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The Selten School of Behavioral Economics pp 73–87Cite as

Deviations from Equilibrium in an Experiment on Signaling Games: First Results

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Abstract

In this paper we provide a summary of results concerning two series of experiments we ran based on a modified signalling game, which was presented graphically to subjects on a screen. The game for the initial experiment was selected by Reinhard Selten in coordination with the first named author. It has the interesting property that the strategically stable outcome (Kohlberg and Mertens 1986) does not coincide with the outcome of the Harsanyi-Selten solution (Harsanyi and Selten 1988). However, it is a complex game insofar as standard refinement concepts like the intuitive criterion, or the never-a-weak-best-response criterion, do not help to refine among the equilibria. The second motive for the design was to analyse, how the change in the reward at a particular terminal node would affect behaviour.

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Notes

  1. 1.

    We would like to thank Reinhard Selten for the design of the game used in the initial set of experiments; the staff working at the Bonn Laboratory of Experimental Economics and the Finance and Economics Experimental Laboratory in Exeter (FEELE), for their support while conducting the experiments; and Karim Sadrieh for the organisation of the “Scientific Excursions with Reinhard Selten” which motivated us to conduct the new experiments.

  2. 2.

    The term is due to Reinhard Selten.

  3. 3.

    Detailed proofs are available on request.

  4. 4.

    The 2 × 2 game was added following the strategically safe choice of type 1b, but then moves were coalesced.

  5. 5.

    These experiments were designed and conducted under the supervision of Reinhard Selten.

  6. 6.

    However, we did not see any indication that this difference of information mattered.

  7. 7.

    We calculated the average and standard deviation of the percentage of times Player 1 chose left at information set 1a, relative to the number of times this information set was reached for each session. The following tables are calculated in a similar manner.

  8. 8.

    The test is highly significant for Rounds 1–25, but not for Rounds 26–50. Thus, the original stronger incentive for Player 1 to take the strategically risky option gets somewhat dampened by experience.

  9. 9.

    Except for Rounds 51–55 in the new set of experiments which just misses the 5% level of significance.

  10. 10.

    We disregarded the sessions of the old experiments since information set 2α was not reached often enough.

  11. 11.

    The fractions are calculated relative to the number of times Nature chose right and Player 1 did not choose left.

  12. 12.

    In the impulse balance equilibrium, right is chosen with probability ½ by Player 1 and with probability 2/3 by Player 2. In the action sampling equilibrium, right is chosen with probability 0.56 by Player 1 and with probability 0.66 by Player 2.

  13. 13.

    Our programme initially highlights each choice at the relevant information set with equal probability. Subject can then change which choice is highlighted with the left and right cursor keys. Once the desired choice is highlighted, subjects decide on it by pressing the Enter key.

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Author information

Authors and Affiliations

  1. Department of Economics, University of Exeter Business School, Streatham Court,Rennes Drive, Exeter, EX4 4PU, UK

    Dieter Balkenborg & Saraswati Talloo

Authors
  1. Dieter Balkenborg
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  2. Saraswati Talloo
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Editor information

Editors and Affiliations

  1. Magdeburg, Otto-von-Guericke-Universität, Magdeburg, 39106, Germany

    Abdolkarim Sadrieh

  2. Staatswissenschaftliches, (Volkswirtschaftliches) Seminar, Universität Köln, Albertus-Magnus-Platz, Köln, 50923, Germany

    Axel Ockenfels

Appendix

Appendix

Old Experiment, Terminal Nodes Reached in Rounds 1–25a

 

A

B

C

D

E

F

G

H

I

1 (x = 4)

75

0

4

0

1

11

22

10

27

2 (x = 4)

15

59

5

8

0

12

20

6

25

3 (x = 4)

30

44

8

4

1

7

19

9

28

4 (x = 5)

66

3

10

0

2

9

24

17

19

5 (x = 5)

46

13

14

1

1

10

22

11

32

6 (x = 5)

53

9

20

3

3

10

19

11

22

7 (x = 6)

21

37

21

1

0

4

16

22

28

8 (x = 6)

