2.1. Motivations and motivation scores

Suppose the individuals in Fig. 1B anticipate that the first mover will hand off control to the second mover and that the second mover will respond with generosity. How will they assess the motivation underlying the second mover’s strategy?

Our model takes the anticipated strategy profile as given and generates an assessment in three steps. First, it identifies all alternative pure strategies that would change at least one individual’s material payoff. In the game of Fig. 1B, the second mover would have to act miserly in any such strategy. Second, it compares the payoffs from the selected and alternative strategies and on that basis classifies the second mover’s strategy into one of the four cells of Table 1. The second mover’s generosity belongs in the upper-right cell: Relative to the alternative, it materially “helps” the other player, the first mover, because he receives 50 and would receive less – 20 – if the second mover were miserly. Furthermore, relative to the alternative, the second mover’s strategy materially “hurts” the second mover herself. She receives 20 but would receive 50 by defecting. Third, based on this classification, the model assigns the strategy a “motivation score” ranging from + 1, which corresponds to unambiguous kindness, to −1, which corresponds to unambiguous unkindness. Because the second mover has forsaken a greater material payoff to improve the lot of the first mover, her generosity is deemed a + 1. Thanks to her sacrifice, in the model her social motivation stands undoubted. She could not have been motivated by material self-interest.

Table 1

Motivation scores for a player’s strategy as a function of how it impacts her counterpart as well as the player herself

What about the first mover’s decision to hand off control? Our analysis stresses that in Fig. 1B, this strategy can be viewed questioningly. First, the only alternative has him act unilaterally. Second, handing off control yields the players 50 and 20, respectively, rather than the 35 and 0 they would receive if the first mover acted unilaterally. So, while the first mover materially “helps” the second mover (20 > 0), he also materially “helps” himself (50 > 35). His handoff is thus classified in the upper-left cell. Third, on that basis, it receives a motivation score of 1 – θ_i, where θ_i is an individual-specific discounting parameter satisfying 0 ≤ θ_i ≤ 1. This parameter dilutes assessments of the first mover’s kindness (or unkindness) to account for the possibility that he is acting out of calculated self-interest rather than genuine social motivation. Greater θ_i reflects greater discounting by individual i.Footnote ²

The remainder of Table 1 is similarly derived. If a player sacrifices to reduce a counterpart’s material payoff, her strategy is classified into the lower-right and scored – 1 (cf. Fehr & Gächter, Reference Fehr and Gächter2002; Guala, Reference Guala2012). Because she effectively paid to hurt the other player, the strategy is unambiguously mean. On the other hand, reducing a counterpart’s material payoff while increasing one’s own receives a motivation score of – 1 + θ_i. Because such behavior may be driven by self-interest, it is not seen as inherently mean. A second mover’s miserly response to a first mover’s handoff provides one example. It materially hurts the first mover (relative to the alternative of generosity). But it also maximizes the second mover’s own material payoff, so her intentions need not be unkind. In sum, $\theta $ dilutes attributions of both kindness and unkindness.Footnote ³

Player i’s total utility v_i is given by v_i = u_i + λ_iu _jM_iM_ij. Here, u_i is the player’s utility for his material outcome. The latter term is his nonmaterial, socioemotional payoff. It reflects his utility from reciprocity or the lack thereof. It includes his counterpart’s utility for her material outcome, u_j, weighted by several parameters. λ_i ≥ 0 indexes the player’s degree of social motivation; the greater is λ_i, the more the player cares about reciprocating kindness with kindness and unkindness with unkindness. M_i, and M_ij are player i’s assessments of her and the other player’s motives. Combining motivation scores multiplicatively allows for reciprocity. If a counterpart is kind, a player’s total utility rises as she is increasingly kind in return. Likewise, if a counterpart is unkind, a player’s total utility rises as she is increasingly unkind in return.

