Abstract
The emergence of economic inequality has often been linked to individual differences in mental or physical capacities. By means of an agent-based simulation this paper shows that neither of these is a necessary condition. Rather, inequality can arise from iterated interactions of fully rational agents. This bears consequences for our understanding of both inequality and rationality. In a setting of iterated bargaining games, we claim that expected utility maximizing agents perform suboptimally in comparison with other strategies. The reason for this lies in complex feedback effects between an agents’ action and the quality of beliefs used to calculate expected utility. Consequentially, we argue that the standard notion of rationality as maximizing expected utility is insufficient, even for certain standard cases of economic interaction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
While poverty is a property that can be ascribed to one person, inequality is relational in nature. By inequality we refer to a concept that captures one’s relative position compared to a group of relevant others (Haughton and Khandker 2009).
In general, economic interaction consists of first-level economic problems addressing the coordination problems surrounding the production of goods (i.e., positive-sum games) and bargaining games as zero-sum games representing the second-level economic problems of allocating a surplus generated.
Hence, we allow for egalitarian solutions. However, in light of the competitive environment, these are not reached through egalitarian offers, but they arise if both partners have a similar bargaining strength.
Within each run, the number of interaction rounds is constant. Between different runs, we varied the values of this parameter systematically between 10 and 20.
Skyrms (2014) emphasizes the existence of a fair solution as a special focal point. However, in most economic interactions, no saliently egalitarian distribution exists. When an employer bargains about wages with an employee, the different possible agreements might benefit either the employer or the employee more. No possible wage offer could be regarded as obviously egalitarian in any way. Notably, we do not preclude that some distribution actually divides the achieved surplus fairly. We merely claim that this property is by no means transparent enough for both parties involved to qualify as a focal point. We hold that this is a common feature of many bargaining situations, from wage negotiations to partners with complimentary skills setting up a joint endeavor. While a numerical representation of pay-offs in the chicken game seems to suggest that there is an egalitarian solution, this might often be an artifact of the modeling.
This rule is conceptually related to Erev and Roth (1998) type reinforcement learning. Also in this framework, past information is temporally discounted in order to facilitate learning about a changing target system. Unlike in our model, in most approaches to reinforcement learning (Bush and Mosteller 1953; Skyrms 2014) agents do not form beliefs about their environments or the behavior of an opponent, but simply learn which actions have proven more or less successful. For the present model, however, agents form and update beliefs about the toughness of others. This has two reasons. First, our agents assess the toughness distributions of an entire set of opponents. Different opponents will employ different strategies, hence even bounded agents will likely conceptualize and keep track of behavioral differences mirrored by the distribution. Second, the relationship between the agent’s probability distribution and her optimal toughness is intricate. Even small variations in the distribution may trigger major differences in optimal toughness. Hence, we hold that forming beliefs about the toughness of others increases the agent’s potential to select for optimal action.
To check robustness, we ran various simulations with other distributions of the agent types and for different numbers of bargaining rounds. We also varied the overall length of a simulation run up to 100,000 steps and studied control runs, where we initiated wealth measurements only after 1000 steps, so that agents had time to calibrate their behavior. For a broad variety of input parameters the results are similar to those reported here. Most notably, the performance of Maximax agents varies. Depending on agent distribution and the number of bargaining rounds per game, Maximax agents may perform very well or fall behind Experimenter and MaxEU. Our main finding, however, holds for a large class of parameter values: Experimenter agents always outperform MaxEU types and, in many settings, also Maximax types.
We have also considered different proxies for assessing the content of agents’ beliefs, such as mean or median. These have turned out largely uninformative.
A further candidate explanation for MaxEU’s lack of performance is that the chosen uniform initial beliefs are far off. To rule out this interpretation, we ran an extended simulation run over 2000 interaction rounds and measured the wealth accumulated only in the last 1000 rounds. This setup allowed MaxEU agents to adjust their beliefs well before pay-off collection began. The observed wealth distribution was similar to the one depicted in Fig. 2, ruling out this explanation.
Between-type performance differences in comparison to the first experiment stem from the altered agent constellation, which slightly favors some types more than others relative to the prior experiment.
