The Effects of Costless Preplay Communication: Evidence fromGames with

Pareto-ranked Equilibria

Andreas Ortmann

Center for Economic Research and Graduate Education,

Charles University

Economics Institute,

Academy of Sciences of the Czech Republic

Prague, Czech Republic

(joint work with Andreas Blume, University of Pittsburgh, USA)

Earnings Table Median game

Median value of X chosen

7 6 5 4 3 2 1

7 1.30 1.15 0.90 0.55 0.10 -0.45-1.10

6 1.25 1.20 1.05 0.80 0.45 0.00-0.55

Your 5 1.10 1.15 1.10 0.95 0.70 0.35-0.10

Choice 4 0.85 1.00 1.05 1.00 0.85 0.60 0.25

of X 3 0.50 0.75 0.90 0.95 0.90 0.75 0.50

2 0.05 0.40 0.65 0.80 0.85 0.80 0.65

1 -0.50 -0.05 0.30 0.55 0.70 0.75 0.70

Earnings Table Minimum game

Smallest value of X chosen

7 6 5 4 3 2 1

7 1.30 1.10 0.90 0.70 0.50 0.300.10

6 1.20 1.00 0.80 0.60 0.400.20

Your 5 1.10 0.90 0.70 0.500.30

Choice 4 1.00 0.80 0.60 0.40

of X 3 0.80 0.700.50

2 0.700.60

1 0.70

Motivation: Past experiments

Symmetric coordination games of the stag hunt variety

-> Van Huyck, Battalio, Beil 1990, 1991: in minimum and median games with multiple Pareto-ranked equilibria, the Pareto-efficient equilibrium (PeE) typically not selected.

-> Berninghaus, Ehrhart 1998: frequency of play crucial

-> VHBB 1993: adding pre-play auction each period facilitates coordination on PeE

-> Cachon, Camerer 1996: asking participants to pay fixed price for participation facilitates coordination on PeE

-> VHBB 1996: refining action space facilitates climbing toward PeP

Signals in all of the above both tacit and costly.

Motivation (2): Past experiments

Costless signaling in coordination games

-> Cooper, DeJong. Forsythe, Ross (1992):

- two-player games with two Pareto-ranked equilibria

- one-sided as well as two-sided pre-play communication

- cheap talk has potential to facilitate equilibrium play,

two-sided pre-play communication more so than one-sided

-> VHBB 1990 suggest that results of two-player games may be very different from those that involve more than two players

We combine the experimental frameworks of VHBB 1990, 1991, and CDFR 1992, to explore whether costless pre-play communication with a priori meaningful messages by all players is effective in coordination games with more than two players.

Motivation (3): Theoretically interesting issues

“ … the equilibrium notion does not serve in general as a guide to action.” (Luce, Raiffa, 1957, p. 172) Hence Nash equilibria frequently viewed as self-enforcing agreements emerging from pre-play communication.

Transformation of base game into communication game: Does it move strategic uncertainty game from the former to the latter?

Depends on credibility of messages (Farrell, Rabin 1996):

- are they self-committing?

- are they self-signaling? (Aumann 1990)

- to what extent does the riskiness of equilibria in the base game affect effectiveness of communication? (Blume 1998)

- how to define credibility of messages when more than two players are involved? How does one define credibility of message profiles involving more than two players?

Motivation (4): Theoretically interesting issues

Can multiple communication rounds preceding the base game provide the opportunity to repeatedly try to achieve unanimity and thus to renegotiate Nash equilibria as in Farrell (1987), Rabin (1994), and Jamison (2002)?

