Bargaining under large risk – an experimental analysis

Abstract

We experimentally study behavior in bargaining situations under large risks. To implement realistic risks involved in the field, we calibrate the experimental parameters from an environment involving substantial variation in profits, the motion picture industry. The leading example is the production of a movie that may give rise to a sequel, so actors and producers negotiate sequentially. We analyze the data in light of alternative behavioral approaches to understanding bargaining behavior under large risk.

Keywords:

• negotiation experiment
• ultimatum bargaining
• parameter calibration
• movie production
• risk sharing

Acknowledgements

We gratefully acknowledge the very helpful and constructive advice of two anonymous referees leading to a major revision. We thank Tim Grebe for his help conducting the experiment, Charles Bellemare for providing his non-parametric OX-package, and Jan Potters, Karim Sadrieh, Kristian Rydqvist for helpful discussions. Financial support from the Deutsche Forschungsgemeinschaft, SFB 373 and the Max Planck Institute of Economics is gratefully acknowledged.

Notes

1. Results are reported in Mitzkewitz & Nagel (1993), Straub & Murnighan (1995) and Rapoport et al. (1996), who study ‘offer games’ in which the distribution of the stochastic surplus is common knowledge but its realization is private information of the proposer, who offers an amount to the responder. Kagel et al. (1996) observe similar strategic behavior of proposers when exchange rates, which are private information and differ between proposer and responder, are revealed to the proposer only. Mitzkewitz and Nagel (1993) and Seale et al. (2001) study additionally ‘demand games’ in which the distribution of the stochastic surplus is common knowledge but its realization is private information of the proposer, who demands an amount from the (to the responder unknown) realized surplus of the responder.

2. Experiments with relatively large losses are Güth & Tietz (1986), who auctioned the positions of ultimatum bargainers before letting the auction winners play the game, and Lind & Plott (1991).

3. Once in the framework of two-stage ultimatum bargaining, one could, of course, distinguish all possibilities of certainty, one or two-sided uncertainty about the first and second round pie.

4. De Vany & Walls (2002) note that ‘Motion pictures are among the riskiest of products; each movie is a one-off innovation with highly unpredictable revenues and profits.’

5. Our calibrations and the data for our study are based on a case study (Teichner & Luehrman, 1992) that contains data on 99 movies in the 1989-season and some additional data on the profitability of sequels, based on 60 sequels produced between 1970 and 1990. Teichner & Luehrman base their data on Variety Magazine and some other industry sources.

6. There exist a few studies (Grether & Plott, 1984, and Hong & Plott, 1982), in which experimental parameters have been chosen to resemble those in the field.

7. Venture capital firms finance their portfolio firms in stages. At each stage, the venture capitalist either negotiates another round of financing or refuses further financing and terminates the relationship (Gompers, 1995).

8. Outside options are also explored by Binmore et al. (1989).

9. Notable exceptions are the James Bond movies that led to a remarkable number of sequels, albeit with constant blocks of different actors.

10. It is common for actors to sign profit sharing contracts. For those contracts, a contrast is often drawn between actors who have little bargaining power and sign contracts over profit shares, and big stars who are able to sign for shares of the revenues (Weinstein, 1998).

11. Although actors often help to finance film projects we admit that this rarely applies when actors are unknown. But, of course, even such actors or actresses may have rich friends.

12. We do not allow for output-contingent contracts. Chisholm (1997) provides an empirical analysis of profit sharing versus fixed pay contract choice in the motion picture industry. Her findings suggest that actor share contracts may be offered when the marginal impact of additional effort on the commercial success of the film is expected to be significant. However, we do not model effort-incentives, so the usual reasons for output-related pay do not apply. See Holström (1979) and Grossman & Hart (1983) for the traditional argument for output-contingent contracts. See Güth & Maug (2007) for an example of a principal-agent model with effort-incentives.

13. Sequels are a much safer bet. Evidence comes from the case study (Teichner & Luehrman, 1992), we base our calibration on, as well as from Prag & Casavant (1994), who find a positive relation between a film's revenue and the film being a sequel.

