Abstract
In this paper we use an experimental approach to investigate how linguistic conventions can emerge in a society without explicit agreement. As a starting point we consider the signaling game introduced by Lewis (Convention 1969). We find that in experimental settings, small groups can quickly develop conventions of signal meaning in these games. We also investigate versions of the game where the theoretical literature indicates that meaning will be less likely to arise—when there are more than two states for actors to transfer meaning about and when some states are more likely than others. In these cases, we find that actors are less likely to arrive at strategies where signals have clear conventional meaning. We conclude with a proposal for extending the use of the methodology of experimental economics in experimental philosophy.
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Notes
There exists a significant experimental literature on conflict of interest signaling games. Lewis signaling games are common interest and have been investigated less thoroughly.
Many variations exist on the signaling game. We do not, for example, consider games where the interests of the actors conflict, or where approximately correct guesses of the state of nature are rewarded.
Reinforcement learning is one type of learning model commonly used in evolutionary game theory.
Instructions are available upon request.
We completed only four unbiased \(2 \times 2\) runs because this experimental set-up had already been considered by Blume et al. (1998).
It might be argued that players could still use keyboard ordering to assist coordination. By checking individual trials, we verified that different groups associated different signals with states, indicating that these associations were not formed using keyboard ordering.
Using individual behavior from the last round of our four unbiased sessions as independent observations, we also employ a one-sided t test to reject the null hypothesis of independence (that states are independent of signals sent and signals are independent of actions taken) with p \(<< .01\).
We once again employ a one-sided t test with a null hypothesis that a sender and receiver successfully coordinate 70 % of the time. This is the highest possible success rate if no information is tranferred. Using data taken from the last round of play in our eight .7 bias runs, we reject the null hypothesis (p value\(<<\)0.01).
We conducted a one-sided t test and in these four runs, we cannot reject the null hypothesis that sender-receiver pairs are successful 90 % of the time. This may seem like an odd null hypothesis because in the unbiased and .7 bias cases, 90 % coordination levels counted as signaling systems. Inspection of the strategies of the actors in these cases (see Fig. 5) though, makes clear that these populations truly did not reach separating strategies.
Because this case was unusual, we looked at data from the last 25 rounds of play as well. In this larger sample, the senders sent \(m_1\) in \(s_2\) with higher probability (.66 %). This partial separation on the part of the senders may help explain why non-equilibrium separating was seen by the receivers.
One caveat should be noted which is that in the biased cases actors encountered the unlikely state of the world less often than in the unbiased cases. This may mean that they simply has less time to learn a signaling system.
The number of strategies goes from four to twenty seven when we move from the \(2 \times 2\) game to the \(3 \times 3\) game.
A one-sided t test confirms this. As in the unbiased \(2 \times 2\) case, we once again reject the null hypothesis of independence (with a p value\(<<\) 0.01).
Huttegger et al. (2010) found convergence to partial pooling equilibria to be rare (4.7 % of initial populations) in unbiased \(3 \times 3\) signaling games under the discrete time replicator dynamics.
Barrett (2006) found that under Herrnstein reinforcement learning \(8 \times 8\) Lewis signaling games converged to partial pooling equilibria with greater frequency than \(4 \times 4\) games, which in turn converged to these more often than \(3 \times 3\) games.
Herrnstein reinforcement learning dynamics were used for this model. For a more detailed description of this dynamics see Skyrms (2010). Blume et al. (2002) find that Herrnstein reinforcement learning provides a good approximation of human learning in signaling games. The model otherwise conformed to the features of the experimental setup, i.e., there were 12 agents, etc.
In 200 runs of simulation, we found that actors playing the unbiased \(2 \times 2\) game reached a success rate of .95 (as defined by expected payoff given learned strategy divided by highest possible expected payoff) in 6,789 rounds on average. Actors in a \(3 \times 3\) game, on the other hand, took 43,993 rounds to reach this success rate.
Perhaps surprisingly, in these simulations, actors in biased \(2 \times 2\) games had even more difficulty reaching separating strategies than those in the \(3 \times 3\) game. This is contrary to our experimental results. One potential explanation for this discrepancy may be that as our subjects are language users they are predisposed to use signaling strategies. In the \(2 \times 2\) biased cases they were able to do so because the number of available strategies was still quite small. In the \(3 \times 3\) cases, they were stymied by the greater number of strategies.
There is an existing literature on information transfer with costly signals in experimental economics. The proposed work would explore signaling when signal costs are less than the amount needed to sustain full information transfer.
References
Alexander, J. (2010). Local interactions and dynamics of rational deliberation. Philosophical Studies, 147(1), 103–121.
Allais, P. M. (1953). Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americane. Econometrica, 21, 503–546.
Argiento, A., Pemantle, R., Skyrms, B., & Volkov, S. (2009). Learning to signal: Analysis of a micro-level reinforcement model. Stochastic Processes and their Applications, 119, 373–390.
Barrett, J. A. (2006). Numerical simulations of the Lewis signaling game: Learning strategies, pooling equilibria, and the evolution of grammar. Institute for Mathematical Behavioral Sciences. Paper 54. http://repositories.cdlib.org/imbs/54.
Bicchieri, C., & Chavez, A. (2013). Norm manipulation, norm evasion: Experimental evidence. Economics and Philosophy, 29(2), 175–198.
Bicchieri, C., & Lev-On, A. (2007). Computer-mediated communication and cooperation in social dilemmas: An experimental analysis. Politics, Philosophy, and Economics, 6(2), 139–168.
Binmore, K., McCarthy, J., Ponti, G., Samuelson, L., & Shaked, A. (2002). A backward induction experiment. Journal of Economic Theory, 104, 48–88.