- message meanings might degrade

- opportunities for learning and abandoning of unsuccessful message profiles (“secret handshake” argument underlying much of evolutionary literature on pre-play communication in games: Robson 1990, Matsui 1991, Waerneryd 1991, Kim, Sobel 1995, Hurkens 1996, Blume 1998)

Motivation (5): Theoretically interesting issues

Our design lets us look at a number of these issues. Minimum game more sensitive to strategic uncertainty than

median game:

- deviation of a single player from PeE consequential for former, but not for latter

- maxmin action in minimum game corresponds to strict NE with the lowest payoff whereas in the median game it corresponds to third lowest

- increasing heterogeneity in action profile lowers min action without necessarily affecting the median

No self-signaling messages in minimum game but they do exist in the median game. No reason though to expect the unique PeE to be played in the one-shot version of the communication game.

Do we see evidence of secret handshakes?

Med w/out

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

averageaction

medianaction

Med with

0

12

3

4

56

7

8

1 2 3 4 5 6 7 8

average action

median action

averagemessage

medianmessage

Comparison Med treatments

012

3456

78

1 2 3 4 5 6 7 8

average action median action

01234

5678

1 2 3 4 5 6 7 8

average action median action

average message median message

Min w/out

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

average action

median action

Min with

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

average action

median action

averagemessagemedianmessage

Comparison Min treatments

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

average action median action

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8average action median action

average message median message

Payoffs Med treatments

Med Wout Med With1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

A 1.14 1.09 1.28 1.13 0.98 1.18 0.83 0.99 A 1.30 1.30 1.09 1.23 1.30 1.04 1.30 0.87B 1.11 1.06 1.30 1.18 1.00 1.07 0.91 0.92 B 1.30 1.30 1.29 1.21 1.30 1.30 1.28 0.84C 1.29 1.08 1.28 1.19 0.99 1.13 0.89 0.83 C 1.30 1.30 1.30 1.21 1.16 1.30 1.30 1.00D 1.30 1.09 1.30 1.19 0.99 1.18 0.99 0.96 D 1.30 1.30 1.30 1.22 1.29 1.30 1.14 0.97E 1.24 1.09 1.30 1.11 0.96 1.17 1.00 0.98 E 1.30 1.30 1.14 1.19 1.30 1.03 1.29 0.98F 1.30 1.06 1.30 1.16 0.98 1.17 0.97 0.98 F 1.30 1.30 1.30 1.23 1.29 1.30 1.30 1.00G 1.30 1.09 1.25 1.13 0.89 1.15 1.00 0.96 G 1.30 1.30 1.30 1.22 1.30 1.29 1.30 1.01H 1.30 1.08 1.19 1.18 0.99 1.01 0.99 0.99 H 1.30 1.29 1.30 0.88 1.24 1.27 1.30 1.01I 1.30 1.10 1.30 1.18 0.97 1.14 0.93 0.83 I 1.30 1.30 1.24 1.16 1.27 1.30 1.30 0.76Av. 1.25 1.08 1.28 1.16 0.97 1.13 0.95 0.94 Av. 1.30 1.30 1.25 1.17 1.27 1.24 1.28 0.94

Session wo1Me wo2Me wo3Me wo4Me wo5Me wo6Me wo7Me wo8Me Session w1Me w2Me w3Me w4Me w5Me w6Me w7Me w8MeAvg. 10.04 8.65 10.21 9.28 7.78 9.06 7.57 7.49 Avg. 10.40 10.39 10.01 9.36 10.19 9.89 10.23 7.49Max. 10.40 8.80 10.40 9.50 8.00 9.40 8.00 7.95 Max. 10.40 10.40 10.40 9.80 10.40 10.40 10.40 8.05Min. 8.90 8.45 9.50 8.90 7.15 8.10 6.65 6.60 Min. 10.40 10.35 8.70 7.00 9.30 8.20 9.15 6.05