14. The discount rate of 12% is suggested by the case writers.

15. For further information, e.g. about the distribution of NPVs, see Teichner & Luehrman (1992).

16. The full calibration results for the parameters are listed in Table 9 in Appendix A.

17. See Appendix E for a shortened and translated version of the instructions.

18. Rematching was restricted to matching groups. Participants were not informed about the restriction of rematching within matching groups to discourage repeated game effects.

19. A session lasted on average 140 minutes. Participants were paid their average payoff of all 18 rounds, on average [euro]11.50 plus an initial endowment of [euro]5 which, of course, might have led to idiosyncratic wealth effects and influenced later risk attitudes and equity concerns. The data, however, revealed no such systematic effects.

20. The actor will accept the lower offer and not be compensated with probability (1−ω). If the producer offers at the first stage in case of a hit, the actor can offer C₂/2−Δ. To reach the equal split he should be compensated by Δ.

21. Equity theory would predict .

22. Equity theory does not allow continuous tradeoffs, like aversion against inequity (Fehr & Schmidt, 1999; Bolton & Ockenfels, 2000) or concerns for the least well in the society (Charness & Rabin, 2002). For measuring deviations from equity theory, see also Clark (1998).

23. Equity theory does not take outside options into account as long as and , for i∊{A,P}.

24. The probability that subject i ‘s wage offer (W _1,i ) lies in the theoretically predicted interval with the lower bound b_l and upper bound b_u is estimated as ) with 1(⊕) denoting the indicator function. The confidence bounds are estimated as .

25. The Sign test compares the number of positive and negative deviations from the hypothesized median. For our data, the test is appropriate as it does not require symmetry of the data under consideration. The distribution of second stage offers is skewed to the left.

26. We will analyze the averages of matching groups. Since nobody in one matching group ever interacts with somebody of another matching group averages are independent.

27. This result holds on the individual level at (p = 0.000) where, of course, independence is not guaranteed.

28. In only three out of 12 sessions are average earnings of actors higher than average earnings of producers.

29. Such ‘negative wages’ in the experiment capture the idea that yet unknown actors and actresses must either bear some financial risk or pay a ‘price’ for being hired.

30. Camerer (2003) provides a more recent survey.

31. We only summarize the results of an analysis of risk parameters as well as of different individual reactions in stage two in the Appendix (B and C).

32. In general, risk aversion means that (cardinal) utility is concavely increasing in monetary gains; CRRA relies on with constant parameter ρ.

33. In total, we excluded 21 subjects from the analysis for one of the following reasons: (1) subjects rejected offers of W ₁ = 2 and higher, which is inconsistent with any interpretation based on risk-aversion; (2) the highest offer rejected was smaller than the lower bound W = −4.5; (3) the lowest accepted offer was higher than the highest offer rejected.

34. We estimate risk aversion by stipulating (see Appendix C) that W ₀ = 20 (approximately equal to average experimental earnings).

35. Another way to estimate risk preferences would be to assume that the acceptance threshold lies in the middle of the interval of the highest rejected and the lowest accepted offer. In this case, we can estimate by averaging the highest rejected and the lowest accepted offer and obtain a larger range of risk parameters [0.21, 26.17]

36. Nevertheless, those findings should be interpreted cautiously as only 44% of the subjects in the actor position could be used in the estimation of the risk aversion parameter. The decisions of all remaining subjects were not informative because their highest rejected offer did exceed their lowest accepted offer. In addition, the estimation of the γ-parameter of the threshold density function cannot account for all data. It considers only offers in the interval [−4.5,2] which comprises only 15% of all first stage offers.

37. Estimation of Π₂ on W ₁ results in for the parameter estimates with standard errors in parentheses and R ² = 0.01.

38. There is a total of 36 actors. Two participants could not be classified. One subject had only once the chance to make an offer at the second stage. The other person received and offered the same amounts in both cases.

39. The reciprocity analysis should be interpreted cautiously as we observe between 2 and 7 second stage responses per actor. Nevertheless, it shows that the current theories are rather questionable in a more complex environment.

40. Two sequels to this film were made, but their economic success was far lower than expected on the basis of the first film.

41. The second order condition for payoff maximization is .

42. The likelihood function is . One then substitutes for and takes logs.