Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

A new monotonicity condition for tournament solutions

We identify a new monotonicity condition (called cover monotonicity) for tournament solutions which allows a discrimination among main tournament solutions: The top-cycle, the iterated uncovered set, the minimal covering set, and the bipartisan set are cover monotonic while the uncovered set, Banks set, the Copeland rule, and the Slater rule fail to be so. As cover monotonic tournament solutions induce social choice rules which are Nash implementable in certain non-standard frameworks (such as those set by Bochet and Maniquet (CORE Discussion Paper No. 2006/84, 2006) or Özkal-Sanver and Sanver (Social Choice and Welfare, 26(3), 607–623, 2006), the discrimination generated by cover monotonicity becomes particularly notable when implementability is a concern.     

What price compromise?

This paper identifies, and tests experimentally, a prediction of the Nash bargaining axioms that may appear counterintuitive. The context is a simple bargaining problem in which two players have to agree a choice from three alternatives. One alternative favours one player and a second favours the other. The third is an apparently reasonable compromise, but is in fact precluded as an agreed choice by the Nash axioms. Experimental results show that agreement on this third alternative occurs rather often. Our subjects’ behaviour could be interpreted as the paying of an irrationally high price, according to the Nash axioms, in order to reach a compromise agreement.     

Pure-strategy Equilibria with Non-expected Utility Players

A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.     

Game-modeling multilateral trade negotiations

Using actual trade and tariff data for the United States and the European Community, this paper demonstrates how a trade negotiation such as the Tokyo Round can be modeled as a game among countries attempting to minimize individual welfare loss functions. First, we construct welfare functions based on suggested trade negotiation goals. We compute both the noncooperative Nash-Cournot equilibrium tariffs and the cooperative Nash equilibrium implied by these welfare functions. Welfare outcomes under the computed equilibrium tariffs are then compared with those arising from the initial tariff structure, as well as the tariff structure actually determined by the negotiation. We find that, while the game model tracks closely the decisions of the negotiators in the Tokyo Round, later unilateral political decisions resulted in less optimal tariffs.     

Social choice, the strong Pareto principle, and conditional decisiveness

This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.     

How to combine pareto optimality with liberty considerations

I argue that the liberty condition of Sen's important impossibility of a Paretian liberal result is not a condition that liberals (or libertarians) would accept. The problem is that an appropriate liberty condition must be formulated in terms of consent - not in terms of preference. To formulate an adequate condition the framework needs to expand from collective choice rules (which only take information about preferences as input) to rights-based social choice rules (which also take as input information about which options have been consented to and which would violate someone's rights). I formulate a more adequate liberty condition based on the notion of consent that is acceptable to liberals, and then show that Pareto optimality is incompatible even with that condition. I then show how the liberty condition can be weakened in a plausible manner, and describe an interesting class of theories - rights-based Paretian theories - that satisfy the Pareto optimality requirement while being sensitive to liberty considerations.     

Strategic behavior under partial cooperation

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.     

Private investment and government protection

Hurricane Katrina did massive damage because New Orleans and the Gulf Coast were not appropriately protected. Wherever natural disasters threaten, the government—in its traditional role as public goods provider—must decide what level of protection to provide to an area. It does so by purchasing protective capital, such as levees for a low-lying city. (“Protection” also consists of prohibiting projects that raise risk levels, such as draining swamps.) We show that if private capital is more likely to locate in better-protected areas, as would be expected, then the marginal social value of protection will increase with the level of protection provided. That is, the benefit function is convex, contrary to the normal assumption of concavity. When the government protects and the private sector invests, there may be multiple Nash equilibria due to the ill-behaved nature of the benefit function. Policy makers must compare them, rather than merely follow local optimality conditions, to find the equilibrium offering the highest social welfare. There is usually considerable uncertainty about the amount of private investment that will accompany any level of protection, further complicating the government’s choice problem. We show that when deciding on the level of protection to provide now, the government must take account of the option value of increasing the level of protection in the future. We briefly examine but dismiss the value of rules of thumb, such as building for 1000-year floods or other rules that ignore benefits and costs.     

Either with us or against us: experimental evidence on partial cartels

This paper analyzes the coordination challenge a partial cartel faces when payoff asymmetries between potential cartel insiders and potential cartel outsiders are large. We introduce two experimental treatments: a standard treatment where a complete cartel can be supported in a Nash equilibrium and a modified treatment where a complete cartel and a partial cartel can both be supported in a Nash equilibrium. To assess the role of communication both treatments are additionally run with a “chat option,” yielding four treatments in total. Our results show that subjects frequently reject the formation of partial cartels in the modified treatments. In all treatments with communication subjects are more likely to form complete cartels than partial cartels. The implications of these results are important for antitrust: payoff asymmetries between cartel members and outsiders may jeopardize the formation of partial cartels. Yet complete cartels may be formed instead, if institutional mechanisms with frequent communication are used to form cartels.

     

Partial cooperation in strategic multi-sided decision situations

We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.     

A note on the two person exchange game

The two person exchange game is analysed using core theory, the Nash solution and the competitive equilibrium. It is shown for specific utility functions that relative to the other trader, the less wealthy trader does better under the Nash solution than he would under the competitive solution. Conversely, the trader with the lower initial utility level does better under the competitive solution than he would under the Nash solution. If traders have disparate initial endowments, it is argued that outcomes should be restricted to a reduced core containing the Nash and competitive solutions as endpoints.     

