Group identity in a network formation game with cost sharing

This paper introduces the choice of group identity, which is comprised of characteristics and commitments to these characteristics, in a network formation model where links costs are shared. Players want to link to the largest group given that linking costs for players of the same (different) characteristic are decreasing (increasing) in their commitments. The equilibrium concepts used are Nash equilibrium as well as one that looks for stability allowing for bilateral negotiations. Conditions are shown under which the endogenous choice of characteristics and commitments allow for multiple groups with segregated or connected networks. When group identity is partly endogenous, such that characteristics are fixed and players only choose commitment, it is shown that the equilibrium population commitment profile dictates whether the resulting network is segregated or connected. When group identity is fully endogenous, it is shown that multiple groups and segregated networks are possible equilibrium outcomes but such outcomes are not stable unless the group size additionally affects the costs of link formation.     

Bilateral commitment

We consider non-cooperative environments in which two players have the power to gradually and unilaterally rule out some of their actions. Formally, we embed a strategic-form game into a multi-stage game, in which players can restrict their action spaces in all but the final stage, and select among the remaining actions in the last stage. We say that an action profile is implementable by commitment if this action profile is played in the last stage of a subgame-perfect equilibrium path. We provide a complete characterization of all implementable action profiles and a simple method to find them. It turns out that the set of implementable profiles does not depend on the length of the commitment process. We show, furthermore, that commitments can have social value in the sense that in some games there are implementable action profiles that dominate all Nash equilibria of the original game.     

A strategic analysis of the war against transnational terrorism

We study a two stage game in which a transnational terrorist organization interacts with an arbitrary number of countries that may differ in their political or economic power, their military effectiveness, the benefit from cooperating against terrorism and the value they assign to damage. Only a subset of countries that emerges endogenously takes proactive measures to fight the terrorist, while all countries incur defensive expenditures to protect their soil. We characterize analytically the pure strategy subgame perfect equilibrium of the game and show how the equilibrium strategies depend on the key model parameters. We provide an algorithm to find the endogenous set of cooperating countries based on their benefit from cooperation and their political/economic power.     

Malice and patience in Rubinstein bargaining

If two players playing a Rubinstein alternating offers game are highly malicious (getting a high utility from “malice” in every period when the other player does not obtain a share in a fixed pie), and highly patient, no equilibrium with an agreement exists and players choose perpetual disagreement. This does not change if the players are subjected to a known deadline after which the pie will be appropriated by outside agencies or disappear: perpetual disagreement is still the only outcome. If in addition players are required to pay endogenously determined fines if they fail to reach agreement, players with discount factors in a certain range do reach agreement, but only at the deadline. However, infinitely patient players would never reach agreement for any feasible level of one-time fines. The result contrasts with spiteful or envious preferences. Our results highlight a novel reason for failure to resolve property disputes.     

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.     

Decompositions and potentials for normal form games

A basic model of commitment is to convert a two-player game in strategic form to a “leadership game” with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.     

Design of reforms with time‐inconsistent voters

Widespread agreement that a political reform is necessary is no guarantee that it is actually undertaken in a timely manner. There is often a delay before action is taken and reform packages that would be most efficient to implement all at once are often done only gradually. We propose a theoretical model explaining this behavior and show that when voters have present‐biased, time‐inconsistent preferences, gradualism can arise in equilibrium and be welfare‐enhancing. This is because without the possibility for gradualism, time‐inconsistent voters would delay implementing the reform even more. Using a citizen candidate model, we allow the agenda setter, who decides which reform schedule to put to vote, to be endogenously determined. We show that voters who are aware of their own time inconsistency can use the election of the agenda setter as a commitment device and appoint an agent who is more patient than the median voter in order to avoid full procrastination and to achieve efficiency‐maximizing gradualism.     

Endogenous technological change,income distribution,and unemployment with inter-class conflict

This paper presents a Kaleckian growth model that incorporates endogenous technological change. The model endogenously determines the rate of capacity utilization, the rate of economic growth, income distribution, and the employment rate in addition to technological change. The paper shows that whether or not an increase in the relative bargaining power of workers raises the long-run equilibrium unemployment rate depends on which regime is realized in the long-run equilibrium. If, for example, the long-run equilibrium corresponds to the wage-led growth regime, a rise in the relative bargaining power of workers leads to a decline in the unemployment rate. This result is never obtained from the mainstream NAIRU model.     

A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.     

Trade, inequality, and the political economy of institutions

This paper investigates the relationship between international trade and the quality of economic institutions. We model institutions as fixed costs of entry, in a framework that has two key features. First, preferences over entry costs differ across firms and depend on firm size. Larger firms prefer to set higher costs of entry, in order to reduce competition. Second, these costs are endogenously determined in a political economy equilibrium. Trade opening can lead to higher entry costs when it changes the political power in favor of a small elite of large exporters, who in turn prefer to install high entry barriers.     

