basics of the model we will try to understand it using designing a payoff matrix. Now,
we assumed that, if both the players are taking high prices-policy, both will reap the benefits of 100 units; if
both players lower the prices, they get benefited with 50 units individually; if vedantu doesn’t lower while
unacademy does, then vedantu: 30 units, unacademy: 120 units; while VEDANTU lower while UNACADEMY
doesn’t lower then vedantu: 120 units and unacademy: 30 units.
The payoff matrix is shown below:
To maintain and expand the market share, both players have two choices: keep price or lower the price and
keep repeated it. From market understanding, consumers will welcome price competition because of selfbenefit. Due to enormous influence of enterprise, price-fixing cannot be bound. If one of them start playing
around with prices it brings the pricing agreement between the players on the verge of bankruptcy. It is the
individual rationality as not every player has the capacity to maintain at that price and this leads price war
among players.
Player’s end-up seeing themselves in a prisoner’s dilemma, if one does not cut the price, others will try to
cut and maximise the profit and if others does cut the prices, we will also cut the prices. Like a prisoner,
every organisation knows the results of an agreement is better, it worrisome that other players will defect,
and it is easy touch for larger price wars. As I said in the beginning unacademy came up with low-cost content
and increase sales and market share which lead vedantu and Toppr to reduce the prices and compete by
breaking the agreement of actual price among the players. They end up being part price war trap.
In prisoner’s dilemma, we know that (Cooperate, Cooperate) is the perfect Nash equilibrium, but they end
up defecting each other, while as it is sequential game, we have used backward induction Fig 3. and we got
Nash equilibrium for our payoff matrix at (Low price, Low price), which is called sub game perfect Nash
equilibrium, which states that both firms will stay at harmony if they run at low prices. This outcome can be
disastrous for both, as they must lead the competition with zero profit margin leading to more cash burn
and no economic growth of the organizations. Every industry prefers a normal pricing technique strategy to
have monopoly in the market and earn profits. If monopoly is created both will get the maximum chunk of
the profit. In such cases the prices go on the higher end.
In our Fig 2, we have a unique Nash equilibrium, but we might face multiple issues related to Nash
equilibrium, If we perform few amendments to our payoff matrix considering facts if unacademy decreases
its price, then consumers will hope vedantu will also decrease its course prices then the focus of the
organization will move to low cost rather than profit generation. Then this leads low profits one rather than
rising profits. We get the following payoff matrix as Fig4.
In the above fig 4, we will use the same backward induction technique and found out that, we have 2 Nash
equilibrium this time at (High price, High price) and (Low price, Low Price). As (High price, High price) will be
the best in sense efficiency. reference
(https://people.math.umass.edu/~lr7q/ps_files/teaching/math456/lecture3.pdf, n.d.).
. As both the education firm decision drivers are rational and because of collective rationality among the two
we have no war on prices. As the best choice one firm depends on the other firm in this game.
From this we can make few conclusions as:
1) Cooperation among both the players is best possible option if they take consideration of others
player interest too and put emphasis on collective rationality.
2) Non-Cooperative equilibrium put more focus self-interest and individual rationality.
Prices are a strategic agreement between the firms and their actions related to prices. Thereafter the firm is
directly involved into business, and it is being assumed that this agreement will be acknowledge in the
business activities. We see price coordination being an important element but is not being paid that
importance as price coordination lacks transparency and legitimacy. As it majorly works as a conspiracy
rather than as an agreement. Now, we will try to analyse price-coordination in the education industry.
Based on above assumptions, prisoner’s dilemma model, if we assume that it is repeated endless time and if both
players have patience, the Nash equilibrium is at (betray, betray). In price war game if it is repeated infinite time,
equilibrium state we get is (High Price, High Price) can be obtained. Based on this we will initiate “grim trigger
strategy”. It is a severe punishment in comparison to “tit-for-tat”. We will consider two points for this:
1. Start selecting high Price.
2. Select high price until one player end up with low price and choose low price thereafter.
We are assuming that grim strategy is Nash equilibrium and n is discounting factor and the value of discounting factor
remains same for both players. As per fig2, understanding the chronology if unacademy chooses low price and
increases its market share by selling 120 units whereas initially vedantu was running at high price with 30 units but
after observing the step taken by unacademy, vedantu took an opportunity to change its direction of working from
high price to low price for forever afterwards as a punishment for unacademy. This will lead to decrease in share for
unacademy from 120 units to 50 units in the later part and increase in share for vedantu from 30 units to 50 units.
