1. Auctions with Toeholds: an Experimental Study
Sotiris Georganas, Ohio State and U Bonn
Rosemarie Nagel, U Pompeu Fabra (Barcelona)
Econometric Society NASM 2008

2. Motivation Takeover battles can be viewed as CV auctions
Often one of the parties already owns a part of the 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?
When company taken over, often there can be a counteroffer, and a counteroffer to that -> takeover battle
More on explosive equilibria later
We do an experiment in a controlled environment to see what is going on
Bulow klemperer huang JPE
Klemperer 1998 almost common values
Sotirios Georganas - Auctions with Toeholds

3. 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):
Next slide showing the bids
Sotirios Georganas - Auctions with Toeholds

4. Equilibrium Bids No toeholds, diagonal
Sotirios Georganas - Auctions with Toeholds

5. 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

6. Results Win frequencies 1-5 1-20 1-50 Actual 0.51 0.451 0.3375
Two types very close, no explosive effect, weak types win far too often
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

7. Tobit regressions
Why tobit? Known to people who work with english auctions: unobservable bids (especially with two persons)
Sotirios Georganas - Auctions with Toeholds

8. 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
Actual and predicted have same ranking, but differ a lot
Explanation?
Sotirios Georganas - Auctions with Toeholds

9. Payoff flatness High type in 1-20
Emphasize when signal 100 you bid 200!
Sotirios Georganas - Auctions with Toeholds

10. Equilibrium has very flat payoffs
we find that when the ratio of the two players toeholds is larger
than 10 (e.g. 1% and 10%), the strong bidder can deviate almost 50% from his optimal
bid with a negligible loss in expected payoff.
Payoffs extremely flat, convergence to equilibrium almost impossible
Alternatively: LOR
Sotirios Georganas - Auctions with Toeholds

11. Generality of flatness
Payoff flatness is a problem 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

12. Consequences of flatness
Suppose subjects’ initial bidding is not close to equilibrium
Flat payoffs mean their incentives to adjust towards 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

13. If equilibrium fails…
Bounded rationality models can describe behavior better
In this case, non equilibrium models like a levels of 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…
I use the level k version used in auctions by Crawford
Sotirios Georganas - Auctions with Toeholds

14. Levels of reasoning L1 starting from random!
LOR is not an equilibrium concept and thus it could describe behavior better
Sotirios Georganas - Auctions with Toeholds

15. Model fit Low likelihood good Only 1-50 does not work well
Sotirios Georganas - Auctions with Toeholds

16. Profitability of toeholds: sunk costs
This means, when you have already bought the toehold
Sotirios Georganas - Auctions with Toeholds

17. Profitability of toeholds: ex ante
Including the cost
Sotirios Georganas - Auctions with Toeholds

18. 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
In kagel rose we have Cv but one person has CV+k, experienced subjects, English auction with 4 bidders, no winners curse (because experienced)
Avery kagel: two person sealed bid wallet game (ti+tj)
Sotirios Georganas - Auctions with Toeholds

19. Extensions Other equilibrium concepts (QRE?) Sealed bids
Vary number of bidders
Different toehold concept (insider gets informational advantage)
Sotirios Georganas - Auctions with Toeholds

20. Conclusions No signs of explosive equilibria LOR describes data better
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

21. Appendix: deviations in payoff space
Sotirios Georganas - Auctions with Toeholds

22. Flatness with actual data…
So with actual behaviour, better incentives to play a best response and it seems this is more or less what subjects are doing.
Sotirios Georganas - Auctions with Toeholds