Lying aversion,lobbying,and context in a strategic communication experiment

Abstract

Almost all institutions within modern democracies depend on a mix of communication and competition. However, most formal theory and experimental evidence ignores one of these two features. We present a formal theory of communicative competition in which senders vary in their aversion to lying, and test hypotheses from this theory using a strategic communication experiment. To influence lying aversion, we compare a Context Condition, in which pre-play instructions are cast in political language, with a Baseline Condition, in which all language is abstract. We find that in early rounds of play, subjects in the Context Condition exaggerated more as a function of their biases than those in the Baseline Condition when we control for the past history of play. However, by the last round of play, subjects in both conditions converged on persistent exaggeration. This finding indicates that competition crowds outlying aversion in settings of strategic communication.

Keywords

Behavioral models experiment lobbying sender–receiver games social preferences

1. Introduction

Communication and competition are the connective tissues of modern democracy. Nearly every democratic institution seeks to resolve some collective choice problem by dividing the responsibilities of governing among branches of government, elites and the public, candidates and the electorate, advocates and judges, lobbyists and legislators, and experts and decision makers. These divisions do not—indeed cannot—eliminate collective choice problems. Instead, they are transmuted into problems of agency and information transmission. The separated institutions are then tethered back to each other by sinews of communicative competition, in which interested actors send competing messages to uninformed, yet empowered agents.

Despite its theoretical and practical importance, our understanding of communicative competition is severely limited. Communication in non-competitive strategic settings is well understood in comparison. In the basic strategic information transmission (SIT) model, a lone sender can only credibly send coarse, categorical messages even if she has access to fine-grained details (Crawford and Sobel, 1982; Gilligan and Krehbiel, 1987). Dozens of studies have applied this single-sender model to democratic politics, even though politics in democratic institutions is almost always competitive. Bankers battle consumer advocates to influence financial regulation, scientists skirmish with skeptics to convince the public whether climate change is a problem worthy of public attention, petitioners confront the government over issues of equal protection and civil liberties, and the president clashes with congressional opposition to persuade the median legislator to support prudent fiscal policy. Competition between competing, informed interests is pervasive. Ignoring this facet of the political world would not be so bad if it were not the case that theoretical predictions for an isolated sender can differ markedly from those of competing senders. For example, competing senders with private information about their preferences can either reveal their information or jam, directly countering the information broadcast by their opponent (Minozzi, 2011).

As underdeveloped as our theoretical understanding of communicative competition is, our empirical understanding is even worse. Very few studies analyze multi-sender SIT experiments.¹ Single-sender SIT experiments are plentiful by comparison (e.g., Blume et al., 1998; Crawford, 1998; Dickhaut et al., 1995; Gneezy, 2005; Lupia and McCubbins, 1998), although findings from these experiments have not faithfully replicated equilibrium predictions. In fact, the fundamental single-sender SIT problem—the lack of credible communication—is substantially reversed in the laboratory, in a phenomenon called overcommunication, which occurs when senders reveal more information about the underlying truth than the theory predicts (Blume et al., 2001; Cai and Wang, 2006). In other words, where the theory predicts that messages reveal only categorical information (e.g., that the truth is ‘high’ or ‘low’), laboratory subjects instead use messages that reveal finer-grained details (e.g., messages that vary continuously with the truth). It remains an open question whether such overcommunication will be evident in the multi-sender SIT experiments that more closely resemble democratic politics.

The prevailing theoretical explanation for overcommunication is pro-social preferences (Hurkens and Kartik, 2009; Sánchez-Pagés and Vorsatz, 2007, 2009). For example, subjects might be simply be averse to lying. However, explanations based on pro-social preferences implicitly assume that individuals have fixed preferences that are not situation-specific. Thus, some individuals may be more averse to lying than others. However, it is not clear how such pro-social preferences will manifest in settings with communicative competition. Moreover, an experimenter cannot simply manipulate pro-social preferences as she might with payoffs.

One possibility is to take advantage of the idea that pro-social preferences depend on context (Levitt and List, 2007). While we cannot directly manipulate pro-social preferences, we can attempt to indirectly influence them by priming subjects. In so doing, we can then learn how pro-social preferences and competition interact in a strategic communication setting.

