Speech Is Silver, Silence Is Golden

: This paper experimentally investigates free-riding behavior on communication cost in a coordination game and finds strong indications of such free-riding. Firstly, the subjects wait for others to send a message when communication is costly, which does not happen when communication is costless. Secondly, the proportion of games where no communication or one-way communication takes place is much higher when communication is costly compared to when it is free.


Introduction
Cheap-talk experiments suggest that communication is effective in achieving coordination in many situations (see Cooper et al. [1,2] and Blume and Ortmann, [3] for an overview). However, the bulk of this literature has dealt with games where the choice of communication has been exogenous and costless. From a real world perspective such choices can be challenged on several grounds. For example, it is not hard to argue that communication is usually endogenously and individually chosen. Moreover, in many situations communication is associated with a cost (e.g., the cost of a phone call or advertising costs). In a symmetric coordination game without a focal point all players would be willing to use a communication device to solve the coordination problem, if it is costless. If, on the other hand, the communication device is costly to use then a player would prefer that another player uses the communication device to solve the coordination issue. Of course, a player would be OPEN ACCESS willing to communicate if the gains from coordination outweigh the communication cost, but she would strictly prefer to remain silent herself and to let another player communicate. With a slight abuse of terminology one might call this free-riding on communication cost. 1 We investigate this by way of economic experiments and find strong evidence of such free-riding attempts. To the best of our knowledge we are the first to document this type of behaviour. More specifically, we conduct a coordination game experiment without tacit coordination cues. A communication window is open pre-play where subjects can, at any time, choose to send a message (potentially at a cost) to solve the coordination issue. We observe considerable attempts to free-ride on the communication cost, by waiting for the opponent to send a message, but only when communication is costly. As a consequence, this leads to subsequent failure to coordinate in the underlying game.
Devetag and Ortmann [4] survey the literature of the effects of communication on coordination and conclude that communication is effective in achieving coordination. However and as noted above, this literature is concerned with costless communication, where all rational players have incentives to communicate to solve the coordination problem. When communication is costly and avoidable then a communication device will not solve the coordination issue as easily since the communication stage is itself a coordination game where a player prefers that the opponent sends a costly message to solve the coordination problem. Such a communication setup may lead to coordination failure in the same spirit as in a game of "Chicken" or "Hawk and Dove" game.
In a recent paper Kriss et al. [5] investigate the effect of endogenous costly communication on efficient coordination in the minimum-effort game. Like us they find that a cost of communication decreases use of the communication device and decreases (efficient) coordination. 2 Unlike in our setup the minimum-effort game contains tacit coordination cues, so the decrease in communication in their setup can come from both a free-riding effect and that subjects find some strategy profile salient and therefore deem the communication device unnecessary. Interestingly, in a post-experimental questionnaire they find responses supporting both explanations. We take this as further support of the existence of free-riding on communication.
It should be noted that what we observe is not just an instance of the well documented free-riding behavior in public goods games (see e.g., Isaac et al. [6] and Isaac and Walker, [7]). The reason is that our game is not a public good game which means that it is not straightforward to make analogies to this literature. Secondly, the two incentive structures are quite different. In most cases it is a dominant strategy to free-ride in a public goods game, but in the coordination game it is only an equilibrium to free-ride if the opponent communicates (and solves the coordination problem).
In light of the earlier literature we claim that our results contribute to the research of communication in games. The rest of the paper is organized as follows. Section 2 describes the game and the experimental procedures. Section 3 contains the results and section 4 concludes the paper. 1 Free-riding often refers to public goods situations where it is optimal to not provide the public good. In this paper we use the term in the sense of not taking a costly action (i.e., to communicate) that is beneficial for others while taking advantage of others' sacrificing actions.

The Game and the Experiment
The underlying game is a market entry game that combines aspects of coordination and conflict of interest. 3 Two players, 2 , 1  i , choose one of four alternatives: enter market X or Y, both markets (B) or do not enter either market (N). Figure 1 gives the normal form representation of this game.  The set of pure strategy Nash equilibria consists of the diagonal elements starting at the bottom left corner. 4 Apart from the market sharing strategy pairs (X,Y) and (Y,X) this set also includes the market domination strategy pairs (B,N) and (N,B). In the experiment, however, we rarely observed the latter type of equilibria outcomes in either the communication stage or the action stage. 5 One reason for this might be that they seemed unfair or that players did not think that they could credibly implement them. Therefore, we abstract from these in the following discussion.