If we meet the above criteria that is n>=2/7, then vedantu need not to opt for low price and unacademy will not select
the low price. As vedantu will still “grim strategy “and no low price first. As a punishment after understanding vedantu
strategy unacademy will never choose the low-price strategy in future. If vedantu end up choose the low-price strategy
first and for forever, unacademy will initiate “grim trigger strategy” and can earn 50 at the later stage. There is no
other strategy through which unacademy can earn more and makes it a much suitable option. Similarly, “grim trigger
strategy” would be an optimal solution for vedantu too. Hence the strategy would be Nash equilibrium and sub-game
perfect Nash equilibrium.
Now we are assuming that each player vedantu and unacademy has the possibility to stay irrational by (a) and rational
as (a-1). Through this we are trying to justify that the choosing low price is not the best-case scenario under “grim
trigger strategy”.
Equation1: If vedantu adopts low price strategy after understanding unacademy has selected low price first at t(time)
at t=1, then at beginning of t=2, they both will choose low price until t>=2. Whereby maximum earning for unacademy
would be: 120+70(n)+70n2 +…+70nt.
Equation 2: If unacademy opts high price till T time, but vedantu opted to defect with low price in t-phase and move
to selling at lower price then: a*100*T+(1-a) *{(30(n)+ 50(n2) +...+50(nT-1) +50(nT)}.
If equation 2 > equation 1, then this strategy is better than the one selected. Discounting factor is known when the
time interval range is greater than length of the range, rational people don’t end choosing the low-price strategy, no
matter how small (a) is. If t=1 which will be the choice of rational people, this shows that if we opt grim trigger strategy,
we can avoid a price war between vedantu and unacademy and no one will opt for price reduction initially. We could
conclude that competition is the mainstream while cooperation between firms takes back-benchers seat. But to
pursuit for higher profits, various price collusions are available to manage these price coordination’s. But it becomes
very difficult for the organizations to sustain these collusions and monitor them as at the end of the day it will act as a
conspiracy and might defy others to opt a strategy which can get them some sort of benefits.
Application of PMG (Price Matching Group)
To solve the problem of collusion we can use PMG technique which is “price matching Group technique”. Where both
will try undercut each other’s incentive. If both firms provide PMG, then it is the perfect Nash equilibrium. Consumers
pay the lowest price available in the market, but the available prices are higher in the presence of PMG.
We could conclude that both vedantu and Unacademy have a cut-throat price competition, it will help both the
organizations i.e., vedantu and unacademy to grow and gain a unicorn club tag and consumer gets benefitted by
receiving education at cheaper cost. Excessive competition can decline the benefits, so both should avoid playing at
lower cost and should take positive ways to avoid getting trapped in price war. The best possible way of avoiding the
price war is to follow price group matching. Both the firms should start focusing more on content, deliverability, results
and feedback rather than price, It is just the primary stage of market competition.
References
https://people.math.umass.edu/~lr7q/ps_files/teaching/math456/lecture3.pdf, n.d. In: people.math. s.l.:s.n.
https://people.math.umass.edu/~lr7q/ps_files/teaching/math456/lecture3.pdf, n.d. Lecture 3. In: s.l.:s.n.
http://mba.tuck.dartmouth.edu/pages/faculty/robert.shumsky/gametheorymodels.pdf
http://www.sfu.ca/~rda18/302_8_SequentialGames.pdf
https://www.youtube.com/watch?v=5HFGn5FScd4&ab_channel=MattBirch
https://www.investopedia.com/financial-edge/0810/the-pros-and-cons-of-price-wars.aspx
https://www.maa.org/sites/default/files/pdf/ebooks/GTE_sample.pdf
https://www.business-to-you.com/introduction-game-theory-the-basics/
https://www.economist.com/finance-and-economics/2015/02/12/guaranteed-profits