Game Theory

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Advanced Corporate Finance & Strategy
©Michal Kaszas
ISTI Valuation & Strategy Specialist
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Welcome!

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The question is not: “to risk or not to risk?”
“The question is: where do you put your big bets? Coz if
you don‘t place a big bet, you are never going to achieve
exceptional results. Where do you place your big bets and
bound your risks at the same time?”
Make the right bets!

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Know WindowKnow-Window

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https://coggle.it/diagram/WI39NGMMG6JeK03F

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ROG on R&D Case

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The (Simple) Option to Defer
• The most valuablefor
irreversible investments
• Proprietary
• Extraction indust.
• Farming etc.
• Shared
(exogenous competition)
• High-tech indust.

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The (Simple) Option to Defer
Hold my hand valuation (License)
Net Present Value w Scenarios
Option Valuation is risk-neutral
Certainty equivalent
What is INVEST NOW vs WAIT-AND-SEE value?
What is really of interest in an uncertain world is not the value of investment per se, but
rather the value of an opprotunity to invest
Actual Probability = 50%
CoC = 20%
Risk-Free Rate = 8%
Investment Outlay 80 MIO

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Sony & Phillips both consider developing CD technology:
1. Sony goes alone
2. Sony waits and shares the payoffs 50/50
Option value of the incumbent got eroded by exogenous
competitive entry – Game Theoretic element
A firm anticipating competitive entry, tends to commit to
excess capacity building to preempt the market
In the absence of the exogenous competition, firm might choose
to wait and enjoy the flexibility benefits
Shared option to defer
Exogenous competition

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Compound Options

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R&D Valuation
PV(t=0) of Inflows = 852 MIO USD
PV(t=2) of Inflows = 1 127 MIO USD
PV(t=0) of Outflows R&D = 63 MIO USD
Investment outlay (at t=2) = 1 200 MIO USD
PV(t=0) of Investment outl. = 1 109 MIO USD
𝜎 = 0,41
u = e%
= 𝟏, 𝟓
d =
1
u
= 𝟎, 𝟔𝟕
CoC= 15%
RF Rate = 4%
3 steps to value a compounded option
1. Construct an event tree of the underlying values
2. Make decision based on conditional payoffs
3. Calculate the PV of the conditional payoffs

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Smit‘s regular wisdom slam
Fancy Haircut-Soren

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Step 1. Event tree

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Step 1. Extended
Decisions we face:
1. Should we undertake the R&D?
2. Should we invest afterwards?
Flexibility element is absolutely crucial!
Without it only a fool would undertake
R&D ventures.
Notice the similarity with call option:
Time to maturity: 2yr (European)
Exercise price: 1 200 MIO USD
Vega(Volatility): captured by sigma 0,41
The optimal decision is determined at the
end-node!
Remember, the worst possible outcome
after the exploration can be 0!

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Step 2. The Optimal Decision

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Step 3. Calculate PV of the Payoffs
𝑝 =
1 + 0,04 − 0,67
1,5 − 0,67
= 0,45
𝐶 =
𝑝 ∗ 𝑉:
+ 1 − 𝑝 ∗ 𝑉;
1 + 𝑟
𝐶 =
0,45 ∗ 717 + 0,55 ∗ 0
1,04
= 310

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Winners Curse
If the average bid is accurate, than the highest bidder is the sucker!
By definition, winners in auction are lead to overpay
The average bid is unimportant
The more uncertainty there is, the more likely the winner is to overpay
UTS licences – all overpaid!

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Smit‘s regular Wisdom Slam

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Zero-Sum games
Oskar Morgenstern John von Neumann

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Concept of Strategic INTERdependence
Zero-Sum Games – Strategic Decisions
“Making a killing” mindset vs. Co-Opetition mindset
Win-Win solution
Players | Actions | Timing | Payoffs
Game Theory

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• Rationality
• Players aim to maximize their profit
• Players are perfect calculators
• Common knowledge
• Each player knows the rules of the game
• Each player knows that each player knows the rules
• Each player knows that each player knows that each player knows that each
player knows that each player knows the rules
• “Thinking about thinking converges to an equilibrium”
Assumptions

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1. Find Dominant strategies
2. Eliminate Dominated strategies
3. Find Nash equilibrium in pure strategies
4. Find Nash equilibrium in mixed strategies
5. Use backward induction to solve sequential games
6. Find a sub-game perfect equilibrium
7. Use real options or certainty-equivalent valuation in backward inductions
for sequential games under uncertainty
Solving the game

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Innovation Race
Finding Dominant Strategy
Prisoner‘s dilemma
1st mover advantage eroded the optional value

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Simultaneous Innovation
„Grab the Dollar“
Patent Races – Competitors make parallel investments
Usually only 1 standard sticks! (VCR, VHS, DVD)

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Sequential Innovation
Backward Induction
Burning the Bridges
Signalling function of commitment (credibility!)
Intel preempted 80% of the microprocessor market

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Simultaneous Innovation
under Incomplete Information
Firm does not know it‘s competitor‘s precise characteristics but estimates it correctly
Nash-Bayesian Equilibrium
In NB eq. Players correctly anticipatethe strategy for each type of the other player.

