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Christoph Kuhner
Dept. of Financial Accounting and Auditing
University of Cologne
[email protected]
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
1
Agenda
1.
2.
3.
4.
Introduction: Harmonisation vs. competition .....................................................................2
Competition of accounting standards in a stylized 2 person/2 strategies setting................3
The evolutionary game .......................................................................................................5
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
2
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.
3
Global harmonization of accounting
standards as regulatory aim:
• IASB and FASB:
„Commitment to convergence“
4
Two dimensions of Accounting standards usefulnes
• Inherent quality (precision)
• comparability
5
Notation
a -
b -
0 -
expected payoff to the initial owners
(by investors) if adopting the “bad” standard
and its peer adopting the same standard;
expected payoff to the initial owners (by
investors) if adopting the “good” standard and its
peer adopting the same standard;
expected payoff to both parties if adopting
different standards,
b > a > 0, payoff information is common knowledge.
6
Normal Form „tender trap“
Firm 2
Firm 1
„good” standard
„bad” standard
b, b
0, 0
0, 0
a, a
„good”
standard
„bad”
standard
7
Let a = 3, b = 5
Firm 2
Firm 1
„good” standard
„bad” standard
5, 5
0, 0
0, 0
3, 3
„good”
standard
„bad”
standard
8
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.
9
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.
10
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“.
11
Multiple strategies:
Players may adopt both strategies
simultaneously, i.e. draft their financial
statements in both standards.
Multiple strategies imply higher adaption
cost [c].
12
Normal form with multiple strategies
Firm 2
„good”
„good”
standard
b, b
„bad”
standard
0, 0
multiple
0, 0
a, a
a, (a-c)
(b-c), b
(a-c), a
(b-c), (b-c)
b, (b-c)
standard
Firm 1
„bad”
standard
multiple
13
Example: let a = 3, b=5, c = 1,5
Firm 2
Firm 1
„good”
standard
„bad”
standard
multiple
„good”
standard
5, 5
„bad”
standard“
0, 0
multiple
0, 0
3, 3
2, 1,5
3,5, 5
1,5, 3
1,5, 1,5
3, 2,5
In the evolutionary game with multiple strategies, both
equilibria [good; good]; [bad; bad ] are preserved as
evolutionary stable states.
14
With low and medium adoption cost c, „inner“ equilibria
exist in which multiple strategies are played:
• Low adoption cost
→
• Medium adoption cost
→
strategies „bad“
and „multiple“
strategies
„bad“, „good“,
multiple
These inner equilibria are unstable in an evolutionary
sense. They may be characterized as turning point or
„critical masses“ equilibria.
15
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
16
evolutionary stable bad or „good“ equilibrium.
It increases in the medium term if the overall
movement is towards the „good“ equilibrium:
relative weights of strategies
1,20
1,00
0,80
0,60
0,40
0,20
0,00
1
21
41
61
81
number of iterations (k=0,1)
(proportion of multiple strategies in yellow).
101
121
17
It decreases monotonically if the overall
movement is towards the „bad“ equilibrium:
1,20
relative weights of strategies
1,00
0,80
0,60
0,40
0,20
0,00
1
21
41
61
81
101
121
Number of iterations (k=0,1)
(proportion of multiple strategies in yellow).
18
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.
19
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.
20
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
21
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.
22