The Effects of Costless Preplay Communication: Evidence fromGames with Pareto-ranked Equilibria

1. 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)

2. 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

3. 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 0.30 0.10 • 6 1.20 1.00 0.80 0.60 0.40 0.20 • Your 5 1.10 0.90 0.70 0.50 0.30 • Choice 4 1.00 0.80 0.60 0.40 • of X 3 0.80 0.70 0.50 • 2 0.70 0.60 • 1 0.70

4. 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.

5. 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.

6. 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?

7. 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)

8. 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?

9. Med w/out

10. Med with

11. Comparison Med treatments

12. Min w/out

13. Min with

14. Comparison Min treatments

15. Payoffs Med treatments

16. Payoffs Min treatments

17. 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 0 M1Me ‰ M2Me ˆ 1 M3Me 1 1 2 M4Me 2 „ 3 M5Me 1 2 1 M6Me 2 1 1 M7Me ‡ 1 1 M8Me 1 ‡ 1 Sum 39 7 10 10 4 1 1 Table A: Median

18. DISTRIBUTION OF INITIAL MESSAGES Message Session 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 M: Median

19. DISTRIBUTION OF INITIAL ACTION CHOICES Action Choice Session 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 A: Minimum

20. DISTRIBUTION OF INITIAL MESSAGES Message Session 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 Table M: Minimum

21. Conclusion ?