Randomly available outside options in bargaining

We consider an extension of the standard Rubinstein model where both players are randomly allowed to leave the negotiation after a rejection, in which case they obtain a payoff of known value. We show that, when the value of the outside opportunities is of intermediate size, there exist a continuum of subgame-perfect equilibrium outcomes, including some with delayed agreements. Considering outside opportunities of significant value, we prove that efficient delays arise caused by the bargainers' aspirations, in waiting for their outside, option rather than by threats. Moreover, if taking the outside option decreases the probability that the opponent receives an outside option in the future, then it is possible that exactly two equilibrium payoffs coexist. In this latter case, inefficiencies may be created by agreeing too early.     

Inflation: The Invisible Foot of Macroeconomics*

We take a simple, well-known macroeconomic model and treat it as a game between two players—the government and an all-embracing union. The payoffs have the form of a prisoner's dilemma. The equilibrium outcome produces unwanted inflation and is not Pareto optimal. This is despite the fact that all participants are assumed to have full information. This result is shown to be quite robust to the form of the model and is not affected if one of the players is forced to announce its strategy in advance. This we call the invisible foot of macroeconomics.     

A competitive partnership formation process

A group of heterogeneous agents may form partnerships in pairs. All single agents as well as all partnerships generate values. If two agents choose to cooperate, they need to specify how to split their joint value among one another. In equilibrium, which may or may not exist, no agents have incentives to break up any existing partnerships or form new partnerships. This paper proposes a dynamic competitive adjustment process that always either finds an equilibrium or exclusively disproves the existence of any equilibrium in finitely many steps. When an equilibrium exists, partnership and revenue distribution will be automatically and endogenously determined by the process. Moreover, several fundamental properties of the equilibrium solution and the model are derived.     

How elections affect fiscal policy and growth: revisiting the mechanism

This paper reconsiders the popular result that the lower is the probability of reelection, the greater is the incentive of incumbent politicians to choose short-sighted, inefficient policies. The set-up is a general equilibrium model of economic growth, in which fiscal policy is endogenously chosen under electoral uncertainty. Political parties can value possible economic benefits differently depending on whether they are in or out of power, and—by contrast with the literature—the relevant preference coefficient is a choice variable rather than an exogenous taste parameter. The main result is that, when political parties choose both economic policy instruments and preference coefficients, the fundamental reason for short-sighted policy is the extra rents from being in power per se.     

Information acquisition in conflicts

This paper considers incentives for information acquisition ahead of conflicts. First, we characterize the (unique) equilibrium of the all-pay auction between two players with one-sided asymmetric information where one player has private information about his valuation. Then, we use our results to study information acquisition prior to an all-pay auction. If the decision to acquire information is observable, but not the information received, one-sided asymmetric information can occur endogenously in equilibrium. Moreover, the cut-off values of the cost of information that determine equilibrium information acquisition are higher than those in the first best. Thus, information acquisition is excessive. In contrast, with open or covert information acquisition, the equilibrium cut-off values are as in the first best.     

外部掠夺下的国防开支与经济增长

本文建立了一个国际冲突环境中的一国经济长期增长模型。模型假定国际环境为霍布斯状态,一国不得不时刻面临外部掠夺,而阻止外部掠夺的唯一途径是投资国防。掠夺者、政府和家庭的动态博弈均衡决定了长期增长路径。分析表明,国际和国内因素两个层次的均衡决定了长期均衡增长路径;均衡增长路径可分为屈服均衡、容忍均衡和完全防卫均衡三个阶段;政府不同的国防战略会导致不同的增长图景,经济持续增长将导致国防战略的内生调整。     

The single deviation property in games with discontinuous payoffs

We study equilibrium existence in normal form games in which it is possible to associate with each nonequilibrium point an open neighborhood, a set of players, and a collection of deviation strategies, such that at any nonequilibrium point of the neighborhood, a player from the set can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established as an application of a general equilibrium existence result for qualitative games. A new form of the better-reply security condition, called the strong single deviation property, is proposed.     

Endogenous Formation of Coalitions in Noncooperative Games

In this paper we extend the definitions of coalition-proof Nash equilibrium and communication-proof equilibrium to situations of partial communication. Then we use the model of endogenous formation of coalitions of Aumann and Myerson to find that one of these situations in which the corresponding equilibrium exists will be endogenously determined by the players in the game.Journal of Economic LiteratureClassification Numbers: C70, C72.     

Coalitional bargaining games with random proposers: Theory and application

We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient.