Abstract
We study the interaction of the effects of the strategic environment and communication on the observed levels of cooperation in two-person finitely repeated games with a Pareto-inefficient Nash equilibrium and replicate previous findings that point to higher levels of tacit cooperation under strategic complementarity than under strategic substitutability. We find that this is not because of differences in the levels of reciprocity as previously suggested. Instead, we demonstrate that slow learning coupled with noisy choices may drive this effect. When subjects are allowed to communicate in free-form online chats before making choices, cooperation levels increase significantly to the extent that the difference between strategic complements and substitutes disappears. A machine-assisted natural language processing approach then shows how the content of communication is dependent on the strategic environment and cooperative behavior, and indicates that subjects in complementarity games reach full cooperation by agreeing on gradual moves toward it.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Our focus is on finitely repeated games. See Mermer et al. (2021) for an analysis on indefinitely repeated games. Furthermore, we note that the strategic environment definitions are based on stage games and as demonstrated by Echenique (2004), Sabarwal and VuXuan (2018), and Vives (2009), these definitions may not extend to repeated interactions.
The intuition is that in the case of substitute goods (from the consumer’s perspective), the Bertrand price competition model generates upward sloping reaction functions in prices and hence theory predicts that if one seller moves away from Nash equilibrium toward the collusive outcome, the other seller has a unilateral incentive to respond by raising the price toward the collusive outcome. It should be noted that Cournot competition is typically modeled with strategic substitutability and negative externality, whereas Bertrand competition is usually modeled with strategic complementarity and positive externality. However, as in Anderson et al. (2010, 2015), both Cournot and Bertrand competitions can be modeled with either complementarity or substitutability. See Suetens and Potters (2007) for a discussion and review of results on the strategic environment effect and Potters and Suetens (2013) for a survey on oligopoly experiments.
It is important to note that under market framing, Anderson et al. (2010, 2015) observe collusion among firms under Cournot competition with substitute goods (hence, strategic substitutability) and under Bertrand competition with complement goods (also with strategic substitutability), whereas there is no collusion in the opposite cases (Cournot competition with complement goods or Bertrand competition with substitute goods, both leading to strategic complementarity). Barthel et al. (2019) implement a simple design with \(3\times 3\) games of complements and substitutes without market framing, where the NE coincides with the joint payoff maximization strategy pair. Similarly, they observe higher frequencies of NE play under complementarity.
Andersson and Wengström (2012) find, for instance, that more communication possibilities do not necessarily lead to more cooperation in two-stage games. Instead, they find that adding the possibility of communicating intra-play communication can reduce the cooperation boost induced by pre-play communication. Furthermore, Lee and Hoffman (2020) observe that the frequency of the possibility to communicate (pre-play) correlates with the levels of cooperation. Finally, Fonseca and Normann (2012) find that the possibility of communication improves outcomes for any number of firms, but that this gain from communicating is nonmonotonic in the number of firms.
Gomez-Martinez et al. (2016) study the effect of the revelation of firm-specific data in a Cournot game with multiple firms, and reveal that communication helps to reach collusive agreements in both individual and aggregate information treatments. Awaya and Krishna (2016) investigate, in their theoretical study built on a model of repeated oligopoly with secret price cuts, how unverifiable communication about past sales can facilitate collusion. Bigoni et al. (2018) run a series of experiments with an indefinitely repeated noisy Cournot game to examine the effect of flexibility (the ability to respond quickly) on cooperation, and observe rapid convergence to very low levels of cooperation, regardless of flexibility. Finally, Fonseca et al. (2018) discover an increasing and concave relationship between the number of firms and the additional profit firms make from the opportunity to communicate free form in Cournot oligopolies.
Recent works include, among others, Hansen and McMahon (2016), which assesses the impact of content in central bank communication on real economic variables, Gentzkow and Shapiro (2010), which investigates the demand for like-minded news as a reason behind bias in newspapers, Mueller and Rauh (2018), which suggests implementing topic models in the analysis of newspaper articles to predict timing of political violence, and Grajzl and Murrell (2019), which employs a structural topic model to study the features of Francis Bacon’s writings to gauge their importance in the history of economic thought.
