The consistency principle for set-valued solutions and a new direction for the theory of equilibrium refinements

game theory;equilibrium theory

An Axiomatization of Minimal Curb Sets

Norde et al.[Games Econ.Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent.A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games.The minimal curb sets of Basu and Weibull [Econ.Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.Minimal curb set;Consistency

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Preparation and toolkit learning

A product set of pure strategies is a prep set ("prep" is short for "preparation") if it contains at least one best reply to any consistent belief that a player may have about the strategic behavior of his opponents. Minimal prep sets are shown to exists in a class of strategic games satisfying minor topological conditions. The concept of minimal prep sets is compared with (pure and mixed) Nash equilibria, minimal curb sets, and rationalizability. Additional dynamic motivation for the concept is provided by a model of adaptive play that is shown to settle down in minimal prep sets.noncooperative games; inertia; status quo bias; adaptive play; procedural rationality

Compensation and responsibility

This a chapter for the Handbook of Social Choice and Welfare. It deals with the theory of fairness applied to situations when individuals are partly responsible for their characteristics.fairness, responsibility, equal opportunity, compensation, handicap, talent, effort

From Wald to Savage: homo economicus becomes a Bayesian statistician

Bayesian rationality is the paradigm of rational behavior in neoclassical economics. A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes’s rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is far from trivial and of great historiographic importance. The story begins with Abraham Wald’s behaviorist approach to statistics and culminates with Leonard J. Savage’s elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. It is the latter’s acknowledged fiasco to achieve its planned goal, the reinterpretation of traditional inferential techniques along subjectivist and behaviorist lines, which raises the puzzle of how a failed project in statistics could turn into such a tremendous hit in economics. A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools.Savage, Wald, rational behavior, Bayesian decision theory, subjective probability, minimax rule, statistical decision functions, neoclassical economics

Public Choice, Constitutional Political Economy and Law and Economics

The various subdisciplines within the emerging ‘new institutionalism’ in economics all draw special attention to the legal-political constraints within which economic and political agents choose and therefore represent a return of economics to its appropriate legal foundations. By changing the name of his research program to constitutional political economy Buchanan distanced himself from those parts of the public choice literature that remained too close to the traditional welfare economics approach. This chapter draws lessons for law and economics from recent developments in the re-emerging field of constitutional political economy. CPE compares alternative sets of institutional arrangements, in markets and the polity, and their outcomes, using ‘democratic consent’ as an internal standard of comparison. The chapter discusses the methodological foundation of the CPE approach, presents Buchanan’s reconstruction of the Coase theorem along subjectivist-contractarian lines and gives an overview of recent contributions to the literature. JEL classification: B41, D70, H10, K; Keywords: Constitutional Economics, Constitutional Political Economy, Public Choice, James M. Buchanan, Methodological FoundationLaw and Economics, Constitutional Economics

A THEORY OF RATIONAL CHOICE UNDER COMPLETE IGNORANCE

This paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing ""limited information."" Specifically, we consider the limiting case of ""Complete Ignorance"" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. ""Rationality"" is conceptualized in terms of a ""Principle of Preference-Basedness,"" according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called ""Simultaneous Expected Utility Maximization"" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).