In this paper, we develop a formal theory of communicative competition with private information about preferences and lying aversion. After deriving equilibrium predictions, we present several experimental hypotheses about the role of pro-social preferences in communicative competition. Our main design contribution is to use the relationship between context and pro-social preferences to learn about how the latter interact with competition. To do so, we formulate several hypotheses based on the formal theory. We then test these hypotheses with an experiment in which we manipulate context.

The focal treatment in the experiment is a priming and labeling manipulation. Subjects in all sessions play a communicative competition game with an identical strategic and payoff structure. In the Baseline Condition, all labels are abstract (e.g., ‘Player A’). In the Context Condition, all labels are political (e.g., ‘Lobbyist A’), and subjects read a short paragraph about lobbying and the unknown incentives of lobbyists before play begins. We find that subjects in the Context Condition exaggerate more initially as a function of their biases, but that after many rounds, play in the two conditions converges. Based on this finding, we argue that lying aversion has very different consequences in competitive environments than in single-sender environments. With repeated play, it appears that competitive incentives crowd out initial aversion to lying, as overcommunication is transmuted into persistent exaggeration.

2. Theory and hypotheses

In this section, we develop a formal model of communicative competition with lying aversion and use it derive a set of testable hypotheses. But first consider the value of such an exercise. Pro-social preferences such as lying aversion are inherently unobservable. If individuals do have preferences against lying, we cannot simply manipulate those preferences via monetary payoffs, as in standard economics-style experiments. Without the ability to manipulate lying aversion, how can we test any hypotheses?

This argument depends critically on the implicit assumption that pro-social preferences are hard-wired and do not vary with the context of the experiment. However, there is ample evidence that this assumption is false. For example, Ross and Robertson (2000) find that subjects who play a prisoners’ dilemma game labeled as the ‘Wall Street’ game defect at higher rates than those who play the same game labeled as the ‘Community Game.’ Burnham et al. (2000) study trust games in which fellow subjects are labeled variously as ‘opponents’ and ‘partners,’ finding that the latter are trusted more than the former. Indeed, priming and framing effects are well-known from and studied by the literature in political psychology. Therefore, if two sets of subjects play communicative competition games that are strategically equivalent but described differently, their lying aversion may well change.

2.1. Communicative competition and lying aversion

A simple formal theory of communicative competition involves two senders and one receiver.² Each sender learns the value of the targetT and sends a message to the receiver. The receiver does not observe the target but does make a choice that affects all the players. In addition to knowing the target, each sender also knows his own preferences. These preferences are based on the receiver’s choice as well as the sender’s message.

More formally, each sender I ∈ {L,R} (privately) knows three things—the target T, his shift S_I, and his lying aversion functionK_I(⋅). He sends a message m_I ∈ R (the set of real numbers) to the receiver, who then chooses c ∈ R. Each sender’s ideal point is T + S_I, the receiver has ideal point T, and the payoffs for each player depend on the distance between c and the ideal point. Thus, each sender’s payoff includes the term u_I = v(|c − (T + S_I)|), and the receiver’s payoff includes v(|c − T|), where v(⋅) is a decreasing, concave function. For simplicity of presentation, we focus on the quadratic-loss case v(x) = −x², but this is not necessary for any of the results.

Senders also prefer not to lie too egregiously. We assume that each sender has quasilinear utility over payoffs and lying aversion, and that this utility is u_I + k_I(|T − m_I|), where k(⋅) is a decreasing, concave function. Therefore, we differentiate between a subject’s payoffs controlled by the experimenter and the choices of the subjects, and a subject’s utility, which includes payoffs as a component. For ease of illustration, we use the functional form k_I(|m_I − T|;λ_I) = −(1 − λ_I)(m_I − T)²∕(4λ_I), where λ_I is a player’s lying tolerance.³ Lying costs are severe for λ_I near 0, and are negligible for λ_I near 1. This functional form of k_I(⋅) permits a very simple representation of equilibrium message strategies based on the parameter λ_I.