PS find no difference between the degrees of cooperation under positive and negative externality cases within strategic environments and pool them for their analyses of strategic environments. Therefore, we focus on only one of the externality cases, i.e., positive externality.
The number of participants and sessions varied across treatments because of variation in show-up rate across our prescheduled sessions that took place at different times of the school semester.
In the trial period, the payoff calculators were used twice to calculate hypothetical payoffs. In chat treatments afterwards, the chat box was trialed by typing “hello” (bonjour) and then a forced decision was required. Payoffs in the trial period did not count in the final earnings.
Although the overall comparison between treatments is the same with PS, several observations should be noted. First, in PS, the average cooperation rate is higher (0.27 in substitutability and 0.41 in complementarity). In both of their treatments, there appears to be a clearly increasing trend in choices after the first few periods. In the case of complementarity, average choices increase as high as to the level of the JPM. Second, choices in PS are both higher than the NE, whereas, in our data, the substitutability treatment has lower average choices than the NE. Finally, the end game effect in PS is stronger than with our data for both treatments. These observations could be explained by differences in subject pools across studies. For instance, as noted by Al-Ubaydli et al. (2016), cognitive skills well predict the average cooperation rates in repeated prisoners’ dilemma games, and Noussair et al. (2016) and Breaban et al. (2020) find that the average Cognitive Reflection Test score in the Tilburg subject pool is around 1.8, whereas it is around 0.4 for our subject pool in Nice, as reported by Babutsidze et al. (2021).
Figure 12 in Appendix A depicts the comparison of payoffs. The average payoffs over all periods with (without) communication are: 35.1 (25.5) for complementarity and 35.3 (20.7) for substitutability, which align with the findings regarding choices.
All WMW tests yield p values of 0.000. We tested if this was because of the extra time given for chat, rather than the effect of communication itself by running two extra sessions with the same extra time (one minute) but without the ability to communicate. The results are in Appendix A.2, which show that the extra time in communication treatments have only a very small effect.
Figures 14 and 15 in Appendix B show the evolution of choices within pairs.
Mengel (2017), in a survey comprising 96 studies with 3,500 subjects in total, finds that risk (loss from unilateral cooperation) and temptation (gain from unilateral defection) play a significant role in the levels of cooperation in prisoners’ dilemma games. If we look at the restricted game with only NE and JPM strategies for defection and cooperation, respectively, the value of the risk parameter is approximately 2.6 for our complementarity treatment and 0.8 for our substitutability treatment. Similarly, the value of the temptation parameter is approximately 1.06 for our complementarity treatment and 1.22 for our substitutability treatment. Mengel (2017) concludes that in repeated games with partner matching, temptation better explains the variation in cooperative behavior. When temptation is higher, sustaining cooperation is more difficult in substitutability. In contrast, as risk is higher in complementarity, fewer subjects tend to try out (jump to) JPM strategies. The latter follows from the argument that risk is crucial in determining short-run incentives (see Blonski et al., 2011).
In addition, there is no visible end-game effect in either of strategic environments, which could indicate that subjects in non-JPM pairs are not strategically involved in the game to the same extent as those in JPM pairs and which show a substantial end-game effect.
Charness and Dufwenberg (2006, 2011) emphasize the effectivity of free-form communication in enhancing efficiency when equilibria can be Pareto-ranked. Cooper and Kühn (2014) conclude that allowing a rich message space leads to persistent collusion in a two-person two-period matrix game resembling Bertrand price competition. Brandts et al. (2015) argue that restricted and unilateral communication is less effective compared with free-form communication in contract games. Andersson and Wengström (2012) argue that free-form communication increases the importance of social preferences as opposed to structured communication. Building on this argument, Cason and Mui (2015) deliver evidence suggesting that rich communication is more effective in facilitating coordinated resistance modeled à la Weingast (1995). Alternatively, Cason et al. (2012) point to contest environments where free-form communication could damage efficiency. Finally, Wang and Houser (2019) find that in coordination games, free-form communication boosts coordination much more than restricted communication. See Brandts et al. (2019) for an extensive survey of laboratory studies using communication.
This is based on the number of times subjects clicked the “send” button.
