Natural and double implementation of public ownership solutions in differentiable production economies

This paper examines the implementation of two public ownership solutions in convex production economies with differentiable production functions. The two public ownership solutions we focus on are the proportional and equal benefit solutions. Two “natural” mechanisms which doubly implement the proportional and equal benefit solutions respectively in Nash and strong Nash equilibria are proposed without assuming free disposal. Received: 7 May 1996 / Accepted: 1 December 1998     

Bargaining over an uncertain outcome:¶the role of beliefs

We study the Nash bargaining solution of a problem in which two agents bargain over an uncertain outcome. Under the assumptions of risk neutrality and of constant absolute risk aversion, we study the way that the solution varies, ex ante, when we vary the beliefs of one agent. Changing an agent's beliefs in a way that makes them “more distant” from the other agent's beliefs makes the second agent better off. Received: 10 May 2001 / Accepted: 22 August 2001     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

Implementation of stable solutions in a restricted matching market

I analyze the admission mechanism used in Spanish universities. The system is open to strategic manipulation. This is because students are not allowed to express the whole list of available options. However, the mechanism implements the set of stable matchings in Nash equilibrium and the student's optimum in strong equilibrium. The mechanism also implements the students' optimum, in Nash equilibrium, under the class of “non-reverse” preferences. All these properties come from the fact that colleges do not have the opportunity to misrepresent their preferences. Received: 30 June 1995 / Accepted: 31 January 1997     

Firm governance and duopoly: in weakness may lie strength

The paper proposes a model of firm governance when two firms compete in a duopoly. The paper assumes that a motivational asymmetry exists between owners and managers: owners wish to obtain maximum profits, managers wish to maximize sales. Managers perceive that salary, social status or future job prospects are more closely associated with firm size (i.e. sales) than with firm profits. The paper takes an agency view of the firm where owners only indirectly influence the behaviour of firms through the level of control they exert over managers. The paper demonstrates that a weakly governed firm, acting as a sales maximizer, can gain a competitive advantage over a strongly governed firm, acting as a profit maximizer. The paper examines the extent of this advantage under cost leadership and differentiation strategies. The paper also demonstrates that the objectives of profit maximization and maximization of competitive advantage are not necessarily congruent. The paper graphically represents the profit functions of the two firms illustrating the Nash equilibrium under Cournot and Stackelberg conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Monotonic extensions on economic domains

The property of “monotonicity” is necessary, and in many contexts, sufficient, for a solution to be Nash implementable (Maskin 1977). In this paper, we follow Sen (1995) and evaluate the extent to which a solution may fail monotonicity by identifying the minimal way in which it has to be enlarged so as to satisfy the property. We establish a general result relating the “minimal monotonic extensions” of the intersection and the union of a family of solutions to the minimal monotonic extensions of the members of the family. We then calculate the minimal monotonic extensions of several solutions in a variety of contexts, such as classical exchange economies, with either individual endowments or a social endowment, economies with public goods, and one-commodity economies in which preferences are single-peaked. For some of the examples, very little is needed to recover monotonicity, but for others, the required enlargement is quite considerable, to the point that the distributional objective embodied in the solution has to be given up altogether. Received: 21 September 1996 / Accepted: 17 August 1998     

Rent-seeking in a unionised monopoly

A unionised monopoly firm, benefitting from some kind of anti-competitive regulation, and its corresponding trade union have a common interest in spending resources to protect the monopoly rents created by the regulation. In the present paper, a situation in which the unionised monopoly is challenged by a consumer organisation fighting for deregulation is analysed as a standard Tullock rent-seeking contest. With unequal sharing of monopoly rents, the free-riding incentives among the rent-defending players turn out to be overwhelming, in the sense that the unique Nash equilibrium is characterised by zero effort contribution by the player with the lower valuation of the contested prize. This implies that being “strong”, in terms of bargaining strength, is not necessarily an advantage for neither player in a unionised monopoly that is threatened by deregulation. Received: June 2000 / accepted: January 2001     

Strategic Delegation and Vertical Integration

This paper proposes a game‐theoretic model to analyze owners' vertical integration choices if they delegate pricing decisions to their managers. We find that all three vertical structures are possible Nash equilibrium outcomes. If the products are weak substitutes, then the outcome is that both owners adopt vertical integration. When the products are close substitutes, both owners adopt vertical separation in equilibrium. When substitution between the products is medium, the coexistence of vertical integration and vertical separation is the equilibrium outcome, and the owner corresponding to vertical separation offers exactly a profit‐maximization contract to his or her manager under this situation. Copyright © 2014 John Wiley & Sons, Ltd.     