Consider a simple, symmetric version of this game. The target T is uniformly distributed on [ − 100,100], one sender is on the left with S_L distributed uniformly on [ − 50,0], and the other is on the right with S_R uniformly distributed on [0,50]. Thus, the average distance between the receiver’s ideal point and each sender’s one is S = E|S_L| = E|S_R|. Lying tolerance λ_I ∈ [0,1] is distributed according to a continuous, atomless distribution F(⋅;θ) with full support and expectation μ_θ, for θ ∈ Θ, which represents the context in which players interact. All random variables are assumed to be independently distributed.

We assume that context affects the lying tolerance distribution in the following way:

Context Assumption. If θ′ < θ, then μ(θ′) < μ (θ), $\forall λ \in [0, 1]$ .

The Context Assumption articulates the idea that the context in which actors engage affects their tolerance for lying. Many technical assumptions about the relationship between F and θ yield the Context Assumption as a consequence. For example, if F(⋅;θ) first order stochastically dominates F(·;θ′), the Context Assumption is satisfied.

We focus on perfect Bayesian equilibria. In equilibrium, messages are exaggerated away from the receiver’s target. This exaggeration takes the form of a linear function of the sender’s shift. The receiver splits the difference between the messages she observes, choosing an action that is at the midpoint.

Equilibrium Characterization. For θ ∈ Θ, the strategies $m_{L}^{*} = T + 2 λ_{L} S_{L} - 2 λ_{L} S A (θ)$ , $m_{R}^{*} = T + 2 λ_{R} S_{R} - 2 λ_{R} S A (θ)$ , and $c^{*} = \frac{1}{2} (m_{L} + m_{R})$ support an equilibrium, where A(θ) =μ (θ)∕(1 − μ(θ)).⁴

To see why these strategies constitute an equilibrium, suppose the receiver splits the difference between the messages, as in c^*. Each sender balances the gains from exaggeration against his aversion to lying. Senders have two incentives to exaggerate their messages away from T. Firstly, even if lying aversion was negligible (λ= 1) and a sender could choose a message that was directly implemented by the receiver, he would want to send the message m_I = T + S_I, which is exaggerated away from T by S_I. This exaggeration is an example of the fundamental SIT problem identified by Crawford and Sobel (1982).

A second incentive for exaggeration is competition. Each sender compensates for the exaggeration he expects from his opponent. In fact, the equilibrium of this game is quite different if there is common knowledge of no lying costs.⁵ Senders who are averse to lying temper their messages, drawing them back toward T. Because senders have symmetrically distributed shifts and lying tolerances, the receiver does not know who lied more. As a result, her posterior expected value of T is $E [T | m_{L}, m_{R}] = \frac{1}{2} (m_{L} + m_{R})$ , and so she splits the difference to maximize her payoffs.

We now consider how these strategies change as one alters the context of the experiment in light of the Context Assumption. Equilibrium message strategies are linear functions of target and shift. In these strategies, the slopes and intercepts depend not only on one’s lying tolerance λ, but also the distribution of the lying tolerance. According to the Context Assumption, changes in context θ directly affect this distribution by increasing μ(θ), the expected value of λ.

How would equilibrium message strategies change if the context parameter θ increases? We should expect exaggeration to increase for two reasons that are intimately related to the two incentives senders have to exaggerate their messages. The lying tolerance parameter λ enters the equilibrium message strategies in both the slope on the shift and the intercept. Firstly, the slope on the shift increases directly with λ, and so we have a clear prediction: as θ increases, so should the slope on shift.

The change of the intercept is similar, but also includes a second effect. Not only does the intercept of the equilibrium message strategy depend on λ, it also depends on A(θ), which is an increasing function of μ(θ), the expectation of λ. Thus, not only does the (absolute value of the) intercept increase with λ_I on average, the change in context increases the intercept directly through its increase on A(θ). Based on this model of communicative competition with lying aversion, we next derive a series of hypotheses to test in the laboratory.

2.2. Hypotheses

To derive hypotheses from this model, we combine its insights with well-known empirical regularities from experimental economics. Firstly, the Context Assumption formalizes the idea that individuals’ lying aversion depends, in predictable ways, on some well-known yet payoff-irrelevant feature of the strategic environment. How might context change senders’ behavior? It is possible that the change will be negligible. In a single-sender setting, Rode (2010) finds that senders behave no differently when they face receivers in a competitive context than in a cooperative context. Alternatively, the equilibrium prediction of the formal model is that senders should exaggerate more in a Context Condition, which diminishes the expected cost of lying relative to a Baseline Condition.