Our model may be applied to any two-player game with finite action sets. Moreover, the total utility functions we specify satisfy a set of conditions identified by Segal and Sobel (Reference Segal and Sobel2007) that guarantee the existence of at least one Nash equilibrium. That is, given the payoffs and motivation scores we have outlined, every two-player game includes at least one strategy profile from which neither player can unilaterally deviate to increase his or her total utility. Many games will, of course, permit multiple equilibria. For instance, if the second mover’s λ is sufficiently large and her θ is sufficiently small, then the game of Fig. 1B supports an equilibrium in which the first mover hands off to the second mover, who then reciprocates with generosity. A unilateral action by the first mover that is met with miserliness by the second mover, however, also forms an equilibrium, for any values of λ and θ.

Note that when players are either mutually kind or mutually unkind, our model has their total utilities increase in each other’s material payoffs. Ceteris paribus, each player is thus better off by granting the other a greater material gain. This feature is compelling in the case of the positive reciprocity on which we focus. It is not compelling in the case of negative reciprocity. Modeling negative reciprocity when motives are ambiguous would require a different approach. For instance, the basic logic underlying our motivation scores could be added to the models by Rabin (Reference Rabin1993) or Dufwenberg and Kirchsteiger (Reference Dufwenberg and Kirchsteiger2004).

Before we derive our model’s predictions for the games in Fig. 1, we note that our model reduces extensive form games to their normal form. Unlike Dufwenberg and Kirchsteiger’s (Reference Dufwenberg and Kirchsteiger2004) theory of reciprocity, which is fully history-dependent, it thus cannot address issues concerning how players might revise assessments of motivations off the equilibrium path. But as suggested by the above discussion of motivation scores, and as we explain in more detail below, anticipated actions off the path of play nevertheless factor into the assessment of motivations.

2.2. Altering the unilateral action impacts attributions

How does increasing the first mover’s incentive for unilateral action from 35 to 70 (Fig. 1B vs. 1A) impact attributions, motivation scores, and behavior? If the players continue to anticipate a handoff and ensuing generosity, the second mover’s material payoff is unaffected. It remains 20. But the first mover’s social motivation is now signaled more clearly: By handing off control, he ends up with 50 rather than 70. He thus now hurts himself to help the second mover, and his motivation score is + 1 rather than 1 – θ. Because foregoing the handoff in favor of unilateral action is materially more profitable than receiving generous behavior, a handoff cannot be motivated by tactical self-interest and must instead reflect genuine caring. As long as  θ> 0, the second mover should therefore be more likely to reciprocate with generosity in Fig. 1A than Fig. 1B.

There are many additional other-regarding motivations beyond a desire for reciprocity. With that in mind, consider the simplified dictator game in Fig. 1C, which eliminates the erstwhile first mover’s decision. Because he has no chance to act, he does not have an opportunity to treat the erstwhile second mover positively and cannot earn any reciprocal treatment. He may still benefit, however, from additional other-regarding motivations. Two such motivations may be particularly pertinent. His counterpart may be altruistic, willing to engage in self-sacrificing, generous behavior that is not conditioned on any antecedent or expected behavior (Falk et al., Reference Falk, Fehr and Fischbacher2003; Fletcher & Zwick, Reference Fletcher and Zwick2007; Krebs, Reference Krebs1970). Or his counterpart could act generously because she believes she is supposed to behave that way, expects that the first mover or the experimenters may judge her on that basis, and is averse to being judged negatively (Dana et al., Reference Dana, Cain and Dawes2006). In Fig. 1C, the erstwhile second mover’s choice between generous and miserly behavior may be seen as tapping a baseline level of other-regard from these two sources. The interest in reciprocity captured by our model will add to this baseline.

Our model therefore makes the intuitive, overall prediction that from Fig. 1C to 1B to 1A, as first movers forego an increasingly attractive unilateral option, second movers should become increasingly likely to respond generously. In Fig. 1C, the erstwhile first mover cannot impact the second mover. He is therefore judged neutrally and as not meriting reciprocity. In Fig. 1A, by handing off, the first mover helps the second mover and hurts himself. His behavior is thus judged as unquestionably kind and fully deserving of reciprocity. Fig 1B engenders a middle ground. By handing off in this game, the first mover helps the second mover but also helps himself. His motives are therefore ambiguous. Consequently, his kindness is discounted, and his behavior is viewed as intermediately deserving of reciprocity.

