On the consistency of conjectures with public goods

This note addresses Sugden's criticisms, levelled against our Non-Nash theory for public goods. In particular, we argue that our previous exercise was not to present a theory of public goods that could escape the voluntary contribution problem by relaxing Nash conjectures. Rather, our non-Nash model was merely an analytical exercise, meant to encompass a widevariety of behaviour. This note also indicates when positive conjectures might be realistic and, therefore, potentially consistent. Finally, we extend our specific example to include negative, zero, and positive conjectures.     

The theory of public goods: non-nash behaviour

Most treatments of equilibrium public goods provision assume zero conjectural variations in the sense that each individual regards the behaviour of the rest of the community as independent of his own. This paper introduces nonzero conjectural variations into the model. A diagram is introduced which can depict both the individual's and the community's equilibrium in the presence of nonzero conjectural variations. Equilibrium and optimal outcomes are compared, and a specific functional form is used to investigate the effect of community size on the nature of equilibrium. Finally, we discuss the requirement that conjectures should be consistent.     

An algorithm of game theory applied to the duopoly problem

In this note, an algorithm of Game Theory — Fictitious Play — is applied to a duopoly model: at each step of the algorithm, each duopolist chooses a quantity which maximizes his expected payoff, given the frequency distribution of his opponent's past choices. The algorithm is interpreted as a dynamic learning process and compared to Cournot's process. The successive pairs of quantities announced by the duopolists are proved to converge to a pair of non-cooperative equilibrium quantities. A more sophisticated version of the algorithm also has the same convergence properties.     

A note on ‘trying to value a life’

Broome's alleged paradox that application of the usual compensation test to the valuation of life would produce an infinite monetary value is shown to be false because it is based on illegitimate generalisation from a special case in which no effective compensation is possible. In the general case, relevant to public sector project appraisal, such compensation is possible, and finite values are to be expected, judging by people's ordinary behaviour.     

Technology and social change: William Fielding Ogburn revisited

This paper reviews William Fielding Ogburn's work on technology and social change. An overview of his basic theory is presented, as well as later refinements found in such works as Recent Social Trends in the United States, Technological Trends and National Policy, The Social Effects of Aviation, and other books and articles. It is suggested that while Ogburn is most widely remembered for his thesis of cultural lag, some of his later work on technology and social change is actually more important and deserves reconsideration and extension. One kind of extension might follow the lines of a systems approach rather than continuing the technological primacy strategy that Ogburn is normally considered to have used. The paper also surveys Ogburn's important work in the areas of technology, planning, and social policy, including materials on technology assessment. Ogburn's nontechnocratic approach to these questions, as well as his insistence that social scientists have a great deal to offer to the formulation of technological and social policies, are some of his most important contributions. Questions of technology and social change remain important contemporary issues, yet there is a surprising paucity of social science work on these crucial topics. Further study, extension, and reformulation of Ogburn's pioneering ideas offer fruitful means of embarking on new social science analyses of technology and society.     

Rational conjectures and evolutionary beliefs in public goods games

This paper applies conjectural variations (CVs) to a model of public good provision and shows that CVs are superior to Nash beliefs. In addition to imposing consistency, as Bresnahan, I show that consistent conjectures (CCs) are obtained from individual payoff maximization. CCs emerge as the unique subgame perfect Nash equilibrium (NE) in a two-stage game in which beliefs are chosen in Stage 1 and quantities in Stage 2. There is an individual payoff advantage to non-Nash behavior, generating a Prisoner's Dilemma in conjectures in addition to the usual free-rider problem associated with public goods. The correct and payoff maximizing conjecture is the unique equilibrium in an evolutionary framework against a player with Nash conjectures. The consistent conjecture equilibrium is the unique evolutionary equilibrium when both players conjectures evolve. Hence, the NE prediction is too optimistic when players have rational conjectures.     

Learning with perfect information

For extensive form games with perfect information, consider a learning process in which, at any iteration, each player unilaterally deviates to a best response to his current conjectures of others' strategies; and then updates his conjectures in accordance with the induced play of the game. We show that, for generic payoffs, the outcome of the game becomes stationary, and is consistent with Nash equilibrium. In general, if payoffs have ties or if players observe more of each others' strategies than is revealed by plays of the game, the same result holds provided a rationality constraint is imposed on unilateral deviations: no player changes his moves in subgames that he deems unreachable, unless he stands to improve his payoff there. Moreover, with this constraint, the sequence of strategies and conjectures also becomes stationary, and yields a self-confirming equilibrium.     