Context Hypothesis. Subjects in the Context Condition will exaggerate more than subjects in the Baseline Condition. Specifically, the coefficient on shift and the absolute values of the intercepts should all be larger in the Context Condition.

A second question is how durable the effects of context might be if subjects play the game multiple times. In our model, context acts via two mechanisms. Firstly, one’s own aversion to lying is assumed to be context dependent. Secondly, one’s beliefs about others’ aversion to lying are assumed to be context dependent (see also Dufwenberg et al., 2011).

In the laboratory, however, both mechanisms may fade with repeated play. To see why, consider a finitely repeated version of the game in which players behave myopically. This description is very close to the experiment that follows, in which players are randomly and anonymously matched with each other as they play the game repeatedly. Such a finitely repeated game also matches the empirical reality of large, diffuse political–economic markets such as that for lobbyists. The setting is well-modeled as a sequence of single-shot games, each with a slightly different context. As subjects play the game repeatedly, the relative information conveyed by the original context fades in comparison with the growing context of past play. Our formal model captures only a single play of the game. The contexts of the two conditions are likely to be more similar during the nth round of play than during the (n − 1)th. Indeed, Blume et al (2001) study a single-sender environment, comparing a condition with meaningless messages and a condition with messages that have a priori meaning, and they find that initial meanings tend to deteriorate over time. Therefore, we hypothesize that context effects will decay with repeated play.

Decay Hypothesis. After many rounds of the game, subjects in both conditions will converge on similar strategies.

As we take this model to the laboratory, we utilize a pair of contexts that is very likely to satisfy this assumption. Lobbyists are associated with lying. In a recent survey, respondents were asked to ‘rate the honesty and ethical standards’ of people in different fields. Sixty-one percent put lobbyists in the ‘low’ or ‘very low’ categories, while only 7% put them in the ‘high’ and ‘very high’ categories.⁶ While 61% is far from complete saturation, it is plausible that the 39% who believe lobbyists to be average or better when it comes to ‘honesty and ethical standards’ are still aware of this negative professional reputation, and allow it to affect their second-order beliefs.

To leverage the apparently widespread belief that lobbyists are less averse to lying than others, we had subjects play a communicative competition game in two different conditions. The conditions only differ in the instructions that subjects were given. In our Baseline Condition, players’ roles were given abstract names (e.g., ‘Player A’). In our Context Condition, subjects play a strategically equivalent game but with descriptive role names (e.g., ‘lobbyist A’). The Context Condition also included a short paragraph that described the relationship between legislators and lobbyists in general terms, emphasizing that, ‘Legislators, however, do not always know whether it is in the best interests of lobbyists to tell the truth.’ The complete paragraph appears in the next section.

3. Experimental procedures

We conducted experiments at the Pittsburgh Experimental Economics Laboratory at the University of Pittsburgh. Subjects were recruited using the laboratory’s database; most were undergraduates at the University of Pittsburgh. No subjects from the authors’ classes were recruited, and each subject participated in only a single session.

We used z-tree (Fischbacher, 2007) to construct the experimental environment. After arriving at the laboratory, subjects gave informed consent and sat at individual computers. All interactions among subjects were computer-mediated and anonymous. Instructions were read out loud, presented on computer screens, and distributed in printed form so that subjects could refer to them as often as desired.⁷ Subjects were clearly instructed not to communicate during the session and were given a quiz on their computers about the instructions. Upon completion, subjects received immediate, private feedback about whether they answered questions correctly and explanations of the correct answers. Consistent with laboratory policy, no deception or false feedback was used in the experiment.

Next, the software randomly assigned each subject to a role. In our Baseline Condition, the instructions only referred to the roles as ‘Player A,’ ‘Player B,’ and ‘Player C,’ for the Left Sender, Right Sender, and receiver, respectively. In the Context Condition, these role labels were replaced with the labels ‘Lobbyist A,’ ‘Lobbyist B,’ and ‘the Legislator.’ Subjects then played 24–32 rounds of the game (depending on the session).⁸ Roles were fixed throughout the session.

