Model 3 players: Acquirer ( A ), Target ( T ), Regulator ( R ) Timeline Period 0 : A learns type, t ∈ { ac , pc } ; ac -type occurs with probability q Period 1: A makes take it or leave it offer { p , b } to T Period 2: R observes contract & costless signal, s ∈ { s h , s l } , of whether the merger is ac or not Probability s = s h if t = i is h i 0 < h pc < h ac < 1 : signal is informative but imperfect Period 3: If R challenges, A & R litigate; court blocks or allows R & pcA spending fixed ( φ and ψ pc ); acA spending ( ψ ac ) endogenous Choi and Wickelgren Breakup Fees June 2019 5 / 1
Model 3 players: Acquirer ( A ), Target ( T ), Regulator ( R ) Timeline Period 0 : A learns type, t ∈ { ac , pc } ; ac -type occurs with probability q Period 1: A makes take it or leave it offer { p , b } to T Period 2: R observes contract & costless signal, s ∈ { s h , s l } , of whether the merger is ac or not Probability s = s h if t = i is h i 0 < h pc < h ac < 1 : signal is informative but imperfect Period 3: If R challenges, A & R litigate; court blocks or allows R & pcA spending fixed ( φ and ψ pc ); acA spending ( ψ ac ) endogenous R never wins against pcA ; R wins against acA with probability π ( ψ ac ) ; π ′ < 0, π ′′ > 0. Choi and Wickelgren Breakup Fees June 2019 5 / 1
Model–Payoffs Offer rejected Choi and Wickelgren Breakup Fees June 2019 6 / 1
Model–Payoffs Offer rejected T gets v ; A gets 0 ; R gets 0 Choi and Wickelgren Breakup Fees June 2019 6 / 1
Model–Payoffs Offer rejected T gets v ; A gets 0 ; R gets 0 Offer accepted Choi and Wickelgren Breakup Fees June 2019 6 / 1
Model–Payoffs Offer rejected T gets v ; A gets 0 ; R gets 0 Offer accepted No challenge: T gets p , A gets u i − p , R gets B or − L Choi and Wickelgren Breakup Fees June 2019 6 / 1
Model–Payoffs Offer rejected T gets v ; A gets 0 ; R gets 0 Offer accepted No challenge: T gets p , A gets u i − p , R gets B or − L Approved: T gets p , A gets u i − p − ψ i , R gets B − φ − z ψ pc or − L − φ − z ψ ac Choi and Wickelgren Breakup Fees June 2019 6 / 1
Model–Payoffs Offer rejected T gets v ; A gets 0 ; R gets 0 Offer accepted No challenge: T gets p , A gets u i − p , R gets B or − L Approved: T gets p , A gets u i − p − ψ i , R gets B − φ − z ψ pc or − L − φ − z ψ ac Rejected: T gets v + b , A gets − b − ψ ac , R gets − φ − z ψ ac Choi and Wickelgren Breakup Fees June 2019 6 / 1
Litigation Stage A ’s litigation strategy Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins acA chooses ψ ac to maximize ( 1 − π ( ψ ac ))( u ac − p ) − π ( ψ ac ) b − ψ ac Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins acA chooses ψ ac to maximize ( 1 − π ( ψ ac ))( u ac − p ) − π ( ψ ac ) b − ψ ac FOC: − ( ψ ac )( u ac + b − p ) = 1 implicitly defines ψ ∗ ac ( b , p ) Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins acA chooses ψ ac to maximize ( 1 − π ( ψ ac ))( u ac − p ) − π ( ψ ac ) b − ψ ac FOC: − ( ψ ac )( u ac + b − p ) = 1 implicitly defines ψ ∗ ac ( b , p ) R challenge decision Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins acA chooses ψ ac to maximize ( 1 − π ( ψ ac ))( u ac − p ) − π ( ψ ac ) b − ψ ac FOC: − ( ψ ac )( u ac + b − p ) = 1 implicitly defines ψ ∗ ac ( b , p ) R challenge decision Define q R as R ’s posterior belief that merger is anti-competitive Choi and Wickelgren Breakup Fees June 2019 7 / 1
Litigation Stage A ’s litigation strategy pcA spends ψ pc and wins acA chooses ψ ac to maximize ( 1 − π ( ψ ac ))( u ac − p ) − π ( ψ ac ) b − ψ ac FOC: − ( ψ ac )( u ac + b − p ) = 1 implicitly defines ψ ∗ ac ( b , p ) R challenge decision Define q R as R ’s posterior belief that merger is anti-competitive Challenge if and only if: q R ( π ( ψ ∗ ac ( b , p )) L − z ψ ∗ ac ( b , p )) − ( 1 − q R ) z ψ pc − φ ≥ 0 Choi and Wickelgren Breakup Fees June 2019 7 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h π ( ψ ac ) > 0 implies acA more likely to pay b than pcA Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h π ( ψ ac ) > 0 implies acA more likely to pay b than pcA Pooling equilibrium for small b Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h π ( ψ ac ) > 0 implies acA more likely to pay b than pcA Pooling equilibrium for small b Larger b worse for acA than for pcA , but Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h