Fiscal and monetary policy co-ordination: A differential game approach

In this paper the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behaviour. Differential games are used in the framework of a continuous-time econometric model of the Italian economy. The Nash and the Stackelberg non-cooperative equilibrium solutions are computed, and the case for cooperation is analysed by considering the Nash and the Kalai-Smorodinsky bargaining models. It is shown that, in the Italian case, the government has a stronger bargaining position than the central bank. A comparison is then made between the different solutions to show that the drawbacks that emerge from non-cooperation are not simply those depending on the players' payoffs. Other features are in fact considered which constitute a further argument for policy co-ordination.     

Mediation and the Nash bargaining solution

This paper analyzes a model of bargaining in which two parties use a mediator who sequentially makes random proposals until agreement by both parties is reached. I show that as the cost of delay shrinks to zero, the subgame perfect payoff converges to the asymmetric Nash bargaining solution with weights determined by the relative discount rates of the players. I also establish conditions for the uniqueness of the subgame perfect equilibrium for arbitrary discount rates.     

Survival and the art of profit maximization

We study the relationship between rationality and economic survival in a simple dynamic model, where agents from different populations interact repeatedly through random matching. An explicit criterion (“bankruptcy”) determines whether agents survive each interaction; all agents are presumed to be aware of this criterion. Survival in each interaction depends on two factors: the strategies agents adopt when they interact, and the wealth levels they bring to the game. The model is completely symmetric with the only difference between the agents of different populations being their objectives. We consider the case where there are two populations of agents in which all agents from one group have as their objective, maximizing the expected profits from each interaction, while all agents from the other attempt simply to maximize the probability of surviving (i.e., not going bankrupt in) the interaction. We show that under the equilibrium dynamics, the proportions of each group in the total population must be bounded away from zero, but the balance is in favor of the survival-probability maximizers in that their numbers as a fraction of total population must always exceed 1/2, and can be arbitrarily close to unity. On the other hand, the fraction of total wealth controlled by the expected profit maximizers must also be at least 1/2, and can asymptotically tend to unity.     

Implementing the nash extension bargaining solution for non-convex problems

Conley and Wilkie (1993) introduced an axiomatization at the Nash extension bargaining solution defined on a domain of comprehensive but not necessarily convex problems. In this paper we present a non-cooperative game which implements the Nash extension solution in subgame perfect equilibria in the limit as the discount rate applied between rounds of play vanishes.     

Economic institutions and horizontal checks and balances in the Chinese bureaucratic system: evidence at the prefecture-city level

Economics of Governance - In China, “democratic centralism” complicates horizontal and vertical bargaining among politicians. Higher-level cadres need to consider not only...     

Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

Recursive Nash bargaining over a productive asset

We propose an equilibrium concept (the recursive Nash bargaining solution) that describes the outcome of repeated negotiations between two rational agents under the assumptions that the state of the economic system under consideration changes according to the actions of the players and that neither party can make binding commitments to future behavior. This equilibrium is dynamically consistent but typically not Pareto-efficient. As an application, we compute the recursive Nash bargaining solution in a model of two heterogeneous agents bargaining over the use of a productive asset with constant gross rate of return and study how the time-preference rates and the elasticities of substitution affect the solution.     

Threshold uncertainty in discrete public good games: an experimental study

A discrete public good is provided when total contributions equal or exceed the contribution threshold. Recent theoretical work shows that an increase in threshold uncertainty will increase (decrease) equilibrium contributions when the public good value is sufficiently high (low). In an experiment designed to test these predictions, I find only limited verification of the prediction. Using elicited beliefs data to represent subjects’ beliefs, I find that behavior is not consistent with expected payoff maximization, however, contributions are increasing in subjects’ subjective pivotalness. Thus, wider threshold uncertainty will sometimes—but not always—hinder collective action.     

Redistribution and individual characteristics

I study a model where personal income is a function of two different groups of individual characteristics, called “talent” and “effort” respectively. The distinction between these two groups is that society has taken the prior decision that the influence of traits from the first group needs to be moderated by any fair redistribution mechanism while differences in income due to traits from the second group must be preserved. I present two solutions that satisfy several intuitive properties of fairness and I use these properties to characterize both of them. Received: 29 October 1995 / Accepted: 6 January 1997     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

The Bargaining–sales‐delegation Game

This article revisits the managerial delegation literature led by Vickers ( 1985 ), Fershtman and Judd ( 1987 ) and Sklivas ( 1987 ) by introducing a bargaining mechanism between owners and managers over managerial contracts. It shows that the degree of bargaining interacts with the extent of product differentiation in determining whether the sub‐game perfect Nash equilibrium is sales delegation or profit maximisation. In contrast with the classical result, no sales delegation emerges and the typical prisoner's dilemma of the managerial delegation literature is solved. This holds in both contexts of Cournot and Bertrand rivalries. The article also provides results for the more general cases with heterogeneous managerial bargaining power and endogenous decisions of the owners regarding the bargaining power of the manager that should be or not be hired in a firm. Copyright © 2016 John Wiley & Sons, Ltd.