At the beginning of each round, subjects were randomly matched (with replacement) into groups, one subject per role per group. To avoid reputation effects, subjects had no identifying information about the other group members in any round. After group composition, targets T and shifts S_L and S_R were drawn. To match the model above as closely as possible, T was drawn uniformly from the integers between –100 and 100, the Right Sender’s shift S_R was drawn uniformly from integers between 0 and 50, and Left Sender’s shift S_L was drawn uniformly from integers between –50 and 0. Throughout the experiment, we referred to each player’s ideal action as her ‘target.’ For example, in the Baseline Condition, T is referred to as ‘C’s target,’ T + S_L is ‘A’s target,’ and T + S_R is ‘B’s target.’ In the text, we continue to use the terms ‘target’ and ‘shift’ as above.

Our goal was to convey the political environment of a spatial model as effectively as possible. As such, we used a very large number of targets, shifts, and actions. To ensure an even distribution of targets and shifts, we use a stratified sampling technique that divides the target set into 8 subsets and each shift set into 2 subsets, for a total of 32 strata. The draw for each round corresponds to one of these strata. The order of the strata was randomized in each session so that, from the subjects’ point of view, the targets and shifts were distributed as described above. Although the target, shift, and action sets are technically discrete, they are large when compared with previous experiments on cheap talk games, which typically involve small state spaces (e.g., four states in Dickhaut et al.,1995, and five states in Cai and Wang, 2006). We use the large state space to more effectively instantiate the spatial model in our experimental environment. This goal is also advanced with our computer interface, which used both text and graphics to present information (see Appendix Figure A1). This display helps to reinforce the idea that the setting is effectively spatial.

After creating groups and selecting targets and shifts, each sender simultaneously observes the target and his own target (i.e., T + S_I). He then chooses a message to send to the receiver. Our interface displays potential messages on a horizontal axis, and to send a message, a sender uses the mouse to drag a slider along the horizontal axis to his desired message (between –150 and 150). In addition to these messages, the interface also displays the range of possible targets, the realized target, the ranges of possible targets for the senders, and the sender’s own target.⁹ The receiver observes messages from both senders simultaneously, via a similar display. The receiver then drags a slider to choose an action between –150 and 150. At the end of each round, subjects see the results from that round for their group: both messages and the action, and every player’s target and payoffs. Subjects also see the results from all previous rounds they played, although they do not see the results for groups to which they did not belong.

Per round payoffs were denominated in points, and the maximum possible points a player could earn in a round was 100. The receiver’s payoff was 100 − |c − T|, and each sender’s payoff was 100 − |c − (100T + S_I)|. At the end of the session, total points were converted to cash: US$1 for 150 points. Subjects were also paid a US$7 participation payment. Our Context Condition featured three changes to the experiment. Firstly, the experiment was entitled, ‘The Lobbying Experiment,’ rather than, ‘The Experiment,’ as in the Baseline Condition. Secondly, all player labels were changed as indicated above. Senders were referred to as ‘lobbyists,’ and receivers were referred to as ‘legislators.’ Thirdly, at the beginning of the experiment, the subjects read a short paragraph:

Senators and representatives vote on many different pieces of legislation covering many different facets of domestic and foreign policy. But they are not experts on everything. Some legislators learn about the details of these issues by talking to lobbyists, who can represent businesses, citizen groups, other countries, or many other interests. Legislators, however, do not always know whether it is in the best interests of lobbyists to tell the truth.

Next, we analyze the effects of this contextual prime.

4. Empirical analysis

We conducted four sessions of the Baseline Condition and two of the Context Condition. Each session involved between 15 and 18 subjects (5–6 groups), who played either 24 or 32 rounds. Throughout the analyses that follow, our main dependent variable is each sender’s Message.¹⁰ However, first we provide a visual representation of the data from the experimental sessions. As a first-cut control for the effect of Target on Message, we define Exaggeration as Target—Message for Left Senders and Message—Target for Right Senders. To see whether there are systematic differences between conditions at the individual level, Figure 1 displays a separate sparkline for each sender’s messages, along with the minimum and maximum Exaggeration by subject.¹¹ Senders are separated by condition (Baseline or Context). Numbers on the left (and down-pointing triangles) indicate minimum Exaggeration; numbers on the right (and up-pointing triangles) indicate maximum Exaggeration. The dashed horizontal lines demarcate zero, or no difference between Target and Message.

