Conventional contracts, intentional behavior and logit choice: Equality without symmetry
GAICIL Insights
How a society splits the pie may depend on how its members make mistakes.1 Conventional contracts, intentional behavior and logit choice: Equality without symmetry, by Sung-Ha Hwang, Wooyoung Lim, Philip Neary and Jonathan Newton, asks which bargaining solution emerges as a long-run social norm, governing the division of gains in countless interactions from wage negotiations to business partnerships. The answer turns on the texture of deviations from optimal behavior.
When coordination games are played under the logit choice rule and agents' non-best response behavior displays intentional bias, the Egalitarian bargaining solution emerges as the long-run social norm. Without intentional bias, a new solution, the Logit bargaining solution, emerges. These results contrast with earlier findings under non-payoff dependent deviations, where the Kalai-Smorodinsky and Nash bargaining solutions emerge. Experiments on human subjects suggest non-best response play is payoff dependent and displays intentional bias, pointing to the Egalitarian solution as the most likely long-run norm. Equality arrives without anyone imposing symmetry.
The authors frame the contribution boldly. Their theory of bargaining solutions as social norms rests on behavior, setting aside the properties of the solutions themselves. Societal interactions take individual behavior as input and produce a social norm as output. In this sense, traditional normative approaches to social choice can be seen as specifying behavioral rules for society itself, a reconciliation of micro and macro behavioral theories. Ethics, on this reading, is downstream of error patterns.
A striking calculation follows. When errors are intentional, the easiest path from one convention to another usually requires 6 or more errors in one of the populations. At error rates of 10%, roughly the frequency observed in the study, 6 or more errors occur in a period with a probability of less than 1/6000. Statements about long-run norms from aggregate data alone would require sessions lasting far more than 6000 periods. Individual-level behavioral evidence is the practical route to prediction. Watching the crowd tells little; watching the individual tells a lot.
Here artificial intelligence enters the bargaining room. AI agents increasingly negotiate on behalf of firms and individuals, in procurement, advertising auctions and customer service. Their deviations from optimal behavior are set by their design. If AI agents deviate in ways that differ from human intentional bias, long-run bargaining norms in AI-populated markets may differ from those among humans. A drift from Egalitarian outcomes toward other solutions could change how surplus is divided, without any regulator, court or negotiator deciding it.
That hands designers of AI negotiators an unexpected role: authors of social norms. How agents explore alternatives and respond to payoffs feeds into the process that determines long-run conventions. Agents whose behavior supports norms considered fair by the people they represent may sustain trust in AI-mediated markets. The exploration settings of a negotiation bot carry distributive weight.
The methodological lesson travels well. Long-run norms are hard to infer from aggregate data over short periods, because transitions between conventions are rare. Understanding the behavioral rules of individual agents, human or artificial, provides a better basis for prediction. For AI, testing and documenting the decision rules of negotiating agents can help anticipate their aggregate effects before markets reveal them the slow way.
The authors raise a further question: what of decision making by small groups that exhibit collective agency and adjust behavior collaboratively? It applies to AI as well, since coordinated groups of agents, or firms using similar AI tools, may behave as collective actors in markets.
Taken together, social norms emerge from the details of individual behavior. Intentional, payoff-dependent deviations from best response produce egalitarian norms in bargaining. As AI agents join human participants, their behavioral rules will influence which norms prevail. Theory and experiments of this kind supply the tools to anticipate that influence and to design AI systems that support fair and stable conventions.
One last test: the fairness of tomorrow's markets may be settled in the error-handling code of negotiating agents, long before anyone thinks to debate it.
Introduction
When coordination games are played under the logit choice rule and there is intentional bias in agents’ non-best response behavior, the Egalitarian bargaining solution emerges as the long run social norm. Without intentional bias, a new solution, the Logit bargaining solution emerges as the long run norm. These results contrast with results under non-payoff dependent deviations from best response behavior, where it has previously been shown that the Kalai-Smorodinsky and Nash bargaining solutions emerge as long run norms. Experiments on human subjects suggest that non-best response play is payoff dependent and displays intentional bias. This suggests the Egalitarian solution as the most likely candidate for a long run bargaining norm.
Takeaway
“What has been presented here is a theory of the emergence of bargaining solutions as social norms that rests on behavior and not on the properties of the solutions themselves. Societal interactions take individual behavior as an input and give a social norm, or to put it another way, a social choice, as output. Thus, if we think of a society as similar to an organism with agency, we can regard the traditional, normative approaches to social choice as specifying behavioral rules for society itself, rather than for the individuals within society.1
To see this via a rough calculation, note that when errors are intentional, the easiest path from one convention to another will usually require 6 or more errors in one of the populations. In a period in which all subjects in a given population have the opportunity to update their strategies, at error rates of 10% (the approximate frequency observed in this study), 6 or more errors will occur with a probability of less than 1/6000. Therefore to make a statement about long run norms using aggregate population data alone would require sessions to last for considerably more than 6000 periods.
As such, the results of the current paper and the rest of the Evolutionary Nash Program can be understood as a reconciliation of micro and macro behavioral theories. But what of decision making that does not occur at the individual level, nor at the societal level? What if small groups exhibit collective agency and collaboratively adjust their behavior? In recent years there has been considerable work on collective agency in behavioral rules and its effect on social norms (Newton, 2012b,a; Newton and Angus, 2015; Newton and Sawa, 2015; Angus and Newton, 2015; Sawa, 2014; Nax and Pradelski, 2014; Klaus and Newton, 2016).2,3,4,5,6”
Notes
- Sung-Ha Hwang et al., Conventional contracts, intentional behavior and logit choice: Equality without symmetry, 110 Games & Econ. Behav. 273 (2018), https://doi.org/10.1016/j.geb.2018.05.002. Takeaway source: Sung-Ha Hwang, Wooyoung Lim, Philip Neary, Jonathan Newton, Conventional contracts, intentional behavior and logit choice: Equality without symmetry (author manuscript), Conclusion. ↩
- Newton, J., 2012a. Coalitional stochastic stability. Games and Economic Behavior 75, 842–54. doi:http://dx.doi.org/10.1016/j.geb.2012.02.014.. ↩
- Angus, S.D., Newton, J., 2015. Emergence of shared intentionality is coupled to the advance of cumulative culture. PLoS Comput Biol 11, e1004587. doi:10.1371/journal.pcbi. 1004587.. ↩
- Sawa, R., 2014. Coalitional stochastic stability in games, networks and markets. Games and Economic Behavior 88, 90–111.. ↩
- Nax, H.H., Pradelski, B.S.R., 2014. Evolutionary dynamics and equitable core selection in assignment games. International Journal of Game Theory 44, 903–932. doi:10.1007/ s00182-014-0459-1.. ↩
- Klaus, B., Newton, J., 2016. Stochastic stability in assignment problems. Journal of Mathematical Economics 62, 62 – 74. doi:http://dx.doi.org/10.1016/j.jmateco.2015.11. 002.. ↩
Cite as: Sung-Ha Hwang et al., Conventional contracts, intentional behavior and logit choice: Equality without symmetry, 110 Games & Econ. Behav. 273 (2018), https://doi.org/10.1016/j.geb.2018.05.002
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