Threat Point Research Articles

Stackelberg leadership and transfers in private provision of public goods

We consider transfers in a Stackelberg game of private provision of a public good. It turns out that the agent who is the follower in the process of making voluntary contributions to a public good may have an incentive to make monetary transfers to the Stackelberg leader even in a situation where neither has a comparative advantage in making contributions to the public good. The Stackelberg leader is willing to accept such transfers if the actual contribution game is fully non-cooperative because the transfer generates a Pareto superior outcome. If the contributions in the Stackelberg equilibrium is the threat point of a possible cooperative Nash bargaining game, the Stackelberg leader will refuse to accept the transfer if she can.

An Economic Analysis of Domestic Violence

While economists have been studying the family as an economic unit for almost thirty years, most models have focused on cooperative family units. Domestic violence, one of the most widespread violent crimes against women, is one example of a family unit that is better explained as a noncooperative re1ationship. In this paper, a noncooperative model of domestic violence is presented. The comparative statics from this model predict that women's incomes and other financial support received from outside the marriage (family, welfare, shelters, divorce settlements, etc.) will decrease the level of violence in intact families because they increase the woman's threat point. Implications of the theoretical model are discussed and empirical evidence is summarized. The results from existing and new analysis provide support for the hypothesis that improved economic opportunities for women will decrease the level of violence in abusive re1ationships.

Voting by veto and the role of the compromise function

This paper analyzes voting by veto procedures in the context of a pure sharing problem. It is shown that the direct intuition about these voting mechanisms fails: the veto power of the players does not by itself make players act in an equitable manner. If the compromise function yields a constant compromise alternative, then it plays the role of a threat point and the behavior of the players in making proposals tends to be selfish. However, if it depends on the individual proposals, and selects a real compromise among them, then egalitarian proposals can be achieved as the unique subgame perfect equilibria with symmetric proposals of the game.

N-PERSON NASH BNARGAINING WITH VARIABEL THREATS

We consider two models of n-person bargaining problems with the endogenous determination of disagreement points. In the first model, which is a direct extension of Nash’s variable threat bargaining model, the disagreement point is determined as an equilibrium threat point. In the second model, the disagreement point is given as a Nash equilibrium of the underlying noncooperative game. These models are formulated as extensive games, and axiomatizations of solutions are given for both models. It is argued that for games with more than two players, the first bargaining model does not preserve some important properties valid for two-person games, e.g., the uniqueness of equilibrium payoff vector. We also show that when the number of players is large, any equilibrium threat point becomes approximately a Nash equilibrium in the underlying noncooperative game, and vice versa. This result suggests that the difference between the two models becomes less significant when the number of players is large. An important constituent of bargaining is the specification of the payoff vector when players fail to achieve an agreement. This payoff vector is called a disagreement point. With the major exception of Nash (1953), a disagreement point is assumed to be exogenously given. I) In some economic examples, exogenous disagreement points such as an endowment point in an exchange economy are naturally determined. In general game situations and in economic situations with externalities, however, we may not find a natural definition of an exogenously given disagreement point. This fact requires us to consider a bargaining model with an endogenous determination of a disagreement point. Nash (1953) gave such a model with two players. The purpose of this paper is to investigate the behaviour of this model with n players. We compare, from both axiomatic and noncooperative game theoretic viewpoints, the n-player extension of Nash’s model with an alternative model where disagreement points are also endogenously determined. Nash’s (1953) model - the first model in this paper - is as follows. An underlying environment is described by a noncooperative strategic game G. The players are allowed to cooperate for obtaining higher payoffs and bargain over possible cooperative payoffs, subject to the possibility of failing to achieve an agreement. If the players fail, they return to the original noncooperative game. For this possibility, each player has to choose a strategy in the case of disagreement, prior to bargaining.

Separate Spheres Bargaining and the Marriage Market

This paper introduces the bargaining model, a new model of distribution within marriage. It differs from divorce threat bargaining models (e.g., Manser-Brown, McElroy-Horney) in that the threat point is not divorce but a noncooperative equilibrium within marriage; this noncooperative equilibrium reflects traditional gender roles. The predictions of our model thus differ from those of divorce threat bargaining models; in the separate spheres model, cash transfer payments to the mother and payments to the father can--but need not--imply different equilibrium distributions in existing marriages. In the long run, the distributional effects of transfer policies may be substantially altered by changes in the marriage market equilibrium.