The number of messages sent by non-JPM subjects in the second half of the experiment (1.49, with \(s.d.=1.96\)) is not statistically significantly different when compared with the JPM subjects (1.45, with \(s.d.=1.95\) and \(p=0.116\) for WMW two-tailed test).
These observations point to the idea that communication benefits subjects in the substitutability treatment more, as they make greater use of it, which could imply that under restricted communication, e.g., regarding the number of messages, we might observe that the strategic environment effect could persist.
The proceeding analysis is executed with the R packages quanteda (Benoit et al., 2018) and tm (Feinerer, 2018). The stopwords we removed that may not be predefined in these packages are listed in the Online Appendix. The details of our preparation for the content analysis, which includes a mild orthographical clean-up necessitated by common mistakes, is provided in the replication package.
We exclude a pair in the substitutability treatment that did not communicate beyond the first period. Some stopwords are removed after the word cloud in Fig. 7 (see Online Appendix). This removal emptied one other subject’s chat content, so we have 201 subjects, thus, 100 pairs, whose chat records could be utilized.
Three terms are not included as they did not appear within the 125 top-ranked terms for substitutability although they were in the top 50 for complementarity. These are “period” (period), “tableau” (table), and “chiffr” (number), which rank 41st, 44th, and 45th in complementarity, respectively.
Note that \(\Delta r_S^C(t)=-\Delta r_C^S(t)/(\Delta r_C^S(t)+1)\).
This difference regarding “mainten” is not observed when the analysis is confined to JPM pairs, whereas it is stronger in non-JPM pairs. Details available upon request.
The term appears as in “ce n’est pas grave”, which translates as “it does not matter” in English, in the chat content of 9 (5) pairs in substitutability (complementarity). They use this term as in this sentence to indicate forgiveness for a cheating attempt or a (self-declared) mistake by the opponent. Details available upon request.
The term “25.5” is used 50 times by the subjects in substitutability as opposed to 36 times in complementarity.
See Andres et al. (2021), where another topic modeling application is implemented following our approach.
We refer the interested reader to Roberts et al. (2016) for formal aspects of the estimation procedure. In short, model estimation uses a fast semi-collapsed, variational expectation maximization algorithm where Laplace approximations are used for the nonconjugate portions of the model.
This procedure incorporates measurement uncertainty from the STM model using the method of composition (see Roberts et al., 2019, for details). Online Appendix G.3 contains the estimated topic proportions for each pair in both treatments and Appendix G.4 delivers a set of examples of chat contents together with estimated topic proportions.
Note that this identification is done among JPM pairs, thus, they manage to cooperate fully eventually. Furthermore, symmetric strategy pairs that are higher than 24 pay very similar to what JPM pays. For instance \(\pi ^S(28,28)=\pi ^S(28,28)=41.272\) and \(\pi ^C(24,24)=\pi ^S(24,24)=41.696\), whereas \(\pi ^C(25.5,25.5)=\pi ^S(25.5,25.5)=41.94\). Thus, subjects may not be able to coordinate on the most efficient cooperation even though they intend to in the first few periods. Our subsequent observations are robust to small changes in the choice of this interval or the choice of 60% of the periods in the first third of the experiment (instead of \(50\%\) for instance), as shown in Figs. 16 and 17 in Appendix C.
Note that the terms that are used less than five times are excluded from the chat records in the STM estimation.
See Eaton (2004) for an overview of the prevalence of strategic environment effects in social dilemma situations in economic studies. These include patent races, international trade policies, arms races, team productions, public goods, and so on.
Similar conclusions can be drawn for team production instances, in which the skills of members of the team might be complements or substitutes, R &D competition in which high spillovers would induce complementarity whereas lower spillovers would induce substitutability, and public good production processes, in which the nature of the returns to scale would imply complementarity or substitutability, among others.
References
Airoldi, E. M., & Bischof, J. M. (2016). Improving and Evaluating Topic Models and Other Models of Text. Journal of the American Statistical Association, 111, 1381–1403.
Al-Ubaydli, O., Jones, G., & Weel, J. (2016). Average player traits as predictors of cooperation in a repeated prisoner’s dilemma. Journal of Behavioral and Experimental Economics, 64, 50–60.