Dynamic Choice Mechanisms

A dynamic choice mechanism (e.g. sophisticated choice) is a rule transforming a sequence of orderings into actual choices. The dynamic choice literature analysing such rules is restricted to the case of strict preferences. The present paper allows also for weak preferences. This generalisation is necessary since in dynamic utility models decision makers are typically endowed with orderings which can be represented by continuous utility functions. Such a representation, however, requires the orderings to be a weak ordering. In the presence of weak orderings the classical choice mechanisms have to be re-examined. This paper develops and analyses new choice mechanisms and relates them to the notion of a subgame-perfect equilibrium.     

An Ethical Interpretation of the Nash Choice Rule

This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.     

政策实施成本与上下级政府讨价还价的发生机制——基于四东县休禁牧案例的分析

讨价还价是中国上下级政府互动关系中很重要的一种形式。本文详细记述了四东县草原休禁牧政策实施过程中上下级政府的多轮讨价还价，县政府制定政策，政策严格落实导致政府与民众的冲突频发，乡镇政府以冲突为策略与县政府讨价还价，最终获得了相对宽松的执行空间。本文使用实施成本分析框架解释了讨价还价行为的发生机制，执行过程成本、上级施加成本、民众施加成本高昂，致使乡镇政府只能选择与上级讨价还价。随着社会冲突的加剧，乡镇政府的讨价还价能力相对提高，使得双方的协议点从严格执行端向宽松执行端移动。执行无僵局、协议点左右摆动、短期均衡与讨价还价的交替发生是政策执行中上下级政府讨价还价的基本特征。     

On the evaluation of solution concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.     

Social ontology,practical reasonableness,and collective reasons for action

I argue that the ontology of human social institutions and collective intentionality could be anchored in the normative notion of ‘practical reasonableness’ as collective reason for action. This involves the deontic idea of mutuality, accepted rules, and shared attitudes of other‐regardedness. I examine John Searle's three primitive notions of social ontology: collective intentionality, assignment of social functions, and constitutive rules and procedures. I use these notions to provide a plausible basis for understanding how people reason, in order to arrive at practically reasonable decisions and collective agency. Searle argues that social reality, institutions, processes, and facts are grounded in collective intentionality and the acceptance of social rules, procedures, and functions. I argue that collective intentionality and socially accepted rules are anchored in the need for human interdependence that engenders the social rules and norms or attitudes of ‘practical reasonableness’. I analyze the concept of ‘practical reasonableness’ as a representation of human mode of reasoning that involves collective intentionality.     

On some suggestions for having non-binary social choice functions

The various paradoxes of social choice uncovered by Arrow [1], Sen [10] and others have led some writers to question the basic assumption of a binary social choice function underlying most of these paradoxes. Schwartz [8], for example, proves an important theorem which may be considered to be a generalization of the famous paradox of Arrow, and then lays the blame for this paradox on the assumption of a binary social choice function. He then proceeds to define a type of choice functions which, like binary choice functions, define the best elements in sets of more than two alternatives on the basis of binary comparisons, but which, as he claims, have an advantage over binary choice functions, in so far as they always ensure the existence of best elements for sets of more than two alternatives irrespective of the results of binary comparisons. The purpose of this paper is to show that even a considerable weakening of the assumption of a binary social choice function does not go very far towards solving some of the paradoxes under consideration, and that if replacing the requirement of a binary social choice function by a Schwartz type social choice function solves these paradoxes, it does so only by violating the universally acceptable value judgment that in choosing from a set of alternatives, society should never choose an alternative which is Pareto inoptimal in that set (i.e., the socially best alternatives in a set should always be Pareto optimal). This argument is substantiated with the help of an extended version of Sen's [10] paradox of a Paretian liberal, and thus a by-product of our analysis is a generalization of the theorem of Sen [10]. The argument itself, however, is more general and applies also to the impossibility result proved by Schwartz [8].We are extremely grateful to Amartya Sen for his helpful comments.

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Rawlsian Nash solutions

We investigate the conditions which guarantee the choice of Rawlsian solutions by players of unequal maximin positions bargaining under Nash rules. The conditions, viz., subsymmetry and the location of the Pareto set, relate to the structure of the utility set,S.     

On the existence of stable states in game problems

Each individual or group of individuals unified by some common interests often have to either accept an offer or reject it. The choice is made on the basis of not only individual or group preferences but on the basis of the reaction to this choice by other people whose preferences are dependent to some extent on this choice. The following question is to be answered: under what conditions is an offer stable, i.e. will it be accepted by each participant in a group with non-coincident interests? To answer this question is to specify in the set of all feasible offers (options or situations) those ones which would be rejected by no participant. According to this intuitive understanding of stable offers a sequence of weak and strong equilibria referred to as active equilibria was defined. A weak equilibrium satisfies the following conditions: (1) It defines stable situations which cannot be changed by a participant because of certain retaliatory actions by the other participants, which would worsen his initial situation. (2) It always exists. (3) Under comparatively wide conditions it has a non-empty intersection with the Pareto set. (4) It includes non-cooperative equilibria well known in the game theory and does not lead to any paradoxes (as, for example, the Nash equilibrium does). These conditions, and especially the third and fourth ones, indicate that the active equilibria can be successfully used in the game theory as well. Strong equilibria define a more stable situation but they do not necessarily meet all four conditions listed above.