Evolutionary dynamics and equitable core selection in assignment games

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.JEL classifications: C71, C73, C78, D83

A one-shot deviation principle for stability in matching problems

“…Another related literature is the literature on convergence to the core in cooperative games with transferable utility (Agastya, 1997;Feldman, 1974;Green, 1974;Newton, 2012). A branch of this literature has recently explicitly focused on the case in which all relevant coalitions are pairs -the transferable utility equivalent of the marriage problem, otherwise known as the assignment problem (Biró, Bomhoff, Golovach, Kern and Paulusma, 2012;Chen, Fujishige and Yang, 2012;Nax and Pradelski, 2013;Shapley and Shubik, 1971). Of particular note is the work of Nax and Pradelski (2013), who adapt the results of the current paper to obtain selection within the core of the assignment game.…”

Equity dynamics in bargaining without information exchange

“…Instead, directionality is born from the fact that players have a tendency to demand more (less) when currently receiving a payoff that matches or exceeds (falls short of) their aspirations. A similar approach has recently been taken by Nax et al (2013), Nax and Perc (2015), Nax and Pradelski (2015), and Burton-Chellew et al (2015).…”

On a spontaneous decentralized market process

“…Chen et al (2016) examined a random decentralized process for the assignment market, as a counterpart of the deterministic processes proposed by Crawford & Knoer (1981) and Demange et al (1986). Nax & Pradelski (2015) discussed a similar issue from the viewpoint of evolutionary dynamics. Ma & Li (2016) studied a decentralized probabilistic double auction process for a financial market.…”