Game Theory Game 10 Winner’s Curse

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

value 1500 1000 bid 1000

value 1500 1000 bid 1000

value 1500 loss profit 1000 bid 1000

value 1500 loss profit 1000 bid 1000

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

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

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

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

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

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

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, - 72 241, 234, 228, 208, 178, 160, 142, 129, 106, 100, 97, 85, 84, 75, 49, 48, 34, 34, 25, 4, 1

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

Simulated Profits for a Bid of 750 losses don’t win gains (avg = $375) (avg = $188) Average Profit = - 140

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

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

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

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