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Most favored customer clause
“All talk, no action” – raising venture capital
Incentive Alignment – comp scheme is a perfect GT example
Commitment

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Outset:
• The plant is currently idle
• Prospective buyer has interest in land (unlikely to pay very much)
• Mrs. Duncan (your CEO) asks you to prepare an assessment of the sale
(get it done until next morning‘s planning meeting )
Case:
• United has 2 plants
• 8 000 tons per year
• 2 000 tons per year – currently idle (for sale)
• Associated Cement (our competitor) has only 1 site 20 000 tons per year.
• Currently the industry is in overcapacity both competitors operate on 50%
• Fixed costs negligible, Variable costs $2 MIO per 1000 ton
• Price $5 MIO per 1000 ton
United Cement Case
Plant sale

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Marketing Study findings:
• Lowering the price to $ 4 MIO per 1000 tons while Associated do nothing
• 50 % of Associated‘s customers switch to us
• Both firms lowers the price
• Each would maintain original share
You dig deeper:
• United‘s B plant has not run for a few years
• Why? Few C level managers believed the demand might go up
• You ask previous CEO why he did not sell the plant and find a capacity issue
• Industry is in chronic overcapacity!
• What will be the impact of lowering it? Can the sale of idle plant have an impact on industry‘s pricing?
United Cement Case

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Plant Sale -> Capacity Decrease -> Pricing Dynamics -> ???
Game Theory
Crack the case

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1. The first step in GT analysis is to ASK PRECISE QUESTION:
“What is the correct pricing strategy for United with and without the sale
of the plant and, given the answer to that question, at what price should the
plant be sold? “
Even with limited information and a number of simplifying assumptions, game theory can produce much
strategic insight.
Crack the Case

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2. Actions to consider
• Pricing – How two companies set prices
• Capacity – Sale of the idle plant
Crack the Case

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Crack the Case

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Should United sell & lower the price?
Crack the Case
1. Find Dominant strategy
2. Eliminate Dominated strategies

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What will Associated do?
Crack the Case
We calculate thair conditional profits and find out

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UNITED is willing to PAY THE BUYER J to take the plant
off its hands and disassemble it!
Case is Cracked!

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Case Debriefing
Why the price decrease resulted only in $ 1 MIO increase in profit?
• Marketing indicated that 50% of customers would leave Associated
• Nevertheless 50% of 10 000 tons = 5 000
• Since we sold the Plant B we have 8 000 tons capacity and had 5 000 tons
sales prior to selling Plant B
• Hence, we accommodate only 3 000 tons from Associated
The sale of the idle plant is effectively a credible commitment by United
not to steal too much demand if it has a lower price than Associated.

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A one-shot game analysis of the pricing dynamics of the current situation
before the sale of the plant suggests that United has a dominant strategy
to lower its price. Associated anticipates this dominant strategy and
chooses its best response to United’s lower price, which in this case is to
lower price as well. Thus, the prediction of the one-shot game with the
idle plant B is that both lower price. This is obviously not what we observe
in reality, where both companies maintain price. How did the managers
achieve this outcome? One possibility is that the multiple rounds of play
explain the difference. United and Associated compete with each other week
after week. This competitive situation is a good example of a repeated game. If
United decided to maintain price in the first round, with the credible
threat to lower the price next round if Associated decided to lower its
price, what would Associated’s best response be? If Associated believes
that United will maintain its price, it has an incentive not to lower. By using
the threat of lowering, United can facilitate cooperation and gain $15
million (every year) rather than the $10 million it would get in the one-
shot game.
Additional Remarks

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You know that management is conservative and know nothing about the
game theory. How would you simplify your explanation?
2nd Approach

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The Wason Card Problem
2 i e8
If the card has a vowel on one side, it must have an even number on the other!

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Firms choose quantity to be produced, market demand
determines the price (e.g. OPEC)
“Clearing price” P – customers buy everything (QA + QB)
Cournot (Q)

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While choosing the quantity, firm might not now the quantity chosen by its
competitor = prepare contingencies.
Reaction curve – “the best response curve” shows the optimal quantity to
be chosen based on the quantity manufactured by competitor
• For every output of one firm, assigns the profit maximizing output of another
Reaction Curves
Cournot-
Nash
Equilibrium

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Total outcome of 8 units is suboptimal!
If the firms could cooperate they would both manufacture
(how much units?) yielding (how much profit?)
Under competitive threat, each firm has an incentive to
increase its production!
Industry POV

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Isoprofit curves
Stackelberg‘s 1st mover advantage
Firms choose their output sequentially!
Aggressive commitment pays off. Build overcapacity!
Second mover would drive down prices if he followed Cournot-Nash eq.
1st mover should calculate with 2nd mover‘s qunatity prior to commiting.
(Prices will be affected!)

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Instead of Q firms choose Price!
In Bertrand‘s framework choosing a lower price bids down industry prices!
𝑸 𝒊 𝑷 𝒊,𝑷 𝒋 = 𝜽 − 𝒃𝑷 𝒊 + 𝒅𝑷 𝒋
The quantity sold by firm i is a negative function of its own price and
positive function of competitor‘s price.
Bertrand (P)

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With game theory a complex strategic problem can be reduced
to an analytical structure with 5 dimensions:
Players | Actions | Timing | Payoff | Backward Induction
A general criticism is that by trying to rationalize known behavior in a
stylized way, standard game theory models often fail to produce
testable predictions (the insights from the analysis can be self-evident
in stable environments ).
Particularly relevant in oligopolistic markets e.g., Unilever and
Procter and Gamble, Coca-Cola and Pepsi, or Boeing and Airbus.
When combined with real options theory novel insights can be
gained for uncertain environments.
Dr.Max | RegioJet vs. LEOex. | SAZKA vs Fortuna
Summary

Game Theory

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