Anderson, L. R., Freeborn, B. A., & Holt, C. A. (2010). Tacit Collusion in Price-Setting Duopoly Markets: Experimental Evidence with Complements and Substitutes. Southern Economic Journal, 76, 577–591.
Anderson, L. R., Freeborn, B. A., & Hulbert, J. P. (2015). Determinants of Tacit Collusion in a Cournot Duopoly Experiment. Southern Economic Journal, 81, 633–652.
Andersson, O., Galizzi, M. M., Hoppe, T., Kranz, S., Van Der Wiel, K., & Wengström, E. (2010). Persuasion in experimental ultimatum games. Economics Letters, 108, 16–18.
Andersson, O., & Wengström, E. (2012). Credible communication and cooperation: experimental evidence from multi-stage games. Journal of Economic Behavior & Organization, 81, 207–219.
Andres, M., Bruttel, L., & Friedrichsen, J. (2021). The leniency rule revisited: Experiments on cartel formation with open communication. International Journal of Industrial Organization, 76, 102728.
Arad, A., & Penczynski, S. (2018). Multi-Dimensional Reasoning in Competitive Resource Allocation Games: Evidence from Intra-Team Communication, Working paper.
Arora, S., Ge, R., Halpern, Y., Mimno, D., Moitra, A., Sontag, D., Wu, Y., & Zhu, M. (2013). A practical algorithm for topic modeling with provable guarantees, in International Conference on Machine Learning, 280–288.
Awaya, Y., & Krishna, V. (2016). On communication and collusion. The American Economic Review, 106, 285–315.
Babutsidze, Z., Hanaki, N., & Zylbersztejn, A. (2021). Nonverbal content and trust: An experiment on digital communication. Economic Inquiry, 59, 1517–1532.
Barthel, A.-C., Hoffmann, E., & Monaco, A. (2019). Coordination and learning in games with strategic substitutes and complements. Research in Economics, 73, 53–65.
Benoit, K., Watanabe, K., Wang, H., Nulty, P., Obeng, A., Müller, S., & Matsuo, A. (2018). quanteda: An R package for the quantitative analysis of textual data. Journal of Open Source Software, 3, 774.
Bergin, J., & Bernhardt, D. (2009). Cooperation through imitation. Games and Economic Behavior, 67, 376–388.
Bigoni, M., Potters, J., & Spagnolo, G. (2018). Frequency of interaction, communication and collusion: an experiment, Economic Theory, 1–18.
Blei, D. M., & Lafferty, J. D. (2007). A correlated topic model of science, The Annals of Applied Statistics, 17–35.
Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent dirichlet allocation. Journal of machine Learning research, 3, 993–1022.
Blonski, M., Ockenfels, P., & Spagnolo, G. (2011). Equilibrium selection in the repeated prisoner’s dilemma: Axiomatic approach and experimental evidence. American Economic Journal: Microeconomics, 3, 164–192.
Brandts, J., Cooper, D. J., & Rott, C. (2019). Communication in laboratory experiments, Handbook of Research Methods and Applications in Experimental Economics, 401.
Brandts, J., Ellman, M., & Charness, G. (2015). Let’s talk: How communication affects contract design. Journal of the European Economic Association, 14, 943–974.
Breaban, A., Noussair, C. N., & Popescu, A. V. (2020). Contests with money and time: Experimental evidence on overbidding in all-pay auctions. Journal of Economic Behavior & Organization, 171, 391–405.
Cason, T. N., & Mui, V.-L. (2015). Rich communication, social motivations, and coordinated resistance against divide-and-conquer: A laboratory investigation. European Journal of Political Economy, 37, 146–159.
Cason, T. N., Sheremeta, R. M., & Zhang, J. (2012). Communication and efficiency in competitive coordination games. Games and Economic Behavior, 76, 26–43.
Charness, G., & Dufwenberg, M. (2006). Promises and partnership. Econometrica, 74, 1579–1601.
Charness, G., & Dufwenberg, M. (2011). Participation. The American Economic Review, 101, 1211–1237.
Cooper, D. J., & Kagel, J. H. (2005). Are two heads better than one? Team versus individual play in signaling games. The American economic review, 95, 477–509.