38

26

18

6

2

4

34

2

20

9 (x = 6)

24

37

21

0

2

9

27

9

21

a“x” denotes the payoff of Player 1 at terminal node B

Old Experiment, Terminal Nodes Reached in Rounds 26–50

 

A

B

C

D

E

F

G

H

I

1 (x = 4)

72

2

3

0

0

13

26

10

24

2 (x = 4)

51

13

13

4

2

2

21

17

27

3 (x = 4)

27

32

14

3

1

13

15

19

26

4 (x = 5)

32

38

7

1

0

13

16

13

30

5 (x = 5)

28

34

14

3

0

8

24

7

32

6 (x = 5)

50

10

13

1

3

15

17

10

31

7 (x = 6)

3

54

20

1

1

11

24

18

18

8 (x = 6)

27

33

13

5

0

9

14

19

30

9 (x = 6)

7

55

11

5

4

8

21

11

28

Old Experiment, Terminal Nodes Reached in Rounds 51–55

 

A

B

C

D

E

F

G

H

I

1 (x = 4)

91

0

0

0

0

10

26

15

38

2 (x = 4)

72

16

3

4

2

10

51

6

16

3 (x = 4)

69

12

14

3

1

22

25

20

14

4 (x = 5)

15

68

8

0

0

16

26

17

30

5 (x = 5)

50

31

11

1

0

5

20

12

50

6 (x = 5)

62

13

20

2

5

13

20

13

32

7 (x = 6)

0

72

19

3

1

3

24

12

46

8 (x = 6)

58

17

20

1

8

8

32

10

26

9 (x = 6)

16

44

35

7

6

13

25

10

24

New Experiment, Terminal Nodes Reached in Rounds 1–25a

 

A

B

C

D

E

F

G

H

I

1

17

45

15

7

5

61

0

0

0

2

4

53

27

7

2

57

0

0

0

3

10

32

28

15

7

58

0

0

0

4

26

16

24

7

8

69

0

0

0

5

4

43

25

6

5

67

0

0

0

6*

28

31

23

5

5

58

0

0

0

7*

15

37

17

17

5

59

0

0

0

8*

14

40

26

3

8

59

0

0

0

9*

9

48

25

15

8

45

0

0

0

10*

30

23

26

17

11

43

0

0

0

∑

157

368

236

99

64

576

0

0

0

aThe * refers to experimental sessions where information on all simultaneous plays was not given to the subjects

New Experiment, Terminal Nodes Reached in Rounds 26–50

 

A

B

C

D

E

F

G

H

I

1

2

49

14

5

1

2

16

6

55

2

1

61

12

13

3

0

2

2

56

3

24

29

34

2

0

2

3

5

51

4

33

21

26

0

1

0

1

4

64

5

17

38

23

6

6

0

14

2

44

6*

35

24

17

8

2

1

9

7

47

7*

36

7

33

4

5

0

2

1

62

8*

10

50

19

2

2

0

1

3

63

9*

5

48

16

5

0

1

7

5

63

10*

43

9

23

5

7

0

7

1

55

∑

206

336

217

50

27

6

62

36

560

New Experiment, Terminal Nodes Reached in Rounds 51–55

 

A

B

C

D

E

F

G

H

I

1

7

59

23

11

3

2

17

1

57

2

0

64

32

10

6

0

2

3

63

3

19

55

20

0

0

1

9

19

57

4

31

22

27

0

0

0

5

6

89

5

16

38

35

7

2

0

26

2

54

6*

39

35

30

2

5

0

15

3

51

7*

25

24

27

0

0

0

0

7

97

8*

7

45

41

4

3

0

2

11

67

9*

0

59

25

7

4

1

7

2

75

10*

32

28

36

13

9

0

15

6

41

∑

176

429

296

54

32

4

98

60

651

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Balkenborg, D., Talloo, S. (2010). Deviations from Equilibrium in an Experiment on Signaling Games: First Results . In: Sadrieh, A., Ockenfels, A. (eds) The Selten School of Behavioral Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13983-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-13983-3_7

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