Evolutionary stability of behavioural rules in bargaining

Khan, Abhimanyu (2018): Evolutionary stability of behavioural rules in bargaining.

Abstract

I study the evolutionary stability of behavioural rules in a bargaining game. Individuals draw random samples of strategies used in the past and respond to it by using a behavioural rule. Even though individuals actually respond to historical demands, a necessary condition for stability is the existence of a state such that it is as-if the individuals are hardwired to make the same demand. Furthermore, the state where all individuals demand half of the pie is the unique neutrally stable state; all other states are unstable in the face of an invasion by a mutant behavioural rule.

• Item Type: MPRA Paper
• Language: English
• Keywords: bargaining; evolution; stable behavioural rules; internal stability; external stability; equal split
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory

References

Binmore K, Samuelson L and Young HP (2003). Equilibrium Selection in Bargaining Models. Games and Economic Behaviour 45 (2): 296-328

Ellingsen T (1997). The Evolution of Bargaining Behaviour. Quarterly Journal of Economics 112 (2): 581-602

Kalai E and Smorodinsky M (1975). Other Solutions to Nash’s Bargaining Problem. Econometrica 43 (3): 513–518

Josephson J (2009). Stochastic adaptation in finite games played by heterogeneous populations. Journal of Economic Dynamics and Control 33 (8): 1543-1554

Juang WT (2002). Rule Evolution and Equilibrium Selection. Games and Economic Behaviour 39 (1): 71-90

Kaniovski YM, Kryazhimskii AV and Young HP (2000). Adaptive Dynamics in Games Played by Heterogeneous Populations. Games and Economic Behaviour 31 (1): 50-96

Khan A and Peeters R (2014). Cognitive hierarchies in adaptive play. International Journal of Game Theory 43 (4): 903-924

Khan A (2018). Games Between Responsive Behavioural Rules. https://ssrn.com/abstract=3235254

Nash, J (1950). The Bargaining Problem. Econometrica 18 (2): 155-162

Oyama D, Sandholm WH and Tercieux O (2015). Sampling Best Response Dynamics and Deterministic Equilibrium Selection. Theoretical Economics 10 (1): 243-281

Rubinstein A (1982). Perfect Equilibrium in a Bargaining Model. Econometrica 50 (1): 97-109

Saez-Marti M and Weibull J (1998). Clever Agents in Young's Evolutionary Bargaining Model. Journal of Economic Theory 86 (2): 268-279

Schaffer ME (1988). Evolutionary Stable Strategies for a Finite Population and a Variable Size Contest. Journal of Theoretical Biology 132 (4): 469-478

Skyrms B (1994). Sex and Justice. The Journal of Philosophy 91 (6): 305-320

Smith JM and Price GR (1973). The Logic of Animal Conflict. Nature 246: 15-18

Young HP (1993). An Evolutionary model of bargaining. Journal of Economic Theory 59 (1): 145-168