Cooper, D. J., & Kühn, K.-U. (2014). Communication, renegotiation, and the scope for collusion. American Economic Journal: Microeconomics, 6, 247–278.
Corazzini, L., Kube, S., Maréchal, M. A., & Nicolo, A. (2014). Elections and deceptions: an experimental study on the behavioral effects of democracy. American Journal of Political Science, 58, 579–592.
Crawford, V. P. (2019). Experiments on Cognition, Communication, Coordination, and Cooperation in Relationships. Annual Review of Economics, 11, 167–191.
Eaton, B. C. (2004). The elementary economics of social dilemmas. Canadian Journal of Economics/Revue canadienne d’économique, 37, 805–829.
Echenique, F. (2004). Extensive-form games and strategic complementarities. Games and Economic Behavior, 46, 348–364.
Ellingsen, T., & Johannesson, M. (2008). Anticipated verbal feedback induces altruistic behavior. Evolution and Human Behavior, 29, 100–105.
Embrey, M., Fréchette, G. R., & Yuksel, S. (2017). Cooperation in the finitely repeated prisoner’s dilemma. The Quarterly Journal of Economics, 133, 509–551.
Erev, I., & Roth, A. E. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria, American economic review, 848–881.
Farrell, J., & Rabin, M. (1996). Cheap talk. The Journal of Economic Perspectives, 10, 103–118.
Feinerer, I. (2018). Introduction to the tm Package Text Mining in R, Retrieved March, 1, 2019.
Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental economics, 10, 171–178.
Fischer, C., & Normann, H.-T. (2019). Collusion and bargaining in asymmetric Cournot duopoly - An experiment. European Economic Review, 111, 360–379.
Fonseca, M. A., Li, Y., & Normann, H.-T. (2018). Why factors facilitating collusion may not predict cartel occurrence–experimental evidence. Southern Economic Journal, 85, 255–275.
Fonseca, M. A., & Normann, H.-T. (2012). Explicit vs. tacit collusion??The impact of communication in oligopoly experiments. European Economic Review, 56, 1759–1772.
Fonseca, M. A., & Normann, H.-T. (2014). Endogenous cartel formation: Experimental evidence. Economics Letters, 125, 223–225.
Gentzkow, M., Kelly, B., & Taddy, M. (2019). Text as data. Journal of Economic Literature, 57, 535–74.
Gentzkow, M., & Shapiro, J. M. (2010). What drives media slant? Evidence from US daily newspapers. Econometrica, 78, 35–71.
Georgalos, K., & Hey, J. (2019). Testing for the emergence of spontaneous order, Experimental Economics, 1–21.
Gomez-Martinez, F., Onderstal, S., & Sonnemans, J. (2016). Firm-specific information and explicit collusion in experimental oligopolies. European Economic Review, 82, 132–141.
Grajzl, P., & Murrell, P. (2019). Toward understanding 17th century English culture: A structural topic model of Francis Bacon’s ideas. Journal of Comparative Economics, 47, 111–135.
Greiner, B. (2015). Subject pool recruitment procedures: organizing experiments with ORSEE. Journal of the Economic Science Association, 1, 114–125.
Hanaki, N., Kirman, A., & Pezanis-Christou, P. (2018). Observational and reinforcement pattern-learning: An exploratory study. European Economic Review, 104, 1–28.
Hanaki, N., Sethi, R., Erev, I., & Peterhansl, A. (2005). Learning strategies. Journal of Economic Behavior & Organization, 56, 523–542.
Hansen, S., & McMahon, M. (2016). Shocking language: Understanding the macroeconomic effects of central bank communication. Journal of International Economics, 99, S114–S133.
Hennig-Schmidt, H., Li, Z.-Y., & Yang, C. (2008). Why people reject advantageous offers: Non-monotonic strategies in ultimatum bargaining: Evaluating a video experiment run in PR China. Journal of Economic Behavior & Organization, 65, 373–384.
Holt, C. A. (1993). Industrial organization: A survey of laboratory research. The handbook of experimental economics, 349, 402–03.
Houser, D., & Xiao, E. (2011). Classification of natural language messages using a coordination game. Experimental Economics, 14, 1–14.