2.3. Comparisons with prior accounts of reciprocating good treatment

As we have mentioned, existing game-theoretic analyses have trouble with middle ground. By Rabin’s (Reference Rabin1993) theory, anyone who stands to gain materially from his own actions is deemed fully undeserving of positive reciprocity, irrespective of the effects his actions have on others. In our handoff games, this approach implies that a first mover forgoing 35 is perceived as entirely undeserving of positive reciprocity, just like a passive, erstwhile first mover who does not get a chance to act. Thus, Rabin’s (Reference Rabin1993) theory implies that second movers will act equivalently across Fig. 1C and 1B.

Dufwenberg and Kirchsteiger’s (Reference Dufwenberg and Kirchsteiger2004) theory views a person as fully deserving of positive reciprocity if he helps his counterpart, and his chosen actions expose him to a potential material loss relative to his alternative actions. It views a person as fully undeserving of positive reciprocity if he helps his counterpart but his actions do not leave him exposed. It thus casts both a first mover who foregoes 35 and a first mover who foregoes 70 as fully deserving of positive reciprocity. By giving up either payoff, the first mover helps the second mover and leaves himself vulnerable to receiving only 20. In sum, Dufwenberg and Kichsteiger’s (Reference Dufwenberg and Kirchsteiger2004) analysis implies that second movers will behave equivalently across Fig 1A and 1B.Footnote ⁴

Falk and Fischbacher’s (Reference Falk and Fischbacher2006) theory of reciprocity and social comparisons is concerned with considerations of equity. It holds that a person is judged as kind if he provides his counterpart with as much or more than he himself receives. He is judged as unkind if he provides his counterpart with less than he himself receives. Judgments are tempered if an individual cannot influence the players’ relative standing. For instance, someone who has no choice but to provide his counterpart with more than he himself receives is viewed as less kind than someone who could have taken the greater share for himself. This setup distinguishes between Fig. 1C and the two handoff games because the erstwhile first mover in Fig. 1C cannot affect the players’ outcomes and is therefore judged neutrally. Contingent on the players’ relative standing being held constant, however, it is beyond the scope of the theory to distinguish behaviors that do or do not improve a player’s own outcome compared to his alternatives. In other words, Falk and Fischbacher’s (Reference Falk and Fischbacher2006) theory does not address ambiguous motivation. It therefore makes equivalent predictions across Fig. 1A and 1B.

In sum, regarding second-mover behavior, Rabin’s (Reference Rabin1993) theory equates Fig. 1B and 1C, while Dufwenberg and Kirchsteiger’s (Reference Dufwenberg and Kirchsteiger2004) and Falk and Fischbacher’s (Reference Falk and Fischbacher2006) theories equate Fig. 1A and 1B. Among accounts of reciprocity, only our model predicts that the frequency of second-mover generosity in Fig. 1B will fall in between that of Fig. 1A and 1C. We will test this prediction in Experiment 1.

4.1. Method

4.1.1. Preregistration

We preregistered our experimental design, data collection, exclusion criteria, and statistical methodology at https://doi.org/10.17605/OSF.IO/GN6H8. In line with our model’s predictions (Table 2), we preregistered that second movers in the unambiguous game (Fig. 1A) would be more generous than second movers in the ambiguous game (Fig. 1B), who would in turn be more generous than dictators in the dictator game (Fig. 1C).

Table 2

Motivation scores in our model and associated predictions about reciprocity, for both Experiments 1 and 2. The motivation scores reflect the strategy profiles and equilibria detailed in the text and formally derived in an online supplement available at https://osf.io/7k5n9/

Participants. We recruited a total of 7,792 US adults on the online platforms Connect and Amazon Mechanical Turk (51.8% identified as female, 47% as male, and 1.2% as nonbinary or other gender; M _age = 41.1). For recruitment on Mechanical Turk, we used CloudResearch (Litman et al., Reference Litman, Robinson and Abberbock2017). This sample size reflects a preregistered target that we explain below. Each participant received $.60 plus a bonus payment based on the outcome of their game.

