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Framing Effects in the Prisoner's Dilemma but Not in the Dictator Game

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Framing Effects in the Prisoner's Dilemma but Not in the Dictator Game Framing effects in the Prisoner’s Dilemma but not in the Dictator Game Sebastian J. Goerga,b, David Randc,d & Gari Walkowitze January 31, 2017 Abstract We systematically investigate prisoner’s dilemma games and dictator games with valence framing. We find that give versus take frames influence subjects’ behavior and beliefs in the prisoner’s dilemma game but not in the dictator game. Keywords: Prisoner’s Dilemma, Dictator Game, Framing, Give, Take, Cooperation, Generosity JEL Codes: A13, C72, C91, F51, Z13 Contacting the authors: [email protected] [email protected], [email protected] a Florida State University, 113 Collegiate Loop, Tallahassee, FL 32306, United States. b Max Planck Institute for Research on Collective Goods, Kurt-Schumacher-Straße 10, 53113 Bonn, Germany. c Department of Psychology, 2 Hillhouse Ave, Yale University, New Haven CT 06511, United States. d Department of Economics, 2 Hillhouse Ave, Yale University, New Haven CT 06511, United States. e Faculty of Management, Economics and Social Sciences, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne, Germany. 1 1. Introduction Countless papers have demonstrated that framing can change behavior despite the underlying information and options remaining the same (see recent reviews by Gerlach and Jaeger, 2016; Cartwrigth, 2016). But when and how, precisely, do frames affect behavior? Without additional assumptions, most theories of other-regarding preferences (e.g., Fehr and Schmidt 1999; Bolton and Ockenfels, 2000; Charness and Rabin, 2002) predict no differences between two frames of the same decision problem. Ellingsen et al. (2012) argue that social frames, i.e, naming a game for example “community” or “stock market” game, provides a coordination device helping to select between multiple equilibria with social preferences. They support this account by showing framing effects in synchronous but not asynchonorous Prisoner’s Dilemmas. The findings of Dreber et al. (2012), who do not observe significant effects of social frames in dictator games, provide further support, because coordination problems do not exist in dictator games. Also compatible with the beliefs account is Dufwenberg et al. (2011), who demonstrate that valence and social-frames in one-shot public good games affect not only subjects’ contributions but also their first- and second-order beliefs. Conversely, Cox et al. (2013) argue based on revealed altruism (Cox et al., 2008) that positive and negative frames result in different games with different degrees of expected reciprocity. Similarly, Gächter et al. (2016) find that give and take frames not only influence beliefs but also increase the share of conditional cooperators. In this paper, we provide new evidence regarding these arguments by systematically investigating prisoner’s dilemma games and dictator games with valence framing. We observe that give and take frames influence subjects’ behavior and beliefs in 2 the prisoner’s dilemma but not in the dictator game. Our data is most simply explained by Ellingsen et al. (2012)’s beliefs account, but cannot rule out frames affecting the extent of reciprocity-based preferences. 2. Experimental Design We investigate a give and a take frame for the prisoner’s dilemma game and the dictator game. The games are implemented as one-shot games. 2.1 Prisoner’s Dilemma Games The prisoner’s dilemma games are implemented as continuous choice games. They allow subjects to choose a degree of cooperation instead of a dichotomous decision to cooperate or to defect (Goerg and Walkowitz, 2010). Cooperation is welfare enhancing and increases the joint payoffs. In the give frame, cooperation is expressed by the amount given to the other player. In the take frame, it is expressed by the amount left to the other player. In both frames, two players are randomly matched and each subject receives an initial endowment of 100 Talers. In the give frame, subject i decides an integer amount a between 0 and 100 to the matched player. The transferred amount is doubled and credited to the matched player’s account. The game is symmetric. The matched player j simultaneously decides on an amount aj to be doubled and transferred to player i. Thus, the payoff function for player i, based on amounts ai and aj, is given as: �! = 100 − �! + 2�!, with �!, �! ∈ 0,1, … ,100 The payoff for player j is derived analogously. 3 The take frame is very similar. However, the players simultaneously decide on amounts ai and aj they want to transfer from the matched player’s endowment. The amount remaining in the matched player’s account is doubled. Player i’s payoff function is given as: �! = 2 ∗ (100 − �!) + �!, with �!, �! ∈ 0,1, … ,100 The payoff for player j is derived analogously. 