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One‐sided bargaining over a finite set of alternatives
Author(s) -
Groseclose Tim
Publication year - 2021
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/jpet.12521
Subject(s) - corollary , outcome (game theory) , nomination , supreme court , order (exchange) , economics , set (abstract data type) , microeconomics , selection (genetic algorithm) , subgame perfect equilibrium , mathematical economics , politics , law and economics , nash equilibrium , law , political science , computer science , mathematics , finance , programming language , artificial intelligence , pure mathematics
I consider a bargaining game in which only one player can make proposals and the space of proposals is finite. Thus, the game is like a situation where: (i) a CEO suggests a possible hire, who must be okayed by a board of directors, or (ii) the US president nominates a potential judge, who must be okayed by the Senate. My main result is an algorithm that finds the unique subgame‐perfect equilibrium. The number of steps in the algorithm is on the order of n , the number of possibilities (e.g., applicants to a job) that the bargainers may consider. By contrast, if one uses backwards induction to solve the game, then the number of steps is on the order of n ! . A corollary of the main result, similar to some results of previous bargaining models, is that the wait costs of only one player, the non‐proposer, is relevant to the outcome. The wait costs of the proposer are irrelevant, provided that they are positive. Applied to the nomination process specified by the US Constitution, the corollary suggests that only the Senate's wait costs are relevant to the outcome—the president's wait costs are irrelevant. As I argue, this result may explain a little‐noticed regularity of American politics. This is that the Senate seems to have much influence in the selection of lower‐court judges but relatively little influence in the selection of Supreme Court justices.