As preregistered, we excluded 809 or 10.4% of participants for failing at least one of two attention checks. The exclusion rate differed significantly across conditions, χ²(1, 7792) = 41.1, p < .0001. But importantly, it did not differ significantly across the three critical conditions, p = .9, and was lower in these conditions (7.5%) than in most other conditions. After exclusions, our final sample included 6,983 participants. All results and their statistical significance remain qualitatively unchanged in analyses that include all participants.

5.1. Less ambiguous first-move cooperation under endogenous sequencing

The ex-ante symmetry across players in our endogenous-sequencing game is reminiscent of the real-time trust game (Murphy et al., Reference Murphy, Rapoport and Parco2006; Rapoport & Murphy, Reference Rapoport, Murphy, Croson and Bolton2012). But in a departure from that setting, first moves in our game can be cooperative. Crucially, our model suggests that the kindness of a first-move cooperator will seem less ambiguous under endogenous sequencing than in the standard game and, more importantly, that this effect will be magnified the more rapidly the person cooperates.

To introduce the relevant intuition, suppose that in each game the players expect that both first-move defection and first-move cooperation will be reciprocated. The model then succinctly characterizes the ambiguity of standard game, first-move cooperation. This strategy yields each player $4, while the first mover’s only pure strategy alternative, defection, yields each player just $2. First-move cooperation thereby “helps” the second mover but also “helps” the first mover. It could potentially reflect kindness or self-interest or some combination thereof. It is perceived as ambiguous and receives a motivation score of + 1 – θ_i.Footnote ⁶

Next, turn to the endogenous sequencing game. In this setting, first-move cooperation can be perceived as less ambiguously motivated. The potential change in perceptions arises because there are now additional alternatives to first-move cooperation, beyond first-move defection. In particular, a player could pursue the maximal payoff by waiting, hoping his counterpart first move cooperates, and if she does, then defect on her. This path of play would yield him $6, while she ends up with nothing. In comparison to this path of play, engaging in first-move cooperation, which is expected to yield each player $4, “helps” the second mover while “hurting” him. Note that the comparison is not ambiguous: By first-move cooperating rather than pursuing the maximal payoff, a player eschews his own self-interest and benefits his counterpart. His motivation score is thus + 1. In essence, while a standard-game first-move cooperator does not bear a cost for helping the counterpart, an endogenous sequencing first-move cooperator does. Bearing this cost lends credence to the possibility that the person is genuinely other-regarding rather than tactically self-interested.

Finally, consider the speed with which a player first-move cooperates under endogenous sequencing. As he acts more rapidly, he more emphatically eschews pursuit of the maximal possible payoff. Immediately cooperating sends the clearest signal: There is no chance the player was trying to wait out his counterpart and planning to defect if she made a cooperative initial move. Waiting dilutes the signal. It generates some ambiguity about the player’s motives – maybe he would have defected if his counterpart had already cooperated.

The foregoing analysis suggests two empirical predictions. First, many endogenous sequencing games will feature rapid, first-move cooperation. Players will be willing to make themselves vulnerable to a counterpart’s defection because they realize that doing so renders their kindness credible and thus best allows them to pursue positive reciprocity. Second, rapid first-move cooperation will be reciprocated at a higher rate than first-move cooperation in the standard game.

5.2. Method

Participants. A total of N = 235 undergraduates at UCSD’s Rady School of Management took part in our experiment and subsequent unrelated studies. Their mean age was 21 years and 129 of them (54.9%) were female. As in Experiment 1, they received course credit for participating and were paid according to their game outcome. Our prior experience at the Rady lab suggested that during the period when the experiment took place, two weeks’ worth of sessions would yield sufficiently many participants. We thus conducted sessions during two Monday through Friday periods.

