Vicki Curtis, Jeremy Wei, Jordan Hill, Cody Rice
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Introduction to Game Theory
Non-Cooperative Game Theory
Cooperative Game Theory
Implications
Holmstrom
Reconciliation and Conclusion of Chapter 9
Article: Project Earnings Manipulation: An
Ethics Case Based on Agency Theory
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Underlies many current issues in financial
accounting theory
Models the interaction of two or more players
Occurs in the presence of uncertainty and
information asymmetry
Game theory is more complex than decision
theory and the theory of investment
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The number of players lies “in between” the
number in single person decision theory and
in markets.
In game theory the number of players is
greater than one, but is sufficiently small
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Many different types of games
 Classified as cooperative or non-cooperative
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Cooperative game: parties can enter into a
binding agreement.
Non-cooperative game: an oligolopolistic
industry is an example of a non-cooperative
game
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Constituencies of financial statement users
Both parties are aware of the other parties
reactions in making their decisions
Game theory provides a framework for
studying the conflict and predicting what
decisions the other party will make
Classified as a non-cooperative game
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RD
Since both parties know the other parties
strategy this is the only strategy pair that
each party will be satisfied with his or her
decision.
This is called the Nash Equilibrium
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Nash equilibrium suggests it is difficult to
make longer-run conclusions from a singleperiod game
Single-period is repeated from an indefinite
number of periods
Government intervention may change the
pay-offs to enforce co-operation
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No
The manager will anticipate the investor’s
move to sell at period 5 and as a result will
distort at period 4.
At this point the manager’s payoff will be 200
rather than the 180 he would receive at
period 5.
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Further to the strategy just explained, the
game would continue to unravel as both
parties anticipate that the other will end the
game on their next turn.
This goes all the way back to period 1 where
the investor will end the game and players
receive the Nash equilibrium pay-offs of the
single-period game
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Involves two or more parties co-operating via
binding contract
Two types of contracts
 Employment contracts
 Lending contracts
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A branch of game theory that studies the
design of contracts to motivate a rational
agent to act on behalf of a principal when the
agent’s interest would otherwise conflict with
those of a principal
 Main concept is principal vs. agent
Game Inc.
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Owner
 Maximize their payoff (expected cash flow)
▪ First Best: option with highest pay off
▪ Second Best: option with second highest pay off
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Manager
 Maximize their utility (expected benefit)
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Agency Cost
 Difference between first best and second best
 Must minimize this cost
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Game Inc. is a company that has a single
owner and single manager
 Owner = principal
 Manager = agent
▪ Manager gets paid $25 per year
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In this company, there are two possible
payouts:
 Good times (G) = $100
 Bad times (B) = $55
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Payout
 Represents the receipt of cash generated by the
company
 Measured by expected cashflows
▪ E(cf) = p(x1) + p(x2)....p(xz)
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Utility
 Represents the net benefit for the manager’s effort
 Measured by square root of monetary compensation
net of disutility
▪ E(u) = √(x) - D
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The manager has two choices
 Work hard
 Slack off
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If the manager works hard:
 Probability of G = 0.6
 Probability of B = 0.4
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If the manager slacks off:
 Probability of G = 0.4
 Probability of B = 0.6
Work Hard (W)
Slack Off (S)
Pay-off Probability Pay-off Probability
Good Times (G)
$100
0.6
$100
0.4
Bad Times (B)
$55
0.4
$55
0.6
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Managerial effort can increase the odds of a
high payout (i.e. $100)
 Therefore a rational owner would want the
manager to work hard
 Can be illustrated by their expected payoff:
E(G) = 0.6(100-25) + 0.4 (55-25) = 57
E(B) = 0.4(100-25) + 0.4 (100-25) = 48
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A rational manager wants to maximize their
utility
Remember:
 Greater effort results in greater cost, therefore
greater compensation must offset this
EU(W) = √25 – 2 = 3
EU (S) = √25 – 1.71 = 3.29
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Manager will choose to slack off
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Moral Hazard
 Manager will choose to slack off despite the
owner wanting them to work hard
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Owner must find a way to overcome this
moral hazard
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3.
4.
5.
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Put up with manager slacking off
Direct monitoring of managerial
performance
Indirect monitoring of managerial
performance
Rent company to manager
Share pay off with manager
Remember: Must find the option that results
in the highest pay off
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Owner allows manager to slack off
Evidently not ideal as this will not result in the
highest expected pay off
Agency Cost = 57 – 48 = 9
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Owner observes the actions of the manager
to ensure they are working hard
 Thus guarantee manager works hard (W)
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Ideally, the best option as this guarantees the
highest pay off (G)
Realistically, impossible as owners do not
have the time or resources to do this
 Results in an information asymmetry between
manager and owner (moral hazard)
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Owner were to determine the manager’s
effort based on the ending payoff
If pay off = B, owner would know manager
slacked off
Realistically impossible since there are
external factors that could effect payoff
 E.g. Recession, natural disaster, etc...
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Owner gives up the risks and rewards of
Game Inc. in exchange for a guaranteed pay
off of $51
Manager will now be willing to work hard (W)
since they take on risks and rewards
Not ideal since the pay off is below ideal
Agency Cost = 57 – 51 = 6
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Based on a performance measure, the owner
could determine the pay of a manager
 Net income is common measure
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By sharing the risks, the manager becomes
risk averse (rather than risk neutral)
 Results in manager wanting to work hard
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This is clearly most ideal option! 