Payoffs Min treatments

Min Wout Min With1 2 3 4 1 2 3 4 5 6 7 8

A 0.61 0.59 0.54 0.44 A 1.05 1.19 0.96 0.56 1.05 1.03 0.44 1.30B 0.70 0.69 0.55 0.58 B 1.11 1.19 0.90 0.61 0.94 1.03 0.63 1.30C 0.61 0.60 0.63 0.60 C 1.11 1.18 0.84 0.60 0.98 1.03 0.50 1.30D 0.54 0.45 0.54 0.41 D 1.09 1.18 0.95 0.55 0.93 1.08 0.25 1.30E 0.60 0.55 0.50 0.53 E 1.10 1.18 0.93 0.48 1.03 1.11 0.40 1.30F 0.76 0.50 0.48 0.49 F 1.11 1.18 0.91 0.54 0.95 1.10 0.55 1.30G 0.53 0.40 0.65 0.64 G 1.06 1.18 0.93 0.63 1.00 1.05 0.33 1.30H 0.40 0.50 0.55 0.70 H 1.10 1.24 0.84 0.64 0.96 1.08 0.75 1.30I 0.76 0.50 0.49 0.39 I 1.18 1.18 0.91 0.71 0.94 1.03 0.55 1.30Av. 0.61 0.53 0.55 0.53 Av. 1.10 1.18 0.91 0.59 0.97 1.06 0.49 1.30

Session wo1Mi wo2Mi wo3Mi wo4Mi Session w1Mi w2Mi w3Mi w4Mi w5Mi w6Mi w7Mi w8MiAvg. 4.90 4.24 4.37 4.23 Avg. 8.81 9.48 7.26 4.72 7.79 8.46 3.90 10.40Max. 6.10 5.50 5.20 5.60 Max. 9.40 9.90 7.70 5.70 8.40 8.90 6.00 10.40Min. 3.20 3.20 3.80 3.10 Min. 8.40 9.40 6.70 3.80 7.40 8.20 2.00 10.40

Table A: Median DISTRIBUTION OF INITIAL ACTION CHOICES

Action Choice Session

7 6 5 4 3 2 1

B1Me † 1   1   1  

B2Me   3 ‚ 4      

B3Me …   3 1      

B4Me 4 ‚ 1 1 1    

B5Me     4 „ 1    

B6Me 1 2 ‚ 4      

B7Me 4     …      

B8Me 1 2   ‚ 4    

Sum 21 10 12 22 6 1 0M1Me ‰            

M2Me ˆ 1          

M3Me … 1 1 2      

M4Me   2 „   3    

M5Me … 1 2 1      

M6Me … 2 1     1  

M7Me ‡   1   1    

M8Me     1 ‡     1Sum 39 7 10 10 4 1 1

Table M: Median DISTRIBUTION OF INITIAL MESSAGES

MessageSession

7 6 5 4 3 2 1

M1Me ˆ 1          

M2Me †   3        

M3Me † 1 1       1

M4Me 1 2 ƒ 2 1    

M5Me 3 ‚ 2 2      

M6Me … 2 1     1  

M7Me †   1   1 1  

M8Me 2   2 ‚ 1 2  

Sum 37 8 13 6 3 4 1

Table A: Minimum DISTRIBUTION OF INITIAL ACTION CHOICES

Action ChoiceSession

7 6 5 4 3 2 1

B1Min 7       1   1

B2Min 7   1       1

B3Min 8           1

B4Min 7     1 1    

Sum 29 0 1 1 2 0 3

M1Min 5 1 2 1      

M2Min 8   1        

M3Min 8   1 5      

M4Min 6 1 1 1      

M5Min 5 1 1 1     1

M6Min 8       1    

M7Min 8           1

M8Min 9            

Sum 57 3 6 3 1 0 2

Table M: Minimum DISTRIBUTION OF INITIAL MESSAGES

MessageSession

7 6 5 4 3 2 1

M1Min 5 1 2 1      

M2Min 8     1      

M3Min 8     1      

M4Min 8            

M5Min 6 1   2      

M6Min 8       1    

M7Min 7       1   1

M8Min 8 1          

Sum 58 3 2 6 2 0 1

Conclusion

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