# Evolutionary dynamics and equitable core selection in assignment games

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## Abstract

We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents’ strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics because it is more stable, not because of any ex ante fairness criterion.

### Keywords

Assignment games Cooperative games Core Equity Evolutionary game theory Learning Matching markets Stochastic stability### JEL Classification

C71 C73 C78 D83## Notes

### Acknowledgments

Foremost, we thank Peyton Young for his guidance. He worked with us throughout large parts of this project and provided invaluable guidance. Further, we thank Itai Arieli, Peter Biró, Gabrielle Demange, Sergiu Hart, Gabriel Kreindler, Jonathan Newton, Tom Norman, Tamás Solymosi, Zaifu Yang and anonymous referees for suggesting a number of improvements to earlier versions. We are also grateful for comments by participants at the 23rd International Conference on Game Theory at Stony Brook, the Paris Game Theory Seminar, the AFOSR MUIR 2013 meeting at MIT, the 18th CTN Workshop at the University of Warwick, the Economics Department theory group at the University of York, the Theory Workshop at the Center for the Study of Rationality at the Hebrew University, and the Game Theory Seminar at the Technion. The research was supported by the United States Air Force Office of Scientific Research Grant FA9550-09-1-0538 and the Office of Naval Research Grant N00014-09-1-0751. This paper supersedes the working paper “The evolution of core stability in decentralized matching markets”. Theorem 1 was reported without proof in the conference proceeding (Nax et al. 2013). Heinrich H. Nax acknowledges support by the European Commission through the ERC Advanced Investigator Grant ‘Momentum’ (Grant No. 324247). Bary S. R. Pradelski acknowledges support of the Oxford-Man Institute of Quantitative Finance.

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