Blume, A., DeJong, D. V., Kim, Y. G., & Sprinkle, G. B. (1998). Experimental evidence on the evolution of meaning of messages in sender-receiver games. The American Economic Review, 88(5), 1323–1340.
Blume, A., DeJong, D. V., Kim, Y. G., & Sprinkle, G. B. (2001). Evolution and communication with partial common interest. Games and Economic Behavior, 37(1), 79–120.
Blume, A., DeJong, D. V., Neumann, G. R., & Savin, N. E. (2002). Learning and communication in sender-receiver games: An econometric investigation. Journal of Applied Economics, 17, 225–247.
Börgers, T., & Sarin, R. (1997). Learning through reinforcement and replicator dynamics. Journal of Economic Theory, 77, 1–14.
Charness, G., & Rabin, M. (2002). Understanding social preferences with simple tests. The Quarterly Journal of Economics, 117(3), 817–869.
Croson, R. (2005). The method of experimental economics. International Negotiation, 10, 131–148.
Davis, D., & Holt, C. A. (1993). Experimental economics: Methods, problems and promise. Estudios Económicos, 8(2), 179–212.
Ernst, Z. (2007). Philosophical issues arising from experimental economics. Philosophy Compass, 2(3), 497–507.
Fehr, E., & Gächter, S. (2000). Cooperation and punishment in public goods experiments. The American Economic Review, 90(4), 980–994.
Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economics experiments. Experimental Economics, 10(2), 171–178.
Frolich, N., & Oppenheimer, J. (1992). Choosing justice: An experimental approach to ethical theory. Berkeley: California University Press.
Guth, W., Schmittberger, R., & Schwarze, B. (1982). An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization, 3, 367–388.
Hofbauer, J., & Huttegger, S. (2008). Feasibility of communication in binary signaling games. Journal of Theoretical Biology, 254, 843–849.
Holt, C., & Laury, S. (2002). Risk aversion and incentive effects. The American Economic Review, 92(5), 1644–1655.
Hopkins, E. (2002). Two competing models of how people learn in games. Econometrica, 70(6), 2141–2166.
Huttegger, S. M. (2007). Evolution and the explanation of meaning. Philosophy of Science, 74, 1–27.
Huttegger, S. M., & Zollman, K. (2010). Dynamic stability and basins of attraction in the sir philip sidney game. Proceedings of the Royal Society B, 94, 1–8.
Huttegger, S. M., & Zollman, K. J. S. (2011). Signaling games: Dynamics of evolution and learning. Language, games, and evolution (pp. 160–176). Berlin: Springer.
Huttegger, S. M., Skyrms, B., Smead, R., & Zollman, K. J. S. (2010). Evolutionary dynamics of Lewis signaling games: Signaling systems versus partial pooling. Synthese, 172(1), 177–191.
Huttegger, S. M., Skyrms, B., Tarrès, P., & Wagner, E. O. (2010). Some dynamics of signaling games. Proceedings of the National Academy of Sciences USA, 111, 10873–10880.
Lewis, D. K. (1969). Convention. Cambridge, MA: Harvard University Press.
Mehta, J., Starmer, C., & Sugden, R. (1994). The nature of salience: An experimental investigation of pure coordination games. The American Economic Review, 84(3), 658–673.
Muldoon, R., Borgida, M., & Cuffaro, M. (2011). The conditions of tolerance. Politics, Philosophy, and Economics, 11(3), 322–344.
O’Connor, C. (2013). The evolution of vagueness. Erkenntnis, 79, 704–727.
Pawlowitsch, C. (2008). Why evolution does not always lead to an optimal signaling system. Games and Economic Behavior, 63, 203–226.
Powell, B., & Wilson, B. (2008). An experimental investigation of hobbesian jungles. Journal of Economic Behavior and Organization, 66, 669–686.
Schelling, T. C. (1960). The strategy of conflict. Cambridge, MA: Harvard University Press.
Skyms, B. (2010). The flow of information in signaling games. Philosophical Studies, 147, 155–165.
Skyrms, B. (2010). Signals: Evolution, learning, and information. Oxford: Oxford University Press.
Smith, A. (1761). Considerations concerning the first formation of languages. Appended to the second edition of The theory of moral sentiments.
Smith, A., Skarbek, D., & Wilson, B. (2012). Anarchy, groups, and conflict: an experiment on the emergence of protective associations. Social Choice and Welfare, 39(2), 325–353.
Smith, V. (1962). An experimental study of competitive market behavior. The Journal of Political Economy, 70(2), 111–137.
Smith, V. (1976). Experimental economics: induced value theory. The American Economic Review, 66(2), 274–279.
Vanderschraaf, P. (2006). War on peace? a dynamical analysis of anarchy. Economics and Philosophy, 22(2), 243–279.
Vanderschraaf, P. (2007). Covenants and reputations. Synthese, 157, 167–195.
Wagner, E. O. (2013). The dynamics of costly signaling. Games, 4, 161–183.
Acknowledgments
The authors would like to thank Andreas Blume and Elliott Wagner for comments on the paper. We would like to thank Michael McBride for advice on experimental economics and Sabine Kunrath for help with the statistical analysis of our data. Thanks to helpful audiences at GIRL 2013 and the ESSL workshop at UC Irvine 2012. This material is based upon work supported by the National Science Foundation under Grant No. EF 1038456. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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Bruner, J., O’Connor, C., Rubin, H. et al. David Lewis in the lab: experimental results on the emergence of meaning. Synthese 195, 603–621 (2018). https://doi.org/10.1007/s11229-014-0535-x
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DOI: https://doi.org/10.1007/s11229-014-0535-x