Huerta, J. M. (2008). Relative rank statistics for dialog analysis, in Proceedings of the Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, 965–972.
Kimbrough, E., Smith, V. L., & Wilson, B. J. (2008). Historical property rights, sociality, and the emergence of impersonal exchange in long-distance trade. The American Economic Review, 98, 1009–1039.
Lee, J. Y., & Hoffman, E. (2020). How much you talk matters: cheap talk and collusion in a Bertrand oligopoly game, Available at SSRN 3423707.
McAllister, P. H. (1991). Adaptive approaches to stochastic programming. Annals of Operations Research, 30, 45–62.
Mengel, F. (2017). Risk and Temptation: A Meta-Study on Prisoner’s Dilemma Games, The Economic Journal.
Mermer, A. G., Müller, W., & Suetens, S. (2021). Cooperation in infinitely repeated games of strategic complements and substitutes. Journal of Economic Behavior & Organization, 188, 1191–1205.
Mimno, D., Wallach, H. M., Talley, E., Leenders, M., & McCallum, A. (2011). Optimizing semantic coherence in topic models, in Proceedings of the conference on empirical methods in natural language processing, Association for Computational Linguistics, 262–272.
Mueller, H., & Rauh, C. (2018). Reading between the lines: Prediction of political violence using newspaper text. American Political Science Review, 112, 358–375.
Noussair, C. N., Tucker, S., & Xu, Y. (2016). Futures markets, cognitive ability, and mispricing in experimental asset markets. Journal of Economic Behavior & Organization, 130, 166–179.
Penczynski, S. P. (2018). Using machine learning for communication classification, Experimental Economics, 1–28.
Potters, J., & Suetens, S. (2009). Cooperation in experimental games of strategic complements and substitutes. The Review of Economic Studies, 76, 1125–1147.
Potters, J., & Suetens, S. (2013). Oligopoly experiments in the current millennium. Journal of Economic Surveys, 27, 439–460.
Roberts, M., Stewart, B., & Tingley, D. (2019). stm: An R Package for Structural Topic Models. Journal of Statistical Software, Articles, 91, 1–40.
Roberts, M. E., Stewart, B. M., & Airoldi, E. M. (2016). A model of text for experimentation in the social sciences. Journal of the American Statistical Association, 111, 988–1003.
Roberts, M. E., Stewart, B. M., Tingley, D., Lucas, C., Leder-Luis, J., Gadarian, S. K., Albertson, B., & Rand, D. G. (2014). Structural Topic Models for Open-Ended Survey Responses. American Journal of Political Science, 58, 1064–1082.
Sabarwal, T., & VuXuan, H. (2018). Two Stage 2x2 Games with Strategic Substitutes and Strategic Heterogeneity, Available at SSRN 3322176.
Schotter, A., & Sopher, B. (2007). Advice and behavior in intergenerational ultimatum games: An experimental approach. Games and Economic Behavior, 58, 365–393.
Selten, R., & Stoecker, R. (1986). End behavior in sequences of finite Prisoner’s Dilemma supergames A learning theory approach. Journal of Economic Behavior & Organization, 7, 47–70.
Suetens, S., & Potters, J. (2007). Bertrand colludes more than Cournot. Experimental Economics, 10, 71–77.
Sutter, M., & Strassmair, C. (2009). Communication, cooperation and collusion in team tournaments: an experimental study. Games and Economic Behavior, 66, 506–525.
Taddy, M. (2012). On estimation and selection for topic models, in International Conference on Artificial Intelligence and Statistics, 1184–1193.
Vives, X. (2009). Strategic complementarity in multi-stage games. Economic Theory, 40, 151–171.
Waichman, I., Requate, T., et al. (2014). Communication in Cournot competition: An experimental study. Journal of Economic Psychology, 42, 1–16.
Wallach, H. M., Murray, I., Salakhutdinov, R., & Mimno, D. (2009). Evaluation methods for topic models, in Proceedings of the 26th annual international conference on machine learning, ACM, 1105–1112.
Wang, S., & Houser, D. (2019). Demanding or deferring? an experimental analysis of the economic value of communication with attitude. Games and Economic Behavior, 115, 381–395.