Optimal incentive contracts with multiple agents

A setting in which a single principal contracts with two agents who possess perfect private information about their own productivity is considered. With correlated productivities, each agent's private information also provides a signal about the other agent's productivity. In contrast to the setting in which there is only one agent, it is shown that such private information may be of no value to the agents. It is only if the agents are risk-averse that their private information may allow them to command rents. Moreover, when the agents are constrained only to reveal their private information truthfully as a Nash equilibrium, the Pareto optimal incentive scheme may induce the agents to adopt strategies other than truth-telling. This leads to the consideration of truth-telling equilibria that are not Pareto dominated in the subgame played by the agents. Among all such equilibria, the one preferred by the principal restricts one agent to tell the truth as a dominant strategy and the other as a Nash response to truth.     

Evolutionary Stability in the Finitely Repeated Prisoner 's Dilemma Game

The dynamic evolutionary stability of mutual defection is proven for the repeated prisoner 's dilemma game where payoffs are cumulative and the number of repetitions is known. This agrees with the classical result that the only Nash equilibrium outcome is to defect at all stages of this repeated game. Moreover, it is shown that, for any initial polymorphic population, the evolutionary dynamic converges to a unique Nash equilibrium strategy that depends on the original polymorphism. Both these results confirm earlier conjectures concerning the application of evolutionary game theory to the repeated prisoner 's dilemma.Journal of Economic LiteratureClassification Numbers: C70, C72.     

Some microfoundations of Austrian economics: Böhm-Bawerk's version

This paper investigates Böohm-Bawerk's version of Austrian microeconomics. It draws some comparisons with Carl Menger's programmatic work on the principles of economic theory which originally established a distinctive Austrian tradition. Böhm-Bawerk's microeconomics is also considered against the background of contemporary Walrasian, Edgeworthian and Marshallian thought as well as twentieth-century work on the theory of games. Böhm-Bawerk offers a theory of micro-structural dynamics. His emphasis on intentionality and imagination in value creation, the scope for bargaining and strategic behaviour in his theory of markets and the avowed indeterminacies and equilibrating tendencies in his theory of price formation, are all consistent with other first-generation Austraian contributions. There is nothing especially Walrasian or Marshallian about Böhm-Bawer's. microeconomics     

Tariff Revenue Competition in a Free Trade Area: The Case of Asymmetric Large Countries

The striking result has been shown by Richardson that tariff revenue competition between two symmetric member countries of a free trade area (FTA) results in complete elimination of external tariffs if there exists a pure‐strategy Nash equilibrium at all. Richardson also conjectures without building a model that if member countries are asymmetric in market size, there exists a pure‐strategy Nash equilibrium in which both countries set positive external tariffs. We explicitly extend his tariff competition model into the case of asymmetric FTA member countries, and confirm his conjecture. We also show that there exists a mixed‐strategy Nash equilibrium in the case of symmetric countries.     

Angus Deaton’s Nobel Prize for Confronting Theory with Facts

Angus Deaton, recipient of the 2015 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, is broadly recognized as an outstanding applied economist who is well deserving of the prize. He has made a myriad of important contributions—alone and with renowned co-authors—across many fields. In this review of his work, I argue that it is his methodological consistency and focus on the two-way connection between empirics and theory, together with his attention to detail of how things are measured, that support his recognition by his peers. Informed by a career of doing careful econometric work using household surveys—especially on consumption, development, well-being and health—in his popular writing, Deaton chooses to focus on the importance of institutions, history and other disciplines.     

Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting

The purpose of this paper is to show how conjectural variations can be derived as a reduced form in an infinitely repeated game of private provision of public goods. We obtain explicit closed forms of conjectural variations associated with maximal sustainable equilibria in which the sum of the utilities of all of a community's members is maximized for both quadratic and Cobb–Douglas preferences, provided that the resulting sequence of contributions can be sustained as a Nash (or subgame perfect) equilibrium in the underlying repeated game. We also show that positive conjectural variations will emerge as long as people place positive weight on the future, and that those conjectures are positively related to the discount factor.     

