Making it Safe to Use Centralized Markets: Epsilon - Dominant Individual Rationality and Applications to Market Design

A critical, yet underappreciated feature of market design is that centralized markets operate within a broader economic context; often market designers cannot force participants to join a centralized market. As such, well-designed centralized markets must induce participants to join voluntarily, in spite of pre-existing decentralized institutions they may already be using. Utilizing the general framework of Monderer and Tennenholtz (2006), we take the view that centralizing a market is akin to designing a mediator to which people may sign away their decision rights. The mediator is voluntary in the sense that it cannot condition the actions of those who participate on the actions of those who do not. Within this setting we propose a new desideratum for market design: Dominant Individual Rationality (D-IR). A mediator is D-IR if every decentralized strategy is weakly dominated by some centralized strategy. While such a criterion does not offer a prediction about how people will behave within the centralized market, it does provide a strong guarantee that all players will use centralized strategies rather than opting out of the centralized market. We show that suitable modification of the Boston mechanism satisfies D-IR and a similar modification of any stable matching mechanism satisfies an approximation of D-IR. In both cases the modification relies on allowing the receiving end of the market to accept offers in either the centralized or decentralized part of the market. This design closely resembles the suggestion of Niederle and Roth (2006) about centralizing the market for gastroenterologists. Relative to their analysis, ours highlights why this design feature coupled with some, but not all, matching algorithms is effective in inducing participation of the proposing side of the market. Further, by highlighting its role in attaining (approximate) D-IR our analysis provides a new non-cooperative justification for stability. In other applications we demonstrate that, suitably modified, Top Trading Cycles satisfies D-IR, and double auctions satisfy approximate D-IR.