the effects of costless preplay communication: evidence fromgames with pareto-ranked equilibria

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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 - PowerPoint PPT Presentation

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

    Andreas Ortmann

    Center for Economic Research and Graduate Education, Charles UniversityEconomics Institute,Academy of Sciences of the Czech RepublicPrague, 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 0.900.550.10-0.45-1.10 61.251.201.050.800.45 0.00-0.55Your 51.101.151.100.950.70 0.35-0.10Choice 40.851.001.051.000.85 0.60 0.25of X 30.500.750.900.950.90 0.75 0.50 20.050.400.650.800.85 0.80 0.65 1 -0.50 -0.050.300.550.70 0.75 0.70

  • Earnings Table Minimum game Smallest value of X chosen 7 6 5 4 3 2 1 71.301.10 0.900.700.500.300.10 61.201.000.800.600.400.20Your 51.100.900.700.500.30Choice 41.000.800.600.40of X 30.800.700.50 20.700.60 10.70

  • Motivation: Past experimentsSymmetric 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 experimentsCostless 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 issuesCan 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 issuesOur 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 medianNo 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

    Chart1

    4.79166666675

    5.15277777785

    5.3755

    5.40277777785

    5.27777777785

    5.36111111115.5

    5.43055555566

    5.45833333336

    average action

    median action

    Graphs

    Summary Statistics

    .3 and .7 percentiles

    .1 and .9 percentiles

    Graphs

    5.305555555665.22222222226

    5.458333333375.44444444447

    5.569444444475.38888888897

    5.583333333375.56944444447

    5.62575.56944444447

    5.763888888975.65277777787

    5.930555555675.63888888897

    5.888888888975.36111111117

    average action

    median action

    average message

    median message

    Med with

    Payoffs

    6.444444444476.45833333337

    5.958333333376.40277777787

    5.986111111176.48611111117

    6.055555555676.6257

    5.722222222276.45833333337

    5.402777777876.30555555567

    5.305555555666.34722222227

    5.861111111176.38888888897

    average action

    median action

    average message

    median message

    Min with

    CountMinWith

    6.13888888897

    5.05555555566

    3.80555555564

    2.58333333331.5

    2.11111111111

    1.58333333331

    1.47222222221

    1.38888888891

    average action

    median action

    Min w/out

    MedWithDirections

    4.79166666675

    5.15277777785

    5.3755

    5.40277777785

    5.27777777785

    5.36111111115.5

    5.43055555566

    5.45833333336

    average action

    median action

    Med w/out

    MedWithWork

    64

    64

    74

    74

    64

    74

    74

    64

    Med w/out

    MedWith

    77

    74

    52.5

    31

    21

    1.51

    21

    1.51

    Min w/out

    MedWoutDirections

    74

    75

    76

    75.3

    76

    77

    77

    77

    Med with

    MedWoutWork

    77

    76

    76

    76

    76

    75.3

    74.3

    76

    Min with

    MedWout

    72.1

    73.1

    74

    74

    74

    74

    74

    74

    Med w/out

    MinWithDirections

    73

    71.5

    71

    61

    4.51

    21

    21

    21

    Min w/out

    MinWithWork

    72.1

    71

    71

    71

    71

    71

    71

    71

    Med with

    MinWith

    75

    73.1

    71.2

    72

    71.1

    71

    71

    71

    Min with

    MinWoutDirections

    Average payoffs

    Med WoutMin Wout

    123456781234

    A1.141.091.281.130.981.180.830.99A0.610.590.540.44

    B1.111.061.301.181.001.070.910.92B0.700.690.550.58

    C1.291.081.281.190.991.130.890.83C0.610.600.630.60

    D1.301.091.301.190.991.180.990.96D0.540.450.540.41

    E1.241.091.301.110.961.171.000.98E0.600.550.500.53

    F1.301.061.301.160.981.170.970.98F0.760.500.480.49

    G1.301.091.251.130.891.151.000.96G0.530.400.650.64

    H1.301.081.191.180.991.010.990.99H0.400.500.550.70

    I1.301.101.301.180.971.140.930.83I0.760.500.490.39

    Av.1.251.081.281.160.971.130.950.94Av.0.610.530.550.53

    Sessionwo1Mewo2Mewo3Mewo4Mewo5Mewo6Mewo7Mewo8MeSessionwo1Miwo2Miwo3Miwo4Mi

    Avg.10.048.6510.219.287.789.067.577.49Avg.4.904.244.374.23

    Max.10.408.8010.409.508.009.408.007.95Max.6.105.505.205.60

    Min.8.908.459.508.907.158.106.656.60Min.3.203.203.803.10

    Med WithMin With

    1234567812345678

    A1.301.301.091.231.301.041.300.87A1.051.190.960.561.051.030.441.30

    B1.301.301.291.211.301.301.280.84B1.111.190.900.610.941.030.631.30

    C1.301.301.301.211.161.301.301.00C1.111.180.840.600.981.030.501.30

    D1.301.301.301.221.291.301.140.97D1.091.180.950.550.931.080.251.30

    E1.301.301.141.191.301.031.290.98E1.101.180.930.481.031.110.401.30

    F1.301.301.301.231.291.301.301.00F1.111.180.910.540.951.100.551.30

    G1.301.301.301.221.301.291.301.01G1.061.180.930.631.001.050.331.30

    H1.301.291.300.881.241.271.301.01H1.101.240.840.640.961.080.751.30

    I1.301.301.241.161.271.301.300.76I1.181.180.910.710.941.030.551.30

    Av.1.301.301.251.171.271.241.280.94Av.1.101.180.910.590.971.060.491.30

    Sessionw1Mew2Mew3Mew4Mew5Mew6Mew7Mew8MeSessionw1Miw2Miw3Miw4Miw5Miw6Miw7Miw8Mi

    Avg.10.4010.3910.019.3610.199.8910.237.49Avg.8.819.487.264.727.798.463.9010.40

    Max.10.4010.4010.409.8010.4010.4010.408.05Max.9.409.907.705.708.408.906.0010.40

    Min.10.4010.358.707.009.308.209.156.05Min.8.409.406.703.807.408.202.0010.40

    MinWoutWork

    Round 1Round 2Round 3Round 4Round 5Round 6Round 7Round 8

    MessActMessActMessActMessActMessActMessActMessActMessAct

    758575542584764496244614060356347

    6339156123121711031318

    52635331138031214

    46302110102331804

    32101010010131100

    20022202323001110

    1123528263861351269

    Min With

    MinWout

    17n7n7n7n7n7n7n7u towards 7

    7n7n7n7n7n7n7n7m towards median

    7n7n7n7n7n7n7n7mu more than median up

    7n7n7n7n7n7n7n7md more than median down

    7n7n7n7n7n7n7n7d down

    7n7n7n7n7n7n7n7n no change

    7n7n7n7n7n7n7n7nn no change, outside median

    7n7n7n7n7n7n7n7

    17n7n7n7n7n7n7n7

    77777777

    27n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    6m7n7n7n7n7n7n7

    27n7n7n7n7n7n7n7

    77777777

    35d3m4m5m6m7n7n7

    6m7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    7n7n7n7n7n7n7n7

    4nn4m7n7d5nn5n7n7

    7n7n

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