Risk sensitivity in bargaining with more than two participants

In two-person bargaining over riskless outcomes where the outcome is chosen according to the Nash solution or the Kalai-Smorodinsky solution, an increase in a player's risk aversion is to the advantage of the opponent. It is shown in this note that for the n-person Nash solution, an increase in risk aversion is to the player's own disadvantage but needs not be advantageous to all the opponents. For the n-person Kalai-Smorodinsky solution, the increase is to the player's own disadvantage and to the advantage of all the opponents.     

Probabilising the consumer: Georgescu-Roegen,Marschak and Quandt on the modelling of the consumer in the 1950s

It is the purpose of this article to confront three attempts by economists at developing models of individual choice that go beyond standard ordinalist utility theory through introducing principles of probabilistic behaviour. We discuss first Georgescu-Roegen's neglected contributions to this subject, though he pioneered the definition of probabilistic preference in 1936 and came back on the subject intensively in the 1950s. We then present Marschak's (and his co-authors) attempts at axiomatising a probabilistic model of choice in the same period. The third contribution studied is that of Quandt, who provides a more operational style of modelling. This set of contributions is discussed against a general background of transformations of the theory of rational behaviour and of the methods proper to it.     

The cost of equity capital: A simplification

Modigliani-Miller's theorem, which asserts that corporate financing policy is of no consequence, has been shown to hold true under a set of assumptions which is less restrictive than the original set used by MM. Preceding proofs were based on the theory of general equilibrium. Basically, this paper examines MM's second proposition—the linearity of the cost of equity capital with respect to financial leverage—when dropping a few of their basic assumptions but retaining their assumption about incomplete markets. In particular, this paper relaxes the assumptions that (a) the inflows are perpetual and that (b) the firm's future returns belong to the same risk class. The results of the analysis indicate that the linearity will be sustained. The nature of the financial risk premium (the slope), however, has to be modified.     

Pricing policies for a two-part exhaustible resource cartel: The case of OPEC

This paper examines pricing policies for OPEC under the assumption that the cartel is composed of a block of spender countries with large cash needs and a block of saver countries with little immediate need for cash and a lower rate of discount. The decision problem for the two-part cartel is embodied in a game-theoretic framework and the optimal bargaining solution is computed using results from the theory of cooperative games developed by Nash. The set of feasible bargaining points—and the corresponding Nash solution—is computed under two assumptions on the behavior of output shares: that they are subject to choice and that they are fixed at historical values. Our results suggest that for fixed output shares, there is little room for bargaining, and the price path approximates the optimal monopoly price path. If the shares are subject to control, optimal paths depend significantly on the relative bargaining power of each block.     

Bargaining and Boldness

We study a multiperson bargaining problem with general risk preferences through the use of Shaked's game of cycling offers with exogenous breakdown. If preferences are “smooth,” then as the risk of breakdown vanishes, the limiting outcome is one in which bargainers are equally marginally bold; where a bargainer's marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his position. Under smoothness, any (ordinal-)Nash solution is an equally marginally bold outcome. However, unlike the concept of the (ordinal-)Nash solution, a unique equally marginally bold outcome exists in natural cases—in particular, if all bargainers have risk-averse preferences of the rank-dependent expected utility type. For these preferences, the equally marginally bold outcome maximizes a “bargaining power”-adjusted (asymmetric) Nash product where the degree of asymmetry is determined by the disparity in the marginal valuation of certainty among bargainers. Journal of Economic Literature Classification Numbers: C72, C78, D81.     

A Note on Laurence Seidman’s Article

Mihail Manoilescu was among the foremost intellectual figures of the interwar period in Romania. He was known as a politician and central banker, as well as an economist. From the very beginning of his theoretical and practical career, or at least from the late 1920s onward, Manoilescu’s ideas and theories (especially his corporatist theory) were marked by clear continuity and consistency based on the theory of protectionism grounded on productivity differences. By developing his model — an alternative to the theory of comparative advantage — Manoilescu endeavored to show the need for protectionist measures to promote the development of peripheral countries. His defense of protectionism is usually presented as clumsy and founded on an incorrect method, even if he is often recognized as the forerunner of the theory of unequal exchange and the dependency theory. Few scholars note the similarity of Manoilescu’s theory with Karl Marx’s labor theory. This paper contributes to validating Manoilescu’s conclusions, the soundness of which we test here by reconstructing the theory from a Marxian perspective. A reconstruction of this type offers new possibilities of evaluating his theory and a better understanding of its contributions and limitations.     

Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.