π ( ψ ac ) > 0 implies acA more likely to pay b than pcA Pooling equilibrium for small b Larger b worse for acA than for pcA , but Revealing ac type implies offer ( 0, v ) and always challenged, instead of challenged with probability h ac Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Fix ψ ac ≥ ψ pc : b doesn’t affect it R makes inferences about A ’ s type (but not litigation effort) from b Assume in pooling eqm, R challenges iff s = s h π ( ψ ac ) > 0 implies acA more likely to pay b than pcA Pooling equilibrium for small b Larger b worse for acA than for pcA , but Revealing ac type implies offer ( 0, v ) and always challenged, instead of challenged with probability h ac ( 1 − h ac π ac ( ψ ac ))( u ac − p ) − h ac π ac ( ψ ac ) b − h ac ψ ac ≥ ( 1 − π ( ψ ac ))( u ac − v ) − ψ ac if b small enough Choi and Wickelgren Breakup Fees June 2019 8 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract acA mixes between high b contract and revealing contract Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract acA mixes between high b contract and revealing contract R mixes with high b contract & s h ; probability of challenge decreasing in b Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract acA mixes between high b contract and revealing contract R mixes with high b contract & s h ; probability of challenge decreasing in b Partial pooling raises R welfare Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract acA mixes between high b contract and revealing contract R mixes with high b contract & s h ; probability of challenge decreasing in b Partial pooling raises R welfare R welfare equivalent to challenging all mergers with high signal and some acA with low signal Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 1: Fixed Litigation Costs Partial pooling for large b If b large & R challenges w/ s h : acA separates rather than risk large breakup fee Complete separation impossible: R won’t challenge if only pcA offers high b contract acA mixes between high b contract and revealing contract R mixes with high b contract & s h ; probability of challenge decreasing in b Partial pooling raises R welfare R welfare equivalent to challenging all mergers with high signal and some acA with low signal Pooling equilibrium only has challenges from all mergers with high signal Choi and Wickelgren Breakup Fees June 2019 9 / 1
Benchmark 2: Complete Information R behavior Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b There might exist a b ∗∗ such that π ( ψ ∗ ac ( b ∗∗ , p )) = ( z ψ ∗ ac ( b ∗∗ , p ) + φ ) / L Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b There might exist a b ∗∗ such that π ( ψ ∗ ac ( b ∗∗ , p )) = ( z ψ ∗ ac ( b ∗∗ , p ) + φ ) / L Optimal merger contracts Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b There might exist a b ∗∗ such that π ( ψ ∗ ac ( b ∗∗ , p )) = ( z ψ ∗ ac ( b ∗∗ , p ) + φ ) / L Optimal merger contracts pcA indifferent because never challenged Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b There might exist a b ∗∗ such that π ( ψ ∗ ac ( b ∗∗ , p )) = ( z ψ ∗ ac ( b ∗∗ , p ) + φ ) / L Optimal merger contracts pcA indifferent because never challenged acA offers b > b ∗∗ if possible and is never challenged, otherwise Choi and Wickelgren Breakup Fees June 2019 10 / 1
Benchmark 2: Complete Information R behavior Never challenge pcA Challenge acA iff π ( ψ ∗ ac ( b , p )) ≥ ( z ψ ∗ ac ( b , p ) + φ ) / L ψ ∗ ac ( b , p ) . is increasing in b , so π is decreasing in b There might exist a b ∗∗ such that π ( ψ ∗ ac ( b ∗∗ , p )) = ( z ψ ∗ ac ( b ∗∗ , p ) + φ ) / L Optimal merger contracts pcA indifferent because never challenged acA offers b > b ∗∗ if possible and is never challenged, otherwise acA offers ( 0, v ) Choi and Wickelgren Breakup Fees June 2019 10 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Not perfect, but better than with small or no breakup fees Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Not perfect, but better than with small or no breakup fees Litigation effects are undesirable Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Not perfect, but better than with small or no breakup fees Litigation effects are undesirable Raising the cost of losing a challenge commits acquirer to fight harder Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Not perfect, but better than with small or no breakup fees Litigation effects are undesirable Raising the cost of losing a challenge commits acquirer to fight harder Makes it harder to block anti-competitive mergers Choi and Wickelgren Breakup Fees June 2019 11 / 1
