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Christoph KuhnerDept. of Financial Accounting and AuditingUniversity of CologneKuhner@wiso.uni-koeln.de

Competition of Accounting Standards, Comparability of Financial Information, and Critical Masses: an Evolutionary

Approach

Paper prepared for the mini-conference n°4 on "Evolutionary Regulation: Rethinking the Role of Regulation in Economy and Society" at the SASE 2010 Meeting of

Philadelphia, 24-26 June 2010

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Agenda

1. Introduction: Harmonisation vs. competition .....................................................................2

2. Competition of accounting standards in a stylized 2 person/2 strategies setting................3

3. The evolutionary game .......................................................................................................5

4. The case of multiple standards............................................................................................7

4.1. Equilibria in the one shot stetting and the evolutionary setting..................................7

4.2. Evolutionary dynamics and multiple standards ..........................................................9

4.2.1. Evolutionary stability...................................................9

4.2.2. Evolutionary Microdynamics..................................................................................11

4.3. Multiple standards and critical masses ..........................................................................15

5. Conclusion ........................................................................................................................19

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Competition of accounting standards as an observable phenomeneon – examples -

• mid 90ties - 2005 : Germany (and other continental European countries).

• since 2008: Foreign issuers listed at US Stock exchanges.

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Global harmonization of accounting standards as regulatory aim:

• IASB and FASB:

„Commitment to convergence“

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Two dimensions of Accounting standards usefulnes

• Inherent quality (precision)

• comparability

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Notation

a - expected payoff to the initial owners (by investors) if adopting the “bad” standard and its peer adopting the same standard;

b - expected payoff to the initial owners (by investors) if adopting the “good” standard and

its peer adopting the same standard; 0 - expected payoff to both parties if adopting

different standards,

b > a > 0, payoff information is common knowledge.

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Normal Form „tender trap“

Firm 2

„good” standard „bad” standard

Firm 1 „good”

standard

b, b

0, 0

„bad”

standard

0, 0

a, a

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Let a = 3, b = 5

Firm 2

„good” standard „bad” standard

Firm 1 „good”

standard

5, 5

0, 0

„bad”

standard

0, 0

3, 3

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Equilibria in the one-shot game:

• „good“ equilibrium: both players adopting the good strategy.

• „bad“ equilibrium: both players adopting the bad strategy.

• „mixed´“ equilibrium: Players adopt mixed strategies: they play with p = 3/8 the good strategy, with p = 5/8 the bad strategy.

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The evolutionary game ….

…. is played in great populations of individual actors choosing one of the two alternative strategies.

Payoffs in the evolutionary games are attributed by randomly matching two actors being part of the great population.

Evolutionary dynamics implies that the matching game is repeated n times and that the players have after each round the option to change their strategy.

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Equilibria in the evolutionary game

• The two Equilibria of the single shot game are preserved as evolutionary stable equilibria.

• There is an „inner“ equilibrium with 37,5% (= 3/8) of the players adopting the good strategy and 62,5% (=5/8) of the players adopting the „bad“ strategy.

• The inner equilibrium has the property of a turning point: The percentages correspond to „critical masses“.

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Multiple strategies:

Players may adopt both strategies simultaneously, i.e. draft their financial statements in both standards.

Multiple strategies imply higher adaption cost [c].

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Firm 2

„good” standard

„bad” standard

multiple

„good”

standard

b, b 0, 0 b, (b-c)

Firm 1 „bad”

standard

0, 0 a, a a, (a-c)

multiple (b-c), b (a-c), a (b-c), (b-c)

Normal form with multiple strategies

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Example: let a = 3, b=5, c = 1,5

Firm 2

„good” standard

„bad” standard“

multiple

„good” standard

5, 5 0, 0 3, 2,5

Firm 1 „bad” standard

0, 0 3, 3 2, 1,5

multiple 3,5, 5 1,5, 3 1,5, 1,5

In the evolutionary game with multiple strategies, both equilibria [good; good]; [bad; bad ] are preserved as evolutionary stable states.

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• Low adoption cost → strategies „bad“ and „multiple“

• Medium adoption cost → strategies „bad“, „good“, multiple

These inner equilibria are unstable in an evolutionary sense. They may be characterized as turning point or „critical masses“ equilibria.

With low and medium adoption cost c, „inner“ equilibria exist in which multiple strategies are played:

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Evolutionary Microdynamics: • Evolutionary dynamics can be captured by the

Hirshleifer/Coll - adoption process.• Evolution is characterized by a sequence of numerous

matching games after which, each time, proportions of the population change their strategies in response to their last experience

• Intuition: After a deviation away from the equilibrium point, proportions of adoptors change in response to changing pay-offs.

• Departing from an inner equilibrium point, the proportion of multiple strategies will decrease or increase in the medium term, depending on wether there is an overall movement towards the evolutionary stable bad or „good“ equilibrium.

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It increases in the medium term if the overall movement is towards the „good“ equilibrium:

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1 21 41 61 81 101 121

number of iterations (k=0,1)

rela

tive w

eigh

ts of

stra

tegi

es

(proportion of multiple strategies in yellow).

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It decreases monotonically if the overall movement is towards the „bad“ equilibrium:

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1 21 41 61 81 101 121

Number of iterations (k=0,1)

rela

tive

wei

ghts

of s

trat

egie

s

(proportion of multiple strategies in yellow).

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Behavior of critical masses in relation to adoption cost c / 1

The critical masses’ threshold necessary to overcome the bad strategy equilibrium is identical with the proportion of players which do not adopt the bad strategy but, alternatively, play one of the other two strategies – good or multiple.

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Behavior of critical masses in relation to adoption cost c / 2

• The relationship between adoption cost and critical masses is nonmonotonious.

• In the range of low adoption cost, critical masses increase with increasing adoption cost.

• In the medium range, critical masses decrease with increasing adoption cost.

• With relatively high adoption cost, critical masses are constant.

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example [a = 3, b = 5]: non-monotonic relationship of critical masses [%] and adoption cost [c]:

crit.

mass

60%

50%

40%

30%

20%

10%

0 0,5 1,0 1,5 2,0 2,5 c

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Regulatory implications

The regulatory implications are ambiguous: With low adoption cost for multiple standards, it follows that the regulator should in tendency renounce enforcement of one single standard.With medium and high cost of multiple strategies, regulatory intervention in this sense may have a better legitimation. At the time, the temporary spread of multiple strategies may indicate a spontaneous evolution towards the Pareto-superior evolutionary stable equilibrium.