Participants answered five training questions during the course of the instructions (and, unlike in our other experiments, they did so before responding to the dependent measures). They correctly answered an average of 4 of the 5 questions. On average, they answered slightly fewer questions correctly in the endogenous sequencing condition, but the difference was not significant (p = .37). We did not exclude any participants from the analyses that follow; our results are qualitatively unchanged if only participants who correctly answered all five questions are included.

Procedure. We conducted sessions of between 6 and 20 participants in the same room and using the same methods as in Experiment 1. Each session was randomly assigned to either the sequential condition or an endogenous-sequencing condition with a countdown length of 20, 60, and 120 seconds (which we varied for robustness). In the sessions featuring the standard, sequential game, participants were then randomly assigned the role of first or second mover. In all sessions with an odd number of participants, a research assistant who was blind to our hypotheses filled in. Research assistants were not remunerated for their choices, and we do not include their data below.

Materials. The experiment was programmed in z-Tree (Fischbacher, Reference Fischbacher2007). Screenshots of the complete instructions, which did not use the terms defection or cooperation, are available on the OSF at https://osf.io/7k5n9/.

Each player was initially credited with $2. At any moment during the countdown, each player could continue to “wait,” choose to “keep” his $2, or choose to “give” his money to his counterpart, with the proviso that if a player chose to give then we as the experimenters would add $2 to the amount conveyed, so that the counterpart would receive a total of $4. Keeping constitutes defection, while giving constitutes cooperation. If either player chose to “keep” or “give,” the countdown immediately stopped, and the other player was informed of the move and provided with the opportunity to respond.Footnote ⁷ Finally, if neither player chose to “keep” or “give” before the countdown expired, the players were placed in a simultaneous prisoners’ dilemma (and this was common knowledge).

6.1. Diverse perceptions of others’ motives

In gift exchange and trust games, a first mover decides what portion of an endowment to transfer to the second mover and what portion to keep, and a second mover then does likewise (for reviews, see Gilchrist et al., Reference Gilchrist, Luca and Malhotra2016; Johnson & Mislin, Reference Johnson and Mislin2011). In these games, in which players choose among several levels of generosity versus miserliness, our model emphasizes that the same action may be viewed as positive, negative, or neutral, depending on a person’s perceptions of self-interest and caring. For instance, is transferring a small portion of the endowment generous or miserly? To someone who believes that self-interest predominates, even a minimal transfer can seem generous and constitute positive treatment. On the other hand, to somebody who believes that kindness predominates, minimal transfers can seem miserly and constitute negative treatment.

This diversity in perceptions can lead to diversity in second movers’ reactions – which suggests that the relationship between first and second moves in gift exchange and trust games may be noisy. Indeed, correlations between first- and second-mover transfers are typically modest (Johnson & Mislin, Reference Johnson and Mislin2011; also Cox, Reference Cox2004) and often not statistically significant (e.g., Pillutla, Malhotra, & Murnighan, Reference Pillutla, Malhotra and Murnighan2003). The low correlations and their lack of robustness are frequently interpreted as a lack of positive reciprocity. In contrast, our model suggests that they reflect diversity in perceptions of motives and that they are entirely consistent with positive reciprocity.

Stanca et al. (Reference Stanca, Bruni and Corazzini2009)’s contrast of standard and “decoupled” gift exchange illustrates the point. In these authors’ experiment, first movers were initially endowed with 20 experimental tokens and could transfer any amount between 0 and 20 to a second mover. But while first movers in the standard treatment knew that the second mover would subsequently have a chance to reciprocate (or not), first movers in the decoupled treatment acted before being informed that the second mover would have a chance to respond.

Stanca et al. (Reference Stanca, Bruni and Corazzini2009) reasoned that tactical motives could only underlie first-mover behavior in the standard but not decoupled game. Only in the former could first movers anticipate that they could influence second movers. Accordingly, Stanca et al. (Reference Stanca, Bruni and Corazzini2009) predicted greater first-mover generosity in the standard game. This prediction, which is in line with our model, was strongly corroborated.