Implications of Benchmarks Informational effects of breakup fees are desirable They can help identify anti-competitive mergers Not perfect, but better than with small or no breakup fees Litigation effects are undesirable Raising the cost of losing a challenge commits acquirer to fight harder Makes it harder to block anti-competitive mergers What happens if both effects are present? Choi and Wickelgren Breakup Fees June 2019 11 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Pooling equilibrium with no challenges Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Pooling equilibrium with no challenges z ψ pc + φ R indifferent to challenging: q ∗ R = π ac ( ψ ∗ ac ) L − z ( ψ ∗ ac − ψ pc ) Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Pooling equilibrium with no challenges z ψ pc + φ R indifferent to challenging: q ∗ R = π ac ( ψ ∗ ac ) L − z ( ψ ∗ ac − ψ pc ) ψ ∗ ac satisfy this for q ∗ Let ¯ R given by pooling & s h Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Pooling equilibrium with no challenges z ψ pc + φ R indifferent to challenging: q ∗ R = π ac ( ψ ∗ ac ) L − z ( ψ ∗ ac − ψ pc ) ψ ∗ ac satisfy this for q ∗ Let ¯ R given by pooling & s h If there is a b ∗ large enough that ψ ∗ ψ ∗ ac ( b ∗ , p ) ≥ ¯ ac , R won’t challenge for any b > b ∗ Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Assumption: If pooling at b = 0, R challenges if and only if s = s h Pooling equilibrium with no challenges z ψ pc + φ R indifferent to challenging: q ∗ R = π ac ( ψ ∗ ac ) L − z ( ψ ∗ ac − ψ pc ) ψ ∗ ac satisfy this for q ∗ Let ¯ R given by pooling & s h If there is a b ∗ large enough that ψ ∗ ψ ∗ ac ( b ∗ , p ) ≥ ¯ ac , R won’t challenge for any b > b ∗ Both types will offer a contract with b > b ∗ Choi and Wickelgren Breakup Fees June 2019 12 / 1
Full Model Equilibria Pooling equilibrium with challenges Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium If b > ˆ b , only partial pooling possible Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium If b > ˆ b , only partial pooling possible pcA offers ( b , p ) and acA mixes between ( b , p ) and ( 0, v ) Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium If b > ˆ b , only partial pooling possible pcA offers ( b , p ) and acA mixes between ( b , p ) and ( 0, v ) R always challenges ( 0, v ) , sometimes challenges ( b , p ) if s h Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium If b > ˆ b , only partial pooling possible pcA offers ( b , p ) and acA mixes between ( b , p ) and ( 0, v ) R always challenges ( 0, v ) , sometimes challenges ( b , p ) if s h Probability of challenge decreasing in b Choi and Wickelgren Breakup Fees June 2019 13 / 1
Full Model Equilibria Pooling equilibrium with challenges There exists a ˆ b s.t., acA is indifferent between Pooling (challenged w/ probability h ac ) and Offering b = 0 and challenged for sure If b ≤ ˆ b : pooling eqm & R challenges iff s = s h Partial pooling equilibrium If b > ˆ b , only partial pooling possible pcA offers ( b , p ) and acA mixes between ( b , p ) and ( 0, v ) R always challenges ( 0, v ) , sometimes challenges ( b , p ) if s h Probability of challenge decreasing in b Probability acA offers ( b , p ) drops at ˆ b & then increases in b Choi and Wickelgren Breakup Fees June 2019 13 / 1
Welfare Comparison Pooling with no challenges worst Choi and Wickelgren Breakup Fees June 2019 14 / 1
Welfare Comparison Pooling with no challenges worst Pooling with challenges best at b = 0 Choi and Wickelgren Breakup Fees June 2019 14 / 1
Welfare Comparison Pooling with no challenges worst Pooling with challenges best at b = 0 Larger b increases litigation costs & harder to block ac mergers Choi and Wickelgren Breakup Fees June 2019 14 / 1
Welfare Comparison Pooling with no challenges worst Pooling with challenges best at b = 0 Larger b increases litigation costs & harder to block ac mergers Partial pooling best at ˆ b Choi and Wickelgren Breakup Fees June 2019 14 / 1
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