Sotiris Georganas, Ohio State and U Bonn
Rosemarie Nagel, U Pompeu Fabra (Barcelona)
Econometric Society NASM 2008
Motivation
 Takeover battles can be viewed as CV auctions
 Often one of the parties already owns a part of the
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company sold (a toehold)
Owning a toehold significantly alters the strategic setup
Toeholds or other asymmetries lead in theory to explosive
equilibria, toehold owners get the company for very low
price (Bulow et al 1999, Klemperer 1998)
However empirical studies (Betton, Eckbo 2000) find that
only 50% of bidders acquire a toehold
Why?
Sotirios Georganas - Auctions with Toeholds
Model
 2 risk neutral bidders i and j compete in an English
auction for one unit of an indivisible good (e.g. a
company)
 Own share θi of the company, common knowledge
 Signals ti ~U[0,100]
 Company value: sum of signals ti+ tj
 Unique Symmetric Equilibrium (Bulow et al. 1999):
Sotirios Georganas - Auctions with Toeholds
Equilibrium Bids
Sotirios Georganas - Auctions with Toeholds
Experimental Design
 Experiments at LeeX in Barcelona, computerised
(zTree), 16 subjects at each session
 3 treatments: toehold pairs 1%-5% (2 ind. obs.), 1%20% (4 obs.) and 1%-50% (6 obs.)
 Toehold common knowledge, players alternate roles
 50 periods, random matching
 No bankruptcies
Sotirios Georganas - Auctions with Toeholds
Results
Win
frequencies
1-5
1-20
1-50
Actual
0.51
0.451
0.3375
Predicted
0.167
0.038
0.0158
Sotirios Georganas - Auctions with Toeholds
Tobit regressions
Sotirios Georganas - Auctions with Toeholds
Results contd.
 Deviation from equilibrium bids very high
 Leads to deviation in prices
Treatment
Mean actual
price
Mean predicted
price
Mean deviation
1-5
88,7
61
27.7
1-20
73.8
60.3
13.5
1-50
76.9
69.2
7.7
 Explanation?
Sotirios Georganas - Auctions with Toeholds
Payoff flatness
Sotirios Georganas - Auctions with Toeholds
Equilibrium has very flat payoffs
Sotirios Georganas - Auctions with Toeholds
Generality of flatness
 Payoff flatness is a problem
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in all explosive equilibria
In our case, weak type bids
less than 100 for almost all
values
Thus, strong type gains
almost nothing by bidding
more than 100
Hence, flat payoff above 100
Payoffs always flat in
equilibria where weak type
bids very passively
Sotirios Georganas - Auctions with Toeholds
Consequences of flatness
 Suppose subjects’ initial bidding is not close to equilibrium
 Flat payoffs mean their incentives to adjust towards
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equilibrium are weak
According to most learning models convergence to
equilibrium will be very slow
If agents have some small unmodeled reasons for
disequilibrium behavior, incentives towards equilibrium
don’t suffice for convergence
In practice : equilibria that suffer from flatness are not good
predictions for real life situations
Corollary: we will never see explosive equilibria in real life!
Sotirios Georganas - Auctions with Toeholds
If equilibrium fails…
 Bounded rationality models can describe behavior better
 In this case, non equilibrium models like a levels of
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reasoning model (Nagel 95, Stahl/Wilson 95,
Crawford/Iriberri 2008)
LOR models assume people best respond
But consistency of beliefs assumption is relaxed
Players are characterized by their beliefs
L1 players believe others randomize and best respond to
this belief, L2 players assume everyone else is L1 and best
respond, L3 best respond to L2 and so on…
Sotirios Georganas - Auctions with Toeholds
Levels of reasoning
Sotirios Georganas - Auctions with Toeholds
Model fit
Sotirios Georganas - Auctions with Toeholds
Profitability of toeholds: sunk costs
Sotirios Georganas - Auctions with Toeholds
Profitability of toeholds: ex ante
Sotirios Georganas - Auctions with Toeholds
Comparison with previous results
 Avery and Kagel (1997), Kagel and Rose (forthcoming)
analyse somewhat similar games (almost common values,
sealed bid and English resp.)
 Do not vary toehold size
 Similarly to us do not find explosive equilibria
 Attribute deviation to naïve players (just add advantage to
signal, similar to L1)
 No analysis of payoff flatness
 No levels of reasoning
Sotirios Georganas - Auctions with Toeholds
Extensions
 Other equilibrium concepts (QRE?)
 Sealed bids
 Vary number of bidders
 Different toehold concept (insider gets informational
advantage)
Sotirios Georganas - Auctions with Toeholds
Conclusions
 No signs of explosive equilibria
 Equilibrium payoffs extremely flat
 No convergence in reasonable time
 LOR describes data better
 Toeholds do raise probability of winning
 But sometimes not enough to cover the cost to acquire
them
 This may be the explanation why bidders acquire no
toeholds
Sotirios Georganas - Auctions with Toeholds
Appendix: deviations in payoff space
Sotirios Georganas - Auctions with Toeholds
Flatness with actual data…
Sotirios Georganas - Auctions with Toeholds