2.2. Dictator Games The dictator games mimic our prisoner’s dilemma games but with one player remaining passive.1 One player is endowed with 200 Talers. The other player receives no initial endowment. In the give frame, the endowment is allocated to the dictator i, who decides on an integer amount a between 0 and 200 to be transferred to the passive receiver j. As in the Prisoner’s Dilemma Game with the give frame, the transfer is doubled. Thus, the payoffs functions for dictator i and receiver j are given as: �! = 200 − �!, with �! ∈ 0,1, … ,200 �! = 2�!, with �! 0,1, … ,200 In the take frame, the endowment is given to the passive player j. The dictator i decides on the amount to be transferred away from the passive player. The amount left to the passive player is doubled, resulting in the following payoff functions: �! = �!, with �! ∈ 0,1, … ,200 �! = 2 ∗ (200 − �!), with �! 0,1, … ,200 1 Other studies on dictator games with give and take options increase the action set into the take domain (List, 2007) or use give and take frames to investigate social norms (Krupka and Weber, 2013) and property rights (Hoffmann et al., 1994; Eichenberger and Oberholzer-Gee, 1998; Oxoby and Spraggon, 2008). Our game differs in the following ways: a very neutral framing is applied to identical action sets, we avoid terms like “give” or “take”, we induce efficiency gains from generosity, and the initial endowment is not earned. 4 2.3. Implementation The experiments were conducted at the Cologne Laboratory for Economic Research at the University of Cologne. While we confronted subjects with the different frames, we implemented the frames using language that was as neutral as possible. Instead of labeling decisions as “give” or “take” decisions, only the recipient of the transfers was changed in the description. In the give frame, subjects were told that they had the opportunity to transfer any part of their endowment to Person B. In the take frame, they had the opportunity to transfer any part of Person B’s endowment to themselves.2 After the decision, we elicited first order beliefs.3 To avoid session effects, we played all four games in each of the eight conducted sessions.4 Subjects were recruited from the local ORSEE database (Greiner, 2015). Decisions, beliefs and normative statements were gathered using pen and paper, followed by a questionnaire programmed in z-Tree (Fischbacher, 2007). Game Frame # ind. Observations # subjects %female av. age Prisoner’s Dilemma Give 52 52 55.7 24.4 Prisoner’s Dilemma Take 54 54 50 23.1 Dictator Give 40 (16) 56 55.4 22.5 Dictator Take 41 (16) 57 50.9 23.9 Table 1: Summary of gathered observations. Numbers in the brackets for the dictator games denote the number of recipients. 2 This is in contrast to other papers which used give and take frames. A translation of the instructions is provided in Appendix A. 3 In addition we elicited second order beliefs and statements on normatively fair. For brevity we will focus on first order beliefs and transfers. 4 In four sessions 31 subjects participated, in two sessions 24 subjects, in one session 22 subjects and one with 17 subjects. 5 In total 219, subjects participated: 106 in the Prisoner’s Dilemma Games, 113 in the Dictator Games (81 in the role of the dictator and 32 in the role of the passive receiver).5 53% of the subjects were female and the average age was 23.5 years (see Table 1). 3. Results Figure 1 depicts the transfers exhibited in the Prisoner’s Dilemma games and in the dictator games, as well as the corresponding first-order beliefs and standard errors.6 In the Prisoner’s Dilemma game, transfers are significantly higher in the give frame than in the take frame (p<0.001)7. On average, the cooperation level is more than twice as high if subjects were allowed to transfer to the matched player instead of transferring to themselves. Table 2 gives the results of Tobit regressions confirming the negative and significant influence of the take frame. This main effect remains significant when controlling for gender and age. 5 To generate more independent observations per session, we matched one passive receiver to several dictators. 6 To make transfers comparable across give and take frame, transfers in the take frames needed to be transformed. In the negative frame of the Prisoner’s Dilemma game, cooperation is measured by (100-a) and generosity in the dictator game by (200-a). 7 Two-sided Mann-Whitney u-tests are applied if not stated otherwise. 6 Behavior Belief Prisoners Dilemma PG Give PG Take Dictator Game DG Give DG Take 0 20 40 60 80 100 0 20 40 60 80 100 % Cooperation/Generosity Figure 1: Box plot for the degree of cooperation in the Prisoner’s Dilemma games and the degree of generosity in the dictator games. Bold line gives the median, the box the 25th and 75th quartiles, and whiskers the 1.5xIQR. Transfers in the take frames are transformed for comparability.
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