In the experiment the cost of communication was varied, so that communication was either costless (c = 0) or costly (c = 3 or c = 5). 6 The cost was set to be substantial, but low enough to give players an incentive to use the communication opportunity. Indeed, in the absence of communication the most plausible outcome is the mixed Nash equilibrium wherein both players earn 12. Hence coordination by communication would be profitable under both c = 3 and c = 5.
Both players were informed that they could send messages, for 90 s, to the other player through a "chat" function before they made their strategy choices in the game. 7 In treatments with c > 0, 3 We use data from an experiment described and motivated in detail in Andersson and Holm [8]. That paper is focussed on the resulting equilibria, welfare effects and the type of communication with a specific emphasis on market entry situations. It does not discuss the general phenomenon of free-riding in the communication stage. 4 Let the probabilities of choosing strategies N, X, Y, B for a player be given by (p N , p X , p Y ,1-p N -p X -p Y ).
Then the symmetric mixed Nash equilibria are given by for each More importantly, all of these equilibria give rise to the same payoff of 12 for both players. In Andersson and Holm [8] we investigate both a symmetric game and an asymmetric game. To avoid the complications with tacit coordination in the asymmetric game we concentrate on the symmetric variant where the only way to coordinate is through communication. 5 The proportion of the (B,N) and (N,B) outcomes varied between 0 and 6 percentages of the coordinated outcomes. See Table 3 in Andersson and Holm [8]. 6 The difference in communication cost (c = 3 and c = 5) was motivated by the desire to study effects of variation in communication cost in Andersson and Holm [8]. We will not stress this treatment difference in the present paper since there were no substantial differences in free-riding between these treatments. 7 Instructions are available in Appendix A. the cost of communication was incurred by a player as soon as she sent her first message in the corresponding round.
When c = 0 a player is indifferent to whether she, her opponent, or both solve the coordination problem by sending a message. To the contrary, with c > 0 a player would prefer to free-ride and let the opponent solve it. 8 This game is hard to analyze theoretically in a stringent way since the communication stage is endogenous and dynamic. To get some understanding of the strategic aspects of the communication stage we note that when c > 0 it is optimal to remain silent until the very last seconds of the communication window. Once the players are at this stage the choice to send a message can be considered to be simultaneous and one may think of it as a normal form game where the choice is to communicate or not. Using this reduction we note that without communication the most likely outcome in the coordination game is the mixed Nash equilibrium payoff of 12. Furthermore, if any player communicates it is reasonable to expect the payoff of the equal split equilibria, i.e., (X, Y) or (Y, X), that is 24 minus communication cost for the communicating player. Figure 2 shows this reduced game. For positive communication costs c such that 0 < c < 12 no strategy is dominant and there is no equilibrium in pure strategies attainable without coordination. In the symmetric mixed equilibrium of this simultaneous game "No communication" is played with a positive probability, which is increasing in c. Thus, the incentive to free-ride by choosing "No communication" is stronger when the communication cost is positive. The reduced game can be perceived as a variant of the "Chicken" game or the "Hawk and Dove" game. 9 Clearly in the case of zero communication cost the choice to communicate is a dominant strategy and hence we should expect no coordination failure. And even though it is hard to pin down exactly when players will communicate in this situation one might suspect that the distribution of communication times is less skewed towards the very last seconds of the communication window. 8 Clearly, with 0  c , the game allows for many equilibria, but these do not necessarily imply free-riding. For instance, in the following equilibrium profile both players bear the same communication cost: I.) The Row player sends the initial message that they should play (X,Y) and then plays X if he gets a confirmation from the Column player that she will play Y. If Row does not get this confirmation, he plays a mixed strategy consistent with Nash-equilibrium. II) The Column player initiates communication, but if she receives the suggestion to play "(X,Y)" she sends a confirming message and acts according to the message. If she does not get this message, she will play a mixed Nash-equilibrium. Still, even if this profile shows that some equilibrium behaviour excludes free-riding in communication, there may be an incentive to free-ride since many probably consider the confirmation message to be redundant.
