Auctions with Toeholds: an Experimental Study 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 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

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

Equilibrium Bids No toeholds, diagonal 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 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

Tobit regressions Why tobit? Known to people who work with english auctions: unobservable bids (especially with two persons) 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 Actual and predicted have same ranking, but differ a lot Explanation? Sotirios Georganas - Auctions with Toeholds

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

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

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

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

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

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

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

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

Profitability of toeholds: ex ante Including the cost 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 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

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 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

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

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