Stable Matching, Friendship, and Altruism

11^th November 2014, 13:00 Ashton Lecture Theater
Prof Elliot Anshelevich
Computer Science Department
Rensselaer Polytechnic Institute
USA

Abstract

We will discuss both integral and fractional versions of "correlated stable matching" problems. Each player is a node in a social network and strives to form a good match with a neighboring player; the player utilities from forming a match are correlated. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. We especially focus on networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions.

When the benefits from a match are the same for both players, we show that incorporating the well-being of other players into their matching decisions significantly improves the quality of stable solutions. Furthermore, a good stable matching always exists and can be reached in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different utilities from the match. For this more general case, we show that incorporating social context (i.e., "caring about your friends") can make an even larger difference, and greatly reduce the price of anarchy. Finally, we extend most of our results to network contribution games, in which players can decide how much effort to contribute to each incident edge, instead of simply choosing a single node to match with.