On the other hand, Stanca et al. (Reference Stanca, Bruni and Corazzini2009) also predicted greater second-mover generosity in the decoupled game because any generosity in that game must be genuine rather than tactical. Yet collapsing across all possible first-mover gifts, the average second-mover return gift was only modestly greater under decoupling (their Tables 2 and 7). This finding appears to beg the question of whether second movers distinguished between different first mover motivations. By our model, however, it simply highlights the importance of diversity in perceptions of motivations.

Consider a decoupled first mover who gives 5 of his 20 tokens to the second mover. Is he acting kindly or unkindly? Compared to more generous gifts, the first mover has hurt the second mover and helped himself, so that the motivation score is – 1 + θ. Compared to less generous gifts, the first mover has helped the second mover and hurt himself, so that the motivation score is + 1. Averaging over the 15 more generous and 5 less generous gifts yields a total motivation score of [15(–1 + θ) + 5(+1)]/20 = – ½ + ¾θ, which can be negative or positive for different values of θ. Whether the first mover has been kind or unkind is thus open to interpretation.

The same first-mover gift may then elicit disparate return gifts, depending on whether a second-mover discounts a lot or a little. The relationship between initial and return gifts will in turn be noisy in both the standard and decoupled games, rendering it difficult to isolate the impact of specific motivations. In this way, rather than revealing a limited impact of distinct first-mover motives on second-mover reciprocity decisions, Stanca et al.’s (Reference Stanca, Bruni and Corazzini2009) gift exchange data reveal how diverse perceptions attenuate the correlation between initial and return gifts.

6.2. Positive reciprocity in repeated prisoners’ dilemmas

In finitely iterated prisoners’ dilemmas, cooperation rates are initially high but then “unravel,” so that defection becomes increasingly common as the final period approaches (see, e.g., Andreoni & Miller, Reference Andreoni and Miller1993). Many authors suggest that unraveling is inconsistent with a preference for reciprocating good treatment. They argue that given this preference, a history of mutual cooperation should engender subsequent mutual cooperation (Selten & Stoecker, Reference Selten and Stoecker1986; see also Axelrod & Hamilton, Reference Axelrod and Hamilton1981; Kreps et al., Reference Kreps, Milgrom and Roberts1982). In contrast, our model implies that unraveling is entirely consistent with a preference for repaying good treatment – once motivational ambiguity is accounted for. Players will note that in early and middle periods, their counterpart’s cooperation may have been genuine. Or it could have been tactical, designed to facilitate a stretch of materially profitable, reciprocal cooperation (Axelrod & Hamilton, Reference Axelrod and Hamilton1981; Kreps et al., Reference Kreps, Milgrom and Roberts1982). But then even long histories of mutual cooperation may be attributed largely to self-interest rather than caring and deemed not to merit late-period reciprocity.

6.3. Positive reciprocity in ultimatum games

By more realistically handling ambiguity, our model also points to the role of positive reciprocity in ultimatum games. In the canonical instantiation of this game, two players divide a pot of money. The “proposer” offers a specific split, which the “responder” can accept or reject. If she accepts the split, it is implemented. If she rejects it, neither player receives anything. A vast experimental literature reveals two stylized facts: many proposers are generous, offering an even or nearly even split, and many responders reject miserly offers of less than about a quarter of the pot (Camerer & Thaler, Reference Camerer and Thaler1995; Güth & Tietz, Reference Güth and Tietz1990; Oosterbeek et al., Reference Oosterbeek, Sloof and van de Kuilen2004; Tisserand, Reference Tisserand2014).

To explain these stylized facts, researchers have focused on “threatening” equilibria and negative reciprocity. In such equilibria, the proposer is generous because he anticipates that the receiver will reject a miserly split. That is, he is compelled to act generously because of his counterpart’s power to reject miserly offers. The stick of negative reciprocity is key (e.g., Falk et al., Reference Falk, Fehr and Fischbacher2003; Levine, Reference Levine1998).