This framework is in line with a modest evolutionary mechanism. The new agent is an exact copy of the old with all her variables, including her wealth. The newcomer is not to represent a newly arriving, vulnerable agent, but should be seen as a further representative of the original society. Compared with most accounts in the literature on epistemic game theory (Easley and Kleinberg 2010, chapter 7), the evolutionary mechanism described here is still rather mild. It is not the absolute economic success of different strategies that determines their evolutionary success, but merely whether or not they generate sufficient funds for survival.
For example, on the internal side, probabilities need to sum to one, impossible events need to receive a probability of zero and so on (Ramsey 1931). On the external side, the agents beliefs have to respond to the available evidence in the right way.
This means, for example, that the order of preferences has to be transitive, complete and connected (Davidson et al. 1955).
References
Atkinson, A. B., & Bourguignon, F. (2014). Handbook of income distribution (Vol. 2a–2b). New York: Elsevier.
Banerjee, A. V., & Newman, A. F. (1991). Risk-bearing and the theory of income distribution. The Review of Economic Studies, 58(2), 211–235.
Becker, G. S. (2013). The economic approach to human behavior. Chicago: University of Chicago press.
Blume, L. E., & Easley, D. (2008). Rationality. In S. N. Durlauf & L. E. Blume (Eds.), The New Palgrave Dictionary of Economics. Basingstoke: Palgrave Macmillan.
Briggs, R. (2017). Normative theories of rational choice: Expected utility. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford: Metaphysics Research Lab, Stanford University.
Bush, R. R., & Mosteller, F. (1953). A stochastic model with applications to learning. The Annals of Mathematical Statistics, 24(4), 559–585.
Carvalho, L. S., Meier, S., & Wang, S. W. (2016). Poverty and economic decision-making: Evidence from changes in financial resources at payday. The American Economic Review, 106(2), 260–284.
Dabla-Norris, M. E., Kochhar, M. K., Suphaphiphat, M. N., Ricka, M. F., & Tsounta, E. (2015). Causes and consequences of income inequality: A global perspective. IMF Staff Disscussion Note SDN/15/13.
Davidson, D., McKinsey, J. C. C., & Suppes, P. (1955). Outlines of a formal theory of value, I. Philosophy of Science, 22(2), 140–160.
Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. New York: Cambridge University Press.
Elster, J. (1988). The nature and scope of rational-choice explanation. In E. Ullmann-Margalit (Ed.), Science in reflection: The Israel Colloquium: Studies in history, philosophy, and sociology of science (Vol. 3, pp. 51–65). Dordrecht: Springer.
Erev, I., & Roth, A. E. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. The American Economic Review, 88(4), 848–881.
Ferejohn, J. (1991). Rationality and interpretation: Parliamentary elections in early stuart england. In K. R. Monroe (Ed.), The economic approach to politics: A critical reassessment of the theory of rational action (pp. 279–305). New York: Harper Collins.
Galeazzi, P., & Franke, M. (2017). Smart representations: Rationality and evolution in a richer environment. Philosophy of Science, 84(3), 544–573.
Gigerenzer, G., & Gaissmaier, W. (2011). Heuristic decision making. Annual Review of Psychology, 62, 451–482.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Boston: Addison-Wesley Professional.
Gottschalk, P., & Smeeding, T. M. (2000). Empirical evidence on income inequality in industrialized countries. In A. Atkinson & F. Bourgignon (Eds.), Handbook of Income Distribution (Vol. 1, pp. 261–307). New York: Elsevier.
Grable, J. E. (2000). Financial risk tolerance and additional factors that affect risk taking in everyday money matters. Journal of Business and Psychology, 14(4), 625–630.
Green, D., & Shapiro, I. (1994). Pathologies of rational choice theory: A critique of applications in political science. New Haven, London: Yale University Press.
Grüne-Yanoff, T. (2012). Paradoxes of rational choice theory. In S. Roeser, R. Hillerbrand, P. Sandin, & M. Peterson (Eds.), Handbook of risk theory: Epistemology, decision theory, ethics, and social implications of risk (pp. 499–516). Dordrecht: Springer.
Halek, M., & Eisenhauer, J. G. (2001). Demography of risk aversion. The Journal of Risk and Insurance, 68(1), 1–24.
Hart, O., & Moore, J. (1999). Foundations of incomplete contracts. The Review of Economic Studies, 66(1), 115–138.
Haughton, J., & Khandker, S. R. (2009). Handbook on poverty and inequality. Washington, DC: World Bank Publications.
