Condition-dependent trade-offs maintain honest signaling

In this study we present the results of a laboratory experiment with human participants to test the role of equilibrium signal cost and signalling trade-offs for the development of honest communication.

Experimental setup
Participants played a simple 2x2 signaling game in a computer lab. 12 sessions were organized, involving different numbers of participants (groups of 12, 16, and 20). A total of 196 students participated in the experiment. A mix of within and between subject design was applied: within a session, each group played three of the nine treatment conditions. Each condition was played as the first, second and third game through 20 rounds each. Since the order of games and the number of participants (Bruner et al. 2014) may affect the speed of learning dynamics in the game, we control for these factors with statistical methods during the analysis. The experiment took place at the Corvinus University of Budapest (CUB) in Hungary between 25th January 2018 and 15th January 2019. Participants were regular or corresponding students and one experiment lasted for approx. 45 minutes. During the experiment, participants were seated randomly in front of the computers, thus participants took part in the experiment anonymously. Computers were connected on a local network with the help of the software z-Tree (Fischbacher 2007). The description of the game was included in the experimental instructions (see S4.) and displayed on participants’ screens. They got the instructions on paper as well because roles participants played in the game have changed round-by-round. In the first step, participants were divided into groups of fours which contained two signalers (S) and two receivers (R). We used unbiased signaling game, where the two types of signaler (S in high condition and S in low condition) were assigned randomly by the computer. Everyone was only aware of their own type, they did not know each other's condition. In the next step, signalers had to choose a signal and send it to the receiver to get the resource. Distinguishable characters were used as signals (e.g. )( and ~ ) and their costs (or benefits) were displayed next to each signal depending on which condition was played. In the next step, receivers had to decide whether they would give the resource after a signal was seen. Signalers succeed if they receive the resource, but receivers’ success depended on the (hidden) type of the signaler (S in high condition was preferred to S in low condition). After these steps, participants have learned the type of the sender, the signal they sent and the success of their decision. In case of a successful decision, they received HUF 1200. The other factor that influenced the payments was the cost of the signals (see Table 1). In addition, participants received a show-up fee of HUF 1000.

本研究报告了一项以人为被试的实验室实验结果，旨在检验均衡信号成本与信号传递权衡在诚实沟通发展中的作用。

实验设计
被试在计算机实验室中完成一项简易的2×2信号传递博弈（signaling game）。本次实验共设置12个实验场次，每组被试人数分别为12、16和20人，总计196名学生参与本实验。本实验采用被试内与被试间混合设计：在单场实验中，每个小组需完成9种实验处理条件中的3种，每种处理条件分别作为第1、第2、第3轮博弈，每轮博弈进行20回合。由于博弈顺序与被试人数（Bruner等人，2014）可能会影响博弈中的学习动态速率，因此我们在数据分析阶段通过统计方法对上述因素加以控制。

本实验于2018年1月25日至2019年1月15日在匈牙利布达佩斯考文纽斯大学（Corvinus University of Budapest, CUB）开展。被试为在校注册学生或在职函授学生，单场实验时长约为45分钟。实验中，被试被随机安排在计算机前就座，所有被试均以匿名方式参与实验。计算机通过局域网连接，并借助z-Tree软件（Fischbacher, 2007）运行实验程序。

博弈规则说明包含于实验指导手册中（详见补充材料S4），并展示在被试的计算机屏幕上。由于被试在每一轮博弈中所扮演的角色会发生变化，因此同时为被试提供纸质版实验指导手册。实验第一步，被试被划分为4人一组，每组包含2名信号发送者（S）与2名信号接收者（R）。本实验采用无偏信号传递博弈，计算机将随机为信号发送者分配两种类型（高状态信号发送者与低状态信号发送者）。每名被试仅知晓自身所处的状态，无法得知其他被试的状态信息。

随后，信号发送者需选择并发送信号给接收者，以获取资源。实验采用可区分的字符作为信号（例如)(与~），信号的成本（或收益）将根据当前所处的实验处理条件显示在对应信号旁。接下来，信号接收者在接收到信号后，需决定是否发放资源。信号发送者成功获取资源即视为博弈成功，而接收者的博弈成功与否则取决于信号发送者的隐藏类型（高状态信号发送者优于低状态信号发送者）。

完成上述流程后，所有被试将获知发送者的类型、所发送的信号以及自身决策的结果。若决策成功，被试将获得1200匈牙利福林（HUF）。除此之外，信号成本（或收益）也会影响最终报酬（详见表1）。此外，所有被试均可获得1000匈牙利福林（HUF）的到场报酬。