Our model also offers this type of explanation. But unlike existing theories, it offers an additional, complementary explanation in terms of ‘nice’ equilibria and positive reciprocity.Footnote ⁸ In a nice equilibrium, the proposer’s generosity is not a reaction to threat. It reflects other-regard. The proposer acts nicely in pursuit of the good feelings that ensue when the responder accepts an equitable outcome and in avoidance of bad feelings that would ensue were he to consign the responder to a meager outcome. The carrot of positive reciprocity plays an important role.Footnote ⁹

We suspect that many investigations of the ultimatum game betray conceptualizations of it akin to threatening rather than nice dynamics. Hoffman et al. (Reference Hoffman, McCabe and Shachat1994), for example, considered altruism as a source of generous offers and argued against it (see also Harrison & McCabe, Reference Harrison and McCabe1992; Marlowe, Reference Marlowe, Henrich, Boyd, Bowles, Camerer, Fehr and Gintis2004, p. 186; Ruffle, Reference Ruffle1998). They observed that proposers were substantially more generous than “dictators” who also split a pot with another individual but could not have their offer rejected. Because altruism should influence both proposers and dictators, Hoffman et al. (Reference Hoffman, McCabe and Shachat1994, pp. 347–348) inferred that “offers in ultimatum games … appear to be determined primarily by strategic … considerations… rather than … preference.” In essence, they concluded that proposer’s generosity reflects fear that meager offers will be rejected, that is, fear of the negative reciprocity underlying threatening dynamics. But nice dynamics that implicate positive reciprocity fit equally well with data presented by Hoffman et al. (Reference Hoffman, McCabe and Shachat1994). As we emphasized with the game of Fig. 1C, because reciprocity is contingent on a counterpart’s behavior, it is relevant to proposers but not dictators: Proposers might make generous offers because it feels good when the responder accepts, but this motivation is not relevant to dictators, who cannot tap such feelings.

Levine (Reference Levine1998) also explains even-split or nearly even-split ultimatum offers in terms of threatening dynamics. Seminal data, however, are at odds with his explanation and instead in line with the nice dynamics our model uncovers. Levine emphasizes that proposers (accurately) believe that a nonnegligible fraction of receivers are spiteful and will thus reject meager offers. The possibility of spiteful rejection is the threat that pushes proposers to be even-handed. Furthermore, by Levine’s theory, altruistic players are relatively likely both to make generous offers as proposers and to accept meager offers as responders, whereas spiteful players are relatively likely to both make miserly offers and reject meager offers. In studies in which each participant plays both roles, Levine’s model thus predicts a negative correlation between the offer a participant proposes and the minimum offer they are willing to accept. But in the original study of the ultimatum game by Güth et al. (Reference Güth, Schmittberger and Schwarze1982), the offers that participants propose are positively correlated with their rejection thresholds, r = 0.30 (p = .07; their Table 7). Blanco et al. (Reference Blanco, Engelmann and Normann2011) later replicated this finding, reporting r = 0.40 (p < .01; their Table 3).

Such positive correlations are consistent with our model’s nice dynamics. By our account, people who place greater weight on socioemotional payoffs are more likely to both seek out the good feelings that emerge when a generous offer is accepted and avoid the bad feelings that emerge when a meager offer is accepted. To do so, they must be generous as proposers and demanding as receivers.

To be clear, we do not claim that threatening dynamics and negative reciprocity are rare in the ultimatum game. They are surely common. We merely claim that nice dynamics involving positive reciprocity may be common too. Indeed, it is notable that several other positive social motivations have been cited for generous offers, including altruism (Camerer & Thaler, Reference Camerer and Thaler1995), fairness (Nowak et al., Reference Nowak, Page and Sigmund2000), and image maintenance (Dana et al., Reference Dana, Cain and Dawes2006), while positive reciprocity has not. In our view, the possibility that good feelings are generated when proposer generosity is met with a positive response is just as plausible as the possibility that, say, image maintenance guides proposer generosity. Yet this possibility appears to have been overlooked, probably because existing work does not allow for ambiguous attributions.