Holland, J. H. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Cambridge, MA: MIT press.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47(2), 263–291.
Kanbur, S. M. (1979). Of risk taking and the personal distribution of income. Journal of Political Economy, 87(4), 769–797.
Kolodny, O., & Stern, C. (2017). Evolution of risk preference is determined by reproduction dynamics, life history, and population size. Scientific Reports, 7(1), 9364.
Lipman, B. L. (1986). Cooperation among egoists in prisoners’ dilemma and chicken games. Public Choice, 51(3), 315–331.
McLeod, J., Lawler, E., & Schwalbe, M. (2014). Handbook of the social psychology of inequality. Dordrecht: Springer.
Mishra, S., Hing, L. S. S., & Lalumière, M. L. (2015). Inequality and risk-taking. Evolutionary Psychology, 13(3), 1–11.
Nash, J. (1953). Two-person cooperative games. Econometrica: Journal of the Econometric Society, 21(1), 128–140.
Neckerman, K. M., & Torche, F. (2007). Inequality: Causes and consequences. Annual Review of Sociology, 33, 335–357.
Ramsey, F. P. (1931). Truth and probability (1926). In R. Braithwaite (Ed.), The foundations of mathematics and other logical essays (pp. 156–198). New York, London: Kegan, Paul, Trench, Trubner & Co., Harcourt, Brace and Company.
Rehm, P. (2011). Risk inequality and the polarized american electorate. British Journal of Political Science, 41(2), 363–387.
Riker, W. H. (1995). The political psychology of rational choice theory. Political Psychology, 16(1), 23–44.
Riley, W. B., & Chow, K. V. (1992). Asset allocation and individual risk aversion. Financial Analysts Journal, 48(6), 32–37.
Salverda, W., Nolan, B., & Smeeding, T. M. (2009). The Oxford handbook of economic inequality. Oxford: Oxford University Press.
Scott, J. (1999). Rational choice theory. In Understanding Contemporary (Ed.), Society: Theories of the Present (pp. 126–138). London: SAGE Publications Ltd.
Sen, A. (2008). Rational behaviour. In S. N. Durlauf & L. E. Blume (Eds.), The New Palgrave dictionary of economics. Basingstoke: Palgrave Macmillan.
Sheehy-Skeffington, J. & Rea, J. (2017). How poverty affects people’s decision-making processes. Joseph Rowntree Foundation. https://www.jrf.org.uk/report/how-poverty-affects-peoples-decision-making-processes. Accessed 31st January 2018.
Skyrms, B. (2014). Evolution of the social contract (2nd ed.). Cambridge: Cambridge University Press.
Spohn, W. (2002). The many facets of the theory of rationality. Croatian Journal of Philosophy, 2(6), 249–264.
Weisberg, M., & Muldoon, R. (2009). Epistemic landscapes and the division of cognitive labor. Philosophy of Science, 76(2), 225–252.
Wood, A. (1995). North-South trade, employment, and inequality: Changing fortunes in a skill-driven world. Oxford: Oxford University Press.
Yee, A. S. (1997). Thick rationality and the missing “brute fact”: The limits of rationalist incorporations of norms and ideas. The Journal of Politics, 59(4), 1001–1039.
Zollman, K. J. (2010). The epistemic benefit of transient diversity. Erkenntnis, 72, 17.
Acknowledgements
We would like to thank Paolo Galeazzi, Frederik Van De Putte, two anonymous reviewers and audiences in Poznan, Oslo, Gent and Paris for valuable feedback and suggestions. The work of DK and JM on this project was partially supported by the Deutsche Forschungsgemeinschaft (DFG) and Agence Nationale de la Recherche (ANR) as part of the joint project Collective Attitude Formation [RO 4548/8-1]. The work of DK was partially supported by the Deutsche Forschungsgemeinschaft (DFG) and Grantov Agentura České Republiky (GAČR) as part of the joint project From Shared Evidence to Group Attitudes [RO 4548/6-1]. The work of SS was supported by the DFG through the Bamberg Graduate School of Social Sciences (BAGSS) and by the Humboldt-Foundation through the Munich Center for Mathematical Philosophy (MCMP).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klein, D., Marx, J. & Scheller, S. Rationality in context. Synthese 197, 209–232 (2020). https://doi.org/10.1007/s11229-018-1773-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-018-1773-0