Figure 1.

Exaggeration by subject. Each sparkline represents the Exaggeration for a sender over a session. Exaggeration is T − m_I for Left Senders and m_R − T for Right Senders. The number to the left of a sparkline is the minimum Exaggeration for a subject, which is marked with a down triangle. The number on the right is the maximum Exaggeration, which is marked with an up triangle. All sparklines are presented on the same horizontal and vertical scales. For simplicity of presentation, only sessions with 32 rounds are presented. Results for those with 24 rounds are similar.

Relatively few subjects ever send a message on the ‘wrong’ side of the Target in Figure 1. That is, only 17 of our 66 subjects have negative values for minimum Exaggeration.¹² For most subjects, there is also a tendency to exaggerate more in later rounds. Only 10 of 66 subjects sent their minimally exaggerated Message after their maximally exaggerated message.

However, Figure 1 also reveals few if any differences between Exaggeration in the Baseline and Context Conditions, even after (crudely) controlling for Target. To test our hypotheses more carefully and systematically, we next report a series of multilevel (i.e., mixed effects) models. The dependent variable in each model is Message, and the predictors are Target, Shift, and separate intercepts for Left Sender and Right Sender.¹³ To control for subject- and round-level variation, each model includes varying intercepts and varying slopes by Subject and by Round. Our treatment is an indicator for the Context Condition. All reported tests are two-tailed.

The Context Hypothesis predicts different intercepts and slopes on Shift for the Baseline and Context Conditions. Therefore, we include the interaction of Context with each of Shift, Left Sender, and Right Sender in our first model.¹⁴ Relative to the Baseline Condition, in the Context Condition we expect the slope on Shift to be larger, the Left Sender intercept to be smaller, and the Right Sender intercept to be larger (i.e., intercepts should both be further from zero in the Context Condition).

The results from our first analysis are mixed (see Figure 2). On the one hand, the slope on Shift is, as predicted, somewhat larger in the Context Condition than the Baseline Condition, although this relationship is not significant (p = 0.18). On the other hand, the intercepts are actually both closer to zero in the Context Condition than in the Baseline Condition, in opposition to our expectations. However, this model assumes that strategies do not change over the course of the experimental session, despite our prediction in the Decay Hypothesis. It is therefore possible that this model obscures initial differences due to the context manipulation that may vanish by the final round. To test this hypothesis, we interact each predictor from our first model with the Round of play (see Appendix Table A2 for details).¹⁵

Figure 2.

Context effects. On average, the coefficient on Shift is larger in the Context Condition, as expected, but the intercepts on Left and Right Sender have the opposite sign from that predicted by the formal model. Estimates are based on a multilevel regression of Message on Shift, Left Sender, Right Sender, the interaction of each of those with Context, and Target. See model [1] from Appendix Table A2 for details.

There is evidence of the Decay Hypothesis in the Shift coefficient, but the results for the intercepts remain at odds with the theoretical predictions (see Figure 3). Firstly, once we condition on the Round of play, a somewhat stronger difference emerges between conditions. The Shift coefficient in the Context Condition is now larger than 0, and this relationship is borderline significant (p = 0.095). However, by the last round this difference reverses. The point estimate of the Shift coefficient is actually lower in the Context Condition than in the Baseline Condition, although this difference is not significant. Moreover, not only are both the Left and Right Sender intercepts closer to zero in the Context Condition than in the Baseline Condition, these distances only seem to grow by the last round.

Figure 3.

Duration of context effects. An initial difference in the slope on Shift diminishes by the last round. Drift over the course of play is also evident in the intercepts. However, the earlier finding that intercepts are closer to zero in the Context Condition than in the Baseline Condition persists. Estimates are based on a multilevel regression of Message on Shift, Left Sender, Right Sender, the interactions of each with Context, Round, and Context × Round, with a control for Target. See model [2] from Appendix Table A2 for details.