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Net Income does not represent pay off, it is
an indicator of potential payoff
 While it is the best indicator, it is not perfect
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Imperfection due to:
 Estimations
 Accruals
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As a result, there is a risk of noisy (imperfect)
net income
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Due to imperfect net income, the
probabilities are now updated:
 If payoff is $100 – net income will be
▪ 80% chance of $115 (correct)
▪ 20% chance of $40 (incorrect)
 If payoff is $55 – net income will be
▪ 20% chance of $115 (incorrect)
▪ 80% chance of $40 (correct)
EU(W) = 0.6(0.8 √(0.3237 x 115) + 0.2 √(0.3237
x 40) + 0.4(0.2 √(0.3237 x 115) +
0.2 √(0.3237x40)) – 2 = 3
EU(S) = 0.4(0.8 √(0.3237 x 115) + 0.2 √(0.3237 x
40) + 0.6(0.2 √(0.3237 x 115) +
0.2 √(0.3237x40)) – 1.71 = 2.9896
E(W) = 0.6(0.8(100-0.3237 x 115)) + 0.2(100 –
(0.3237 x 40)) + 0.4(0.2(55-(0.3237x115) +
0.8(0.3237x40)) = 55.456
Agency Cost = 57 – 55.456 = 1.544
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Appears as though we have minimized the
agency costs due to the moral hazard
If accountants can improve net income to
better reflect pay off, imperfections can be
reduced
Results in reduced compensation risk
 Paying a manager for a high net income when the
actual payoff will be low
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Example of Game Inc. assumed managers
have no control over reporting process
Reality is that they do (positive accounting
theory)
What does this mean?
 Managers are able to manipulate numbers
without the owner knowing
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Through regulations like GAAP, this can
prevent absolute earnings management
Let’s now assume
 Net income is a range
▪ 115 = 111 – 116
▪ 40 = 36 – 41
EU(W) = 0.6(0.8 √(0.3193x116) + 0.2 √(0.3193 x
41)) + 0.4(0.2 √(0.3193x116) + 0.8 √(0.3193 x
41) – 2 = 3
EU(S) = 0.4(0.8 √(0.3193x116) + 0.2 √(0.3193 x
41)) + 0.6(0.2 √(0.3193x116) + 0.8 √(0.3193 x
41) – 1.71 = 2.99
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As you can see, the owner will work hard
E(W) = 0.6(0.8 (100- (0.3193 x 116) + 0.2 (100 (0.3193 x 41)) + 0.4(0.2 (55- (0.3193 x 116) +
0.8 (40 -(0.3193 x 41)) = 55.4981
Agency Cost – 57 – 55.4981 = 1.5091
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Evidently there will always be a moral hazard
between managers and owners
Given the restrictions of owners ability to
influence the managerial actions, there is an
information asymmetry
Through accounting regulations (i.e. GAAP),
accountants can influence managerial actions
Thus, reducing agency cost!
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Agency cost illustrates the role of
accountants in financial reporting
Role 1:
 Create accounting policies that can increase the
accuracy of net income as a predictor
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Role 2:
 Create regulations that reduce a managers ability
to manipulate net income
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Principal cannot observe actions of manager
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Moral hazard problem
 Information Asymmetry
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Conflict of interest
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Divergence of Interests
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Raising interest rates acts as a deterrent for
managers
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Reduce the cost of borrowing capital
 Limit dividends
 Limit additional borrowing
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Recall: Agency theory
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Compensate the managers as a part of the
Holmström Agency Model
Rigidity of Contracts
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Contributed to the agency model
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Use of simultaneous performance measures
 Net income
 Share price performance
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Performance Measure Characteristics
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Sensitivity
 Manager effort
 Understand manager motivation
 Reserve Recognition Accounting
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Precision
 A reciprocal of the variance of the noise
 How good is it predicting payoff?
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Ensure both measures are:
 Jointly observable
 Relates to net income
 Reveals more information
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Managers have no control over share price
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External factors influence the price
performance
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Management’s actions may not be directly
reflected in share prices
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Assume an efficient
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Assumption: Legal system has authority to enforce
contract provisions without cost and resolve disputes
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Once contracts are signed:
 Difficult to change (costly)
 May continue over a long period of time
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Factors to consider:
 Anticipation of contingencies
 “Incomplete” contracts
 Renegotiation
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Manager’s remuneration depends on net
income and lending contracts
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Contract covenants affect the manager’s
actions
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Managers still have the ability to manipulate
accounting policies irrespective of the effect
on decision usefulness to investors
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Investor reaction and cost of capital is
affected by accounting policy choice
regardless of impact on cash flow
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Means of communicating inside information
to the public.
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Conflict theories
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Net income’s role in motivation and
monitoring manager performance
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Net income competes with other
performance measures
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Earnings management allows shirking –
lower payoffs
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$2 million of R&D costs to allocate
Could cause project she manages incur a loss
 Will lose her bonus
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Could allocate to other projects
 Upper management pressure to meet growth
targets
How much cost should be charged to
unfinished products if K(3) is to
a) break even?
What is the impact on Sue’s bonus?
b) earn a normal level of profit?
Which scenario does she have more incentive
to choose, why?
Contract Costs
 Identifiable with or allocable to specific
contracts
 Direct materials
 Direct labour
 Overhead
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Already incurred
Expected costs to complete
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Does Accounting for Contracts provide useful
guidelines in this situation?
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Is the decision material?
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Does it matter if it is material?
Impact on stakeholders
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Who are the stakeholders?
What are their rights and expectations?
What is Sue’s obligation to each?
Decision Time!
Imagine you are Sue Davies, how would you
allocate the remaining $2 million of R&D?
Why?