1. Game Theory
Game 10
Winner’s Curse

2. Bidding for a Company Uncertain Valuation Synergy Adverse Selection
A company is worth between $0 and $1000 per block of shares
Synergy
Worth of company increases by 50% if purchased
Adverse Selection
Offer only accepted if company is worth less than offer

3. value
1500
1000
bid
1000

4. value
1500
1000
bid
1000

5. value
1500
loss
profit
1000
bid
1000

6. value
1500
loss
profit
1000
bid
1000

7. Why? Expected value of the company is irrelevant!
Consider only the expected value of the company if you win!
1000
500 ½b b
1000

8. Expected Profit Bid b dollars Expected value if you win: ½b
If win, company’s value between 0 and b
Synergy: 50% added value: ¾b
1.5 x ½b = ¾b
if win: pay b but receive ¾ b
Expected Loss if you win: ¼ b
Probability of winning: b / 1000
Expected loss: b2 / 4000

9. 100 Random Company Values Place a Bid of 500
711
134
680
269
217
698
356
948
578
366
197
595
863
389
681
533
566
976
921
995
638
404
255 91
729
440
527
129
975
334 51
485
400 20
177
570
350 39
706
365
867
257
894
675
285
419
452
598
594
207
536
142
919
815
558
428
131
624
489
923
810
275
519
763
582 90
109
688
267
390
336
897
926
808
972
705
725 34
163
898
704
848
112
120
790
817
573
494
472
917
383
398 94 14 86 58
854

10. 49 Eliminated ( V > 500)
711
134
680
269
217
698
356
948
578
366
197
595
863
389
681
533
566
976
921
995
638
404
255 91
729
440
527
129
975
334 51
485
400 20
177
570
350 39
706
365
867
257
894
675
285
419
452
598
594
207
536
142
919
815
558
428
131
624
489
923
810
275
519
763
582 90
109
688
267
390
336
897
926
808
972
705
725 34
163
898
704
848
112
120
790
817
573
494
472
917
383
398 94 14 86 58
854

11. Value with Synergies ( 1.5 V )
201
404
326
534
549
296
584
606
383
137
660
194
501 77
728
600 30
266
525 59
548
386
428
629
678
311
213
642
197
734
413
135
164
401
585
504 51
245
168
180
741
708
575
597
141 21
129 87

12. Profits and Losses ( Value minus Bid )
299 96
174 34 49
204 84
106
117
363
160
306 1
423
228
100
470
234 25
441 48
114 72
129
178
189
287
142
303 87
365
336 99 85 4
449
255
332
320
241
208 75 97
359
479
371
413

13. Summary
-479, -470, -449, -441, -423, -413, -371, -365, -363, -359, -336, -332, -320, -306, -303, -299, -287, -255, -234, -204, -204, -204, -189, -174, -117, -114, - 99, - 96, - 87, , 234, 228, 208, 178, 160, 142, 129, 106, 100, 97, 85, 84, 75, 49, 48, 34, 34, 25, 4, 1

14. Summary for a Bid of 500 Lost Auction: 49% Won but Lost: 30%
Profit of 0
Won but Lost: 30%
Average Profit of -279
Won but Won: 21%
Average Profit of 108
Overall profit:
49%(0) + 30%(-279) + 21%(108) = - 61

15. Simulated Profits for a Bid of 750
losses
don’t win
gains
(avg = $375)
(avg = $188)
Average Profit =

16. Results Winners bid (near) $0, lost $0 Cursed bid $1000, lost $250
Tyler, Tyler, Justin V., Bella
Cursed bid $1000, lost $250
Adam, Sameer, Xue

17. Quality of Information
Game 1
Information is very poor
On average, you can’t win
Game 2
A company is worth between $1000 and $2000 per block of shares
On average, you can’t lose

18. Expected Profit Bid b dollars Expected value if you win: 500 + ½ b
Synergy: 50% added value: ¾ b
1.5 x (500+½b)
Pay b but receive 750+¾b
Expected Gain if you win: ¼ b
Probability of winning: (b-1000) / 1000
Expected winnings increase with the bid

19. Game 2 Most profitable bid: Least profitable bid: Bid 2000, win 250