The results so far do not provide much support for the theoretical predictions. However, the above analyses are predicated on the notion that subjects are abiding by the assumptions of equilibrium behavior, for if they are not the regression is misspecified. In particular, equilibrium analysis requires that (1) players use best-response strategies and (2) players have beliefs and strategies that are mutually consistent. It is possible to relax one of these requirements while maintaining the other. The second requirement (mutual consistency) can be relaxed without jeopardizing the best-response assumption. For example, we could assume that players’ beliefs about others’ behavior corresponds to their past experience, and that players then play best responses to those (potentially mistaken) beliefs. In a companion paper (Minozzi and Woon, 2012), we find that such a framework of experiential best response provides a better explanation for how subjects play this communicative competition game. In the next section, we introduce this framework and apply it to the case at hand.

4.1. Experiential best responses and lying aversion

The idea behind experiential best response is that subjects develop expectations about each other’s behavior based on their individual histories of play, rather than based on the strategies identified by equilibrium analysis. Such play would not be surprising. In fact, our experimental interface informs subjects of their past histories immediately after every round. If subjects use past history in their strategies, then the omission of that variable casts some doubt on the results of our previous analysis.

If senders condition their messages on their experience, then their beliefs will not necessarily match the strategies of their opponents. Suppose each sender expects his opponent to send the message $E_{I} [m_{- I}] = T + {\bar{ξ}}_{- I}$ , where ${\bar{ξ}}_{- I}$ is the sender’s expectation of his opponent’s exaggeration. In the experiential best-response framework, ${\bar{ξ}}_{- I}$ is assumed to be based on the sample average of the difference the sender has observed between past Targets and his opponents’ Messages. If sender I also believes the receiver’s action will be the average of the messages she observes, then his best response will be the message $m_{I}^{E B R} = + 2 λ_{I} S_{I} - λ_{I} {\bar{ξ}}_{- I}$ .¹⁶

To apply this framework to our data, we estimate a multilevel model of Message that includes the variables from above (Target, Shift, Left Sender, Right Sender), as well as Opponent’s Past Exaggeration, which, for a particular sender, is the average difference between his opponent’s Message and Target over the past five rounds.¹⁷ We also interact Shift, Left Sender, Right Sender, and Opponent’s Past Exaggeration with Context and Round.

This best-response strategy has both similarities to and differences from the equilibrium message strategy. Like the equilibrium strategy, the experiential best-response framework predicts a positive coefficient on Shift. However, unlike the equilibrium predictions, this framework predicts a negative coefficient on Opponent’s Past Exaggeration, and a null intercept for each sender. Moreover, this framework also predicts a positive coefficient on the interaction of Shift and Context and a negative coefficient on the interaction of Opponent’s Past Exaggeration and Context. Finally, the Decay Hypothesis predicts that these interactive effects become smaller with repetition of the game.

Once we control for Opponent’s Past Exaggeration, a clear difference emerges between the Baseline and Context Conditions (see Figure 4 and Appendix Table A2 for complete details). In the first round, the slope on Shift in the Context Condition exceeds that in the Baseline Condition (p = 0.033). In addition, as predicted, there are no significant differences between either intercept pair in the first round.¹⁸ Consistent with the Decay Hypothesis, this difference vanishes by the last round.

Figure 4.

Context and experience. Controlling for the effect of experience in repeated rounds of the game indicates that context effects decay Estimates are based on a multilevel regression of Message on Shift, Opponent’s Past Exaggeration, Left Sender and Right Sender, and the interaction of each with Context and Round, with a control for Target. See model [3] from Appendix Table A2 for details.

An alternative explanation for our findings is that context might make the strategic incentives clearer and enhance subjects’ ability to learn to play the game. There are several pieces of evidence, however, that suggest against the context-enhanced learning interpretation. Firstly, when we compare the number of correct answers in the pre-game instruction check across conditions, there are actually fewer correct answers in the Context Condition (6.6 per subject) rather than the Baseline Condition (6.9 per subject), but the difference is not statistically significant (p = 0.31, two-tailed). Secondly, we do not find any significant interactions between Context × Round and the other variables, which we would expect if context enhanced learning. Furthermore, when we reanalyze the data without the first five rounds to allow for players to gain initial experience, we do not find the context effect to be strongest in round 6 as the context-enhanced learning interpretation would suggest.¹⁹

Some discrepancies between theory and evidence also emerge. In both conditions, the intercepts do start near zero in the first round, but by the last round they move far away from zero. Thus, messages become more polarized over time as senders learn to exaggerate more later in the game than earlier, but in a way that is unrelated to their payoffs or experiences. Because Receivers consistently choose actions close to the average message, increased polarization combined with the inherent randomness in Senders’ biases implies that Receivers become worse off over time.²⁰ Moreover, there are no significant differences between the coefficients on Opponent’s Past Exaggeration in the two conditions. Thus, the predictions of the experiential best-response framework fare better than do the equilibrium predictions, but anomalous phenomena remain.

