The Roemer model of political competition is a game between political parties in which each party announces a multidimensional policy vector. Since

Nash equilibria In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...

do not normally exist when the policy space is multidimensional,

John Roemer John E. Roemer (; born February 1, 1945 in Washington, D.C., to Ruth Roemer and Milton Roemer, namesake of Roemer's law) is an American economist and political scientist. He is the Elizabeth S. and A. Varick Stout Professor of Political Scienc ...

introduced the concept of party-unanimity Nash equilibrium (PUNE), which can be considered a generalization of the concept of Nash equilibrium in models of political competition. It is also a generalization of the

Wittman model Wittman is a surname. Notable people with the surname include: *Baldy Wittman (born c. 1871), professional football player for the Massillon Tigers * Brian Wittman, American musical instrument maker, inventor of the xaphoon *Carl Wittman (1943–19 ...

of political competition. In Roemer's model, all political parties are assumed to consist of three types of factions—

opportunists Opportunism is the practice of taking advantage of circumstances – with little regard for principles or with what the consequences are for others. Opportunist actions are expedient actions guided primarily by self-interested motives. The term ...

militants The English word ''militant'' is both an adjective and a noun, and it is generally used to mean vigorously active, combative and/or aggressive, especially in support of a cause, as in "militant reformers". It comes from the 15th century Latin ...

, and

reformers A reformer is someone who works for reform. Reformer may also refer to: *Catalytic reformer, in an oil refinery *Methane reformer, producing hydrogen * Steam reformer *Hydrogen reformer, extracting hydrogen *Methanol reformer, producing hydrogen f ...

. Opportunists seek solely to maximize the party's vote share in an election; militants seek to announce (and implement) the preferred policy of the average party member; and reformers have an objective function that is a

convex combination In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1. In other word ...

of the objective functions of the opportunists and militants. It has been shown that the existence of reformers has no effect on what policies the party announces. With two parties, a pair of policy announcements constitute a PUNE if and only if the reformers and militants of any given party do not unanimously agree to deviate from their announced policy, given the policy put forth by the other party. In other words, if a pair of policies constitute a PUNE, then it should not be the case that ''both'' factions of a party can be made weakly better off (and one faction strictly better off) by deviating from the policy that they put forward. Such unanimity to deviate can be rare, and thus PUNEs are more likely to exist than regular Nash equilibria. Although there are no known cases where PUNEs do not exist, no simple necessary and sufficient conditions for the existence of non-trivial PUNEs have yet been offered. (A nontrivial PUNE is one in which no party offers the ideal policy of either its militants or opportunists.) The question of the existence of non-trivial PUNEs remains an important open question in the theory of political competition.

References

* John E. Roemer, ''Political Competition: Theory and Applications'' (2001) Cambridge, MA: Harvard University Press. {{DEFAULTSORT:Roemer Model Of Political Competition Political theories Game theory