Sorting via Screening vs. Signaling

Transcription

1 Sorting via Screening vs. Signaling - Static Frame and Experimental Evidence - Werner Güth and Fabian Winter

2 1. Introduction 2. Static Frame 3. Experimental Design 4. Main Findings 5. Conclusions

3 1. Introduction Sorting via self-selection: important when different types are better treated differently e.g. sickness leave: in Germany sorting by medical doctors when consulted costs of shorter sickness leaves paid by employer self-sorting possible by holiday reduction in case of short-term sickness leave(s)

4 similar problems in case of private information about: neediness (social help programs) trustworthiness (credits, insurance, ) reliability (joint ventures, ) outside options, conflict payoffs (bargaining, territorial fights (incumbent vs. invader) in biology) etc. 4

5 Evolutionary Biology: costly sorting of males (peacocks, elk bulls, e.g. Zahavi and Zahavi) No common knowledge assumption (only by Mother Nature )

6 Game Theory: outragous counterfactual considerations (which choice if I would be what I am not? ) (Harsanyi/Selten, 1972: proving stronger type via not conceding) no trade results when sorting impossible (e.g. Akerlof) Spence: proving one s higher productivity by otherwise inefficient investment also our experimental scenario! 6

7 Sorting via Signaling Screening 1st mover informed party uninformed party 2nd mover uninformed party informed party question revealing one s type or pooling? screening & selfselection? 7

8 Experimentally via sequential protocols (Kübler, Huck, Müller): action sequences as above very different instructions for both implicit & explicit demand effects? different strategy sets and experimental data what is causing what? 8

9 Our approach: common frame as far as possible better control of demand effects! strategy method: not just play data! conditioning instead of timing! less hot? same benchmark equilibria but different off-the-solution play! 9

10 2. Static frame v. Neumann/Morgenstern (1944): normal form captures all what is strategically relevant more recently and similarly: stability concept/refinement of Kohlberg/Mertens (1985) 10

11 both, game form & solution concept, answer: who is the player? the personal omnipotent player (a gametheoretic construct in games with incomplete information the type player the agent player each of several alter egoes (no intrapersonal payoff aggregation) 11

12 Our static setup players: - type (e.g. worker) Other (e.g. employer) private information: - only knows {, } with 1 < - Other expects with prob. p ( with prob. 1 p) where 0 < p < 1 12

13 As in Spence (1973): Signaling via {, } chooses level y 0 wage w may depend on ( ) ( 0) y : w y 13

14 Screening via Other chooses with & Y > 0 wwy, ; 0 w w w is paid to if y < Y w is paid to { } if y Y, chooses y { 0, Y} 14

15 Sorting possible (unlike for lemons, Akerlof): due to costly investment: c y = y ( ) 1 for all y > 0: c y > c y > ( ) ( ) 15

16 Sorting via: Other learns y but not whether y = = y or y y Other s posterior beliefs: e.g. ( y) Prob / = q ( y)( 1 p ) ( )( 1 ) + ( ) q y p q y p where q ( y) : prob. of y y = for {, } requires ( )( ) ( ) q y 1 p + q y p > 0 (e.g. by refinement like uniform perfectness, Güth/Van Damme, 1991) 16

17 Ultimatum Power for { }, : Other pays ( ) = Prob ( / ) + Prob ( / ) w y y y e.g. due to hiring competition of employers 17

18 Equilibria: - here only benchmark equilibria - best pooling: 0 for y = {, } ( ) ( ) w y = p + 1 p for all y 0 prior productivity expectation 18

19 best sorting: y = 0, y = Y ( * ) w(0) =, wy = * where ( ) Y * : = since: 1 * Y > 0 1 * Y = 0 19

20 3. Experimental Design tttt Other (i) Sorting via Screening y Y, w (y ) w,w, Y Signaling y, w (y ) w,w, Y(y) 20

21 3. Experimental Design 2x2 factorial design (i) screening vs. signaling (ii) costs of sorting: either or c y = y c ( ) 1 ( y ) ( ) c 0 if y < Y = c( Y) if y Y 21

22 (i) no difference in physical timing limits demand effects & confounding explanations (like 1st mover advantage) (ii) effect of excessive investments : 0 y Y < < y Y what is due to and? > 22

23 40 rounds with constant role ( or Other) nearly identical instructions, except for (i) and (ii) about 130 minutes 224 participants ( payoff: 15.80) 23

24 4. Main Findings - y y > ( ) 1 but less so when c y = y y - with experience excessive investments must be paid - Y rather stable across rounds 24

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26 - Y does not depend on treatment & insufficient for sorting pooling dominates! more bimodal 26

27 Wage Bargaining: w w w( y) decreases with experience increasing in y but usually ( ) w> w y ( ) w> w y Other reciprocates high y-choices even when they are excessive 27

28 Signaling vs. Screening: w ( y), for both and ( ww, ) Signaling larger for Screening than higher acceptance rates for Screening higher (lower) - earnings of Other ( - types) for Screening efficiency losses due to - conflict: higher in Screening - sorting (y>0): higher in Signaling 28

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30 Aspect Kübler et al.-protocol our protocol wage bargaining hiring competition of two (three) employers ultimatum wage offer of worker to (largest wage offer automatically accepted) single employer single wage offer in case of signaling, two in case of screening two wage demands by worker, two acceptance thresholds by employer sorting play method with only two levels for both, screening and signaling strategy method for one party & a coarse grid incentives flat fee for employer in case of employment variable earnings of both, depending on agreement contract equilibria pooling and separating equilibria in signaling, only separating in screening same best pooling and separating equilibria in both treatments roles number of rounds played role switching after fixed number of periods fixed roles 48 rounds 40 rounds 30

31 5. Qualitatively similar findings (in our notation) - y > y - w(y) y - w > w - earns significantly more than - y independent of treatment - Screening leads to less sorting and more pooling compared to signaling 31

32 Different Results Responsibility for investments y (0, Y) reduces investments w (Y) Y even for Y > Y w does not depend on Y and, of course for our design more informative strategy data less demand effects & confounding explanations 32

33 Thank you for your attention! 33