Weingast, B. R. (1995). The economic role of political institutions: Market-preserving federalism and economic development, Journal of Law, Economics, & Organization, 1–31.
Whinston, M. D. (2008). Lectures on antitrust economics, MIT Press Books.
Acknowledgements
We are grateful to Lisa Bruttel, Colin Camerer, Jernej Čopič, Marco Faravelli, Ben Greiner, Charles Holt, Kenan Huremović, Yukio Koriyama, Nikhil Kotecha, Antonin Macé, Aidas Masiliūnas, Stefan Penczynski, Paul Pezanis-Christou, Charles Plott, Kirill Pogorelskiy, Jan Potters, Owen Powell, Molly Roberts, Erik Wengström, Sevgi Yuksel, and participants in the Murat Sertel Workshop in Paris, Economic Science Association World Meeting in San Diego, Southwest Experimental and Behavioral Economics Workshop in Santa Barbara, the Istanbul Bilgi University Experimental Economics Seminars, Economic Design Workshop at CNAM in Paris, GATE-LSE seminars in Lyon, LAMETA seminars in Montpellier, the Behavioral and Experimental Analyses in Macro-finance Workshop in Nice, the Theory, Organization, and Markets seminar at Paris School of Economics, CREST Workshop in Experimental Economics, and T&C Chen Center lab meetings at Caltech. We are grateful to Erina Hanaki for the translations from French to English, to Mira Toumi, Maxime Perodaud, Imen Bouhlel, and Ismaël Rafaï for their support in conducting the experimental sessions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Part of this work was carried out when N. Hanaki was affiliated with Université Côte d’Azur, CNRS, GREDEG, and when A. I. Ozkes was affiliated with the Aix-Marseille School of Economics, WU Vienna University of Economics and Business, and EMLV De Vinci Research Center. The authors thank these institutions for the supportive environments they provided. This research was supported by ANR grants Investissements d’Avenir under PSL\(^*\) MIFID (IDEX ANR-10-IDEX-0001-02), \(UCA^{JEDI}\) (ANR-15-IDEX-01), an ORA-Plus project BEAM (ANR-15-ORAR-0004), EPURAI (ANR-21-MRS2-0027-01), JSPS Grants-in-Aid for Scientific Research (18K19954, 20H05631), JSPS Core-to-Core Program FY2020 project “Formation of an International Research Center for Experimental Financial Market”, financial aids from the Aix-Marseille School of Economics, De Vinci Research Center, and the Joint Usage/Research Center at ISER, Osaka University. The replication material for the study is available at https://doi.org/10.17605/OSF.IO/QXG8D.
Supplementary Information
Below is the link to the electronic supplementary material.
Appendices
A Payoff evolution and extra sessions
1.1 A.1 Payoff evolution
See Fig. 12.
Average payoffs per period for complementarity and substitutability treatments with and without chat
1.2 A.2 Communication or extra time?
Here, we provide comparisons with the extra sessions we have run to check if the observed effect of communication is due to the extra time in the communication treatments. Figure 13 illustrates the average choices for each of the substitutability treatments, including extra sessions where subjects were given the same amount of time as in the communication treatments but were not able to communicate. As shown in the figure, the choices are very close to the case without extra time and much lower than the treatment with communication. Table 6 details the average choices for each treatment.
Average choices within each substitutability treatment, including extra sessions with extra time without communication
B Choices in treatments without communication
In the graphs below, pair IDs are printed on top of each plot next to the description (non-JPM, early JPM, or eventual JPM according to the definitions in Sect. 4.3.1). The plots are confined to the strategy space, i.e., the interval [0, 28]. The Nash equilibrium is 14 and the JPM is 25.5 (dotted line) for both strategic environments. The optimal defection choice is 18 for complementarity and 10 for substitutability (see Figs. 14, 15 ).
Complementarity without communication
Substitutability without communication
C Choices in treatments with communication
Complementarity with communication
Substitutability with communication
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hanaki, N., Ozkes, A.I. Strategic environment effect and communication. Exp Econ 26, 588–621 (2023). https://doi.org/10.1007/s10683-022-09774-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10683-022-09774-7
Keywords
- Communication
- Cooperation
- Reinforcement learning
- Strategic environment
- Structural topic modeling
- Text mining