All subjects took part in one session only. Each such session consisted of three subsessions. In each subsession, ten rounds of each game were played where subjects were re-matched with a new coplayer (i.e., a strangers' matching protocol was used). 10 Subjects were informed about the outcome after each round. In total the experiment consisted of three sessions (with 18-24 subjects) and three treatments in each. A session took between 75 and 90 min. Subjects were recruited from introductory and intermediate Economics courses at the School of Economics and Management, Lund University. The subjects' total average earning was SEK373 (about USD57 when experiments were conducted). Table 1 presents the sessions relevant for this paper. 11 Table 1. Treatment Design.  We have pooled data from treatments with c = 3 and c = 5 in Figure 3. However, not much variation in the data is masked by such pooling. 13 We now turn to analyzing the data of message timing. To save space we let SSnm denote session n and subsession m (see subsession code in Table 1). In Table 2 we present averages from each subsession. The largest differences are observed between treatments with zero communication cost and those with positive communication cost. In situations with costless communication the timing of the first message is on average in the interval of 1−7 s whereas the corresponding number for costly communication treatments is 34-42 s.  Two-way  32  0  5  5  0  1  99  33  5  42  35  4  57  39  41  0  2  3  0  0  100  42  3  37  31  4  56  40  51  3  34  26  1  52  47  52  0  7  7  0  2  98 Using the fact that the first period message timing data of SS41 and SS51 are independent observations we can perform a valid statistical test of the hypothesis that the incentive to free-ride on communication is stronger when the cost of communication is positive. Wilcoxon-Mann-Whitney test strongly rejects the hypothesis that communication-initiation times comes from the same distribution (n = 22, p= 0.002). With the cautionary note that the observations are not independent we also report the p-values at the very last period in the same subsessions. In both cases we can strongly reject that they come from the same distribution (p = 0.0001).
A second indication of free-riding is the fraction of communication rounds that is one-way. 14 In the game it is possible for the player who sends the first message to achieve coordination without any response from the other player, who may then free-ride. The latter player may of course want to send a message to the former player to reassure her that they have an agreement. 15 However, since this is costly in the treatments with communication cost, we should expect a higher proportion of one-way communication in treatments with costly communication compared to those with costless communication. As the second column from the right of Table 2 shows, the results strongly support this conjecture. When communication is costly one-way communication is potentially more efficient than two-way communication and hence an increase in communication cost might be welfare improving if it leads to a sufficient increase in the proportion of one-way communication. 16 Table 3 presents average per period profits. As can be seen from Table 3 profits are decreasing in the communication cost, implying that the increase in one-way communication does not fully mitigate the increase in communication cost. The most relevant treatments to compare in this respect are c = 3 (SS42 and SS51) and c = 5 (SS33). Here, the average payoffs are higher when the communication cost is lower (i.e., c = 3), which suggests that the potential gain of the increase in one-way communication when c = 5 is dominated by the cost of communication and coordination failures. In addition, as can be seen in Figure 4 the fraction of subjects choosing to communicate is in general not decreasing over time so this phenomenon is not likely to disappear. From Table 3 it can also be noted that in subsessions without communication (i.e., SS31 and SS52) the average profit is close to the mixed Nash equilibrium profit of 12.
14 Since it is also efficient that only one subject sends a message when it is costly one can argue that this is "coordination" on the efficient outcome rather than free-riding. However, this coordination also implies voluntary or involuntary free-riding since it is essential that at least one take the communication cost. Thus, even if this indication not only involves free-riding, we argue that there is an element of it to motivate us using the concept. 15 As noted by Crawford [11], reassurance may have a strong effect on coordination success. 16 For a more elaborate account of the welfare effects of communication, see Andersson and Holm [8]. It can finally be noted that at least some subjects understand and explicitly express the intent to free-ride in their messages. Admittedly, this is not any hard evidence of free riding. However, the following dialogue nicely illustrates that while some subjects understand the free-riding opportunities, this may not be the case for all subjects: In a recent survey of the literature on coordination failure, Devetag and Ortmann [4] maintain that communication can be seen as a successful solution to coordination failure. They also conclude that since communication is often observed in real life, coordination failure should be seen as an exception rather than a rule both inside and outside the lab. Although we agree with this conclusion our results suggest that the exception might be more prevalent than we first thought.