The Nash bargaining solution manipulated by pre-donations is Talmudic

In a world where the Nash bargaining solution is operant, we consider simple two-person bargaining problems with monetary payoffs and threat point at the origin, and before the bargaining solution is applied we allow the alteration of the bargaining set by means of pre-donations of a share in one's would-be payoffs to one's opponent. Thus, a pre-bargain stage is instituted in which the bargainers may manipulate, via pre-donations, the (Nash) bargaining solution as applied in the next (bargaining) stage. We concentrate on the simple bargaining problems with triangular bargaining set and show that these are always manipulated by the luckier bargainer (with greater ideal payoff) giving a pre-donation, her best pre-donation transforming the bargaining set into one on which the Nash bargaining solution distributes payoffs in accordance with the Talmudic rule of dividing disputed property (as applied to the original simple bargaining problem whose ideal payoffs are interpreted as the bargainers' claims on a common pie of size equal to the greater of the ideal payoffs). The other bargainer always remains passive, responding to any pre-donation from his opponent by only a nil pre-donation in reverse.

The Mismarriage of Bargaining Theory and Distributive Justice

Bargaining theory studies the division of utility between or among agents who, if agreement is not reached, each receive a utility designated by a threat point. For example, if there are two agents, then a bargaining problem is specified by a pair {S, d} where S is usually taken to be a convex, comprehensive' set in the plane (representing possible utility pairs for agents) and d is a point in S specifying the utilities each gets in the absence of agreement. A bargaining mechanism is a function F which assigns to each bargaining problem {S, d} a point s in S, the agreement point under that mechanism:

Asymptotic properties of a non-zero sum stochastic game

An example of a non-zero sum stochastic game is given where: i) the set of Nash Equilibrium Payoffs in the finitely repeated game and in the game with discount factor is reduced to the threat point; ii) the corresponding set for the infinitely repeated game is disjoint from this point and equals the set of feasible, individually rational and Pareto optimal payoffs.

Horizontal mergers and collusive behavior

In the Industrial Organization literature, it is generally felt that mergers hurt consumers; not only because of the increased industrial concentration they effect, but also because collusion becomes more likely. In this paper we show that, at least in one important case, this intuition is misguided. If a tacitly collusive agreement enforced by trigger strategies is not initially sustainable, mergers will tend to reduce the chance that it becomes sustainable in the future. This is so because the threat point implicit in the agreement becomes more favorable for outsiders.

A New Approach to the Nash Bargaining Problem

This paper explores a new approach to the Nash bargaining problem in which the axiom of symmetry is dropped and it is assumed that the final allocation depends on both the status quo and the threat point. The resulting final allocation, unlike that formalized by Nash, cannot be represented by a simple analytic expression; rather, it leads to a whole class of solutions. Properties of the final allocation are analyzed. It is shown that for every initial allocation there exists a Nash fiber, corresponding to the Nash allocation, that it is possible to determine the sign of the derivatives of the final allocation with respect to changes in the threat point, and that a Slutsky-like equation relates these derivatives to the derivatives with respect to the initial allocation. It is also shown that, under certaiia conditions, as play is repeated the final allocation asymptotically converges to the Nash allocation.

A Noncooperative View of Oligopoly

THERE ARE TWO BASIC APPROACHES to the theory of oligopoly which may be called the cooperative and the noncooperative. Typically a cooperative approach will utilize a bargaining model under which the several firms in the oligopoly are supposed to bargain among themselves in order to agree on some joint decision (say, a set of prices to be charged-one per firm) which yields to the industry one of the outcomes which is Pareto optimal for them. A noncooperative approach will, by contrast, involve each firm in isolated decision making. This is not to imply that each firm ignores the effects of its rivals' decisions on its own profit or of its own decisions on its rivals' behavior (and hence its own profits). Noncooperative formulations will generally assume the firms not to make decisions jointly. An equilibrium of a noncooperative nature typically features a set of strategies (say a strategy is a rule for choosing one's price), one for each firm, having the following property: For each firm, its equilibrium strategy gives at least as much profit as any other strategy it might choose, given the strategy choices of its rivals. One possible method of finding a cooperative solution is to define a bargaining process, or a set of axioms which the solution must obey, which turns the process of determining a solution into a noncooperative game. The Nash cooperative solution [6] is a case in point. Here, each firm may be regarded as (a) agreeing to abide by the Nash axioms to find the solution which results from the point and (b) choosing a strategy. The several threat strategies determine a threat point, which determines a solution; while the choice of a threat strategy is dictated by the wish to arrive at the threat whose associated solution yields maximum profit to the firm. In the literature some discussion may be found of the relative merits of cooperative and noncooperative theories. The former have appeal because it seems so obviously sensible and in the interest of all oligopolists to jointly exploit their market to the full. On the other hand, making joint agreements is difficult. The more firms there are, the more interests to reconcile; hence, the harder it is to come to agreement. In addition, where each firm has knowledge not shared by others (say knowledge of one's own profit function), it becomes even harder to bargain because no one knows the full alternatives open to the group and it may be in a firm's own interest to misrepresent