5. Conclusion

In this paper, we first develop a formal model of communicative competition and lying aversion and then present evidence from an experiment based on that model. The primary challenge in testing models with pro-social preferences such as lying aversion is that these preferences are unobservable and hence beyond the fine control of the experimenter. In our experiment, we attempted to influence lying aversion by manipulating the context in which subjects play the game. Specifically, in our Context Condition, senders are called ‘lobbyists’ and read a short prompt that primes their uncertain incentives to lie, whereas in our Baseline Condition, all roles have abstract names and there is no prompt. We find that, after conditioning on subjects’ experience in repeated play, there is clear evidence that senders in the Context Condition weight their own preferences more highly than in the Baseline Condition. This finding is especially interesting because the strategic setup of the game is identical in both conditions.

We can infer from this finding that subjects’ behavior in communicative competition settings depends on lying aversion, which can be activated and accentuated. Moreover, we find that senders exaggerate their messages even more in later rounds of the game, regardless of context. This exaggeration emerges even after controlling for payoffs and experiences. This finding is not predicted by analysis of the formal model. Given that subjects do seem averse to lying, it is intriguing that they also seem to lie more later in the game. One intriguing possibility is the emergence of exaggeration via message inflation. In early rounds, subjects might choose messages that reflect their payoffs and their expectations of their opponents’ messages, and then add in an extra dash of exaggeration. If that is true, in later rounds, senders might take initial dashes of exaggeration into account, and then add their own. Thus, exaggeration might accrue round after round, and thereby culminate in the evidence we present. Future research should focus on more fully understanding and exploring the reasons for such inflation in the degree of exaggeration.

The clear message of this study is that lying aversion, which is the theoretical cause of overcommunication in single-sender games, may have very different consequences in multiple-sender environments than it does in single-sender environments. In a single-sender environment, lying aversion leads the lone sender to reveal more information than he should in equilibrium. In a multiple-sender environment, there is no such clear change in the amount of information conveyed to the receiver. Both theoretically and empirically, the best the receiver can do in such an environment is to observe the two messages she receives, and average them together. Regardless of the degree of lying aversion, there is no clear change in the information conveyed to the receiver.

From the perspective of the sender, lying aversion and competition constitute incentives that point in different directions. Without engaging in repeated play, the lying aversion incentive tends to win out, and senders overcommunicate. However, after many repetitions, the incentive to tell the truth is crowded out by the competitive incentive to exaggerate. Indeed, by the final round it appears that senders have moved from a strategy of overcommunication to a strategy of persistent exaggeration.

Substantively, this study provides us with some of the first evidence of behavior in environments with communicative competition, and hence insight into many important political environments. Congressional committees gather information by calling numerous witnesses to testify, many of whom represent competing viewpoints and interests. Regulators rely on data from industries as well as career bureaucrats, whose goals often differ from those of the political principals. Everyday political discourse transmitted through the media typically features relatively well-informed elites making claims about public policy to relatively poorly informed members of the public on a wide range of issues. Consider, for example, conflicting advice the public receives about the economic consequences of raising or lowering marginal tax rates, the imposition of domestic spending cuts, or health insurance mandates. If the elites are even mildly lying averse, our formal model provides some insight into their message strategies, which principally concern the extent to which they should exaggerate. In the experimental findings, exaggeration tended to increase over time, which matches the familiar narrative of the increasingly bitter tone of a dysfunctional and polarized contemporary politics.

Footnotes

Appendix

Acknowledgements

Thanks to Zac Auter for excellent research assistance and to Alan Wiseman for valuable comments and conversations.

Notes

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