Semih Koray

Self‐Selective Social Choice Functions Verify Arrow and Gibbard‐Satterthwaite Theorems

This paper introduces a new notion of consistency for social choice functions, called self-selectivity, which requires that a social choice function employed by a society to make a choice from a given alternative set it faces should choose itself from among other rival such functions when it is employed by the society to make this latter choice as well. A unanimous neutral social choice function turns out to be universally self-selective if and only if it is Paretian and satisfies independence of irrelevant alternatives. The neutralunanimous social choice functions whose domains consist of linear order profiles on nonempty sets of any finite cardinality induce a class of social welfare functions that inherit Paretianism and independence of irrelevant alternatives in case the social choice function with which one starts is universally self-selective. Thus, a unanimous and neutral social choice function is universally self-selective if and only if it is dictatorial. Moreover, universal self-selectivity for such functions is equivalent to the conjunction of strategy-proofness and independence of irrelevant alternatives or the conjunction of monotonicity and independence of irrelevant alternatives again.

Characterization of self-selective social choice functions on the tops-only domain

Abstract. Self-selectivity is a new kind of consistency pertaining to social choice rules. It deals with the problem of whether a social choice rule selects itself from among other rival such rules when a society is also to choose the choice rule that it will employ in making its choice from a given set of alternatives. Koray [3] shows that a neutral and unanimous social choice function is universally self-selective if and only if it is dictatorial. In this paper, we confine the available social choice functions to the tops-only domain and examine whether such restriction allow us to escape the dictatoriality result. A neutral, unanimous, and tops-only social choice function, however, turns out to be self-selective relative to the tops-only domain if and only if it is top-monotonic, and thus again dictatorial.

Job matching: a multi-principal, multi-agent model

A version of Spence’s “job market” model is constructed and studied: There are two groups of individuals, the job applicants (the informed), and the incumbents (the uninformed). The applicants have private information about their types, and their actions (choice of education levels) serve as messages. The incumbents (employers) have only one type, and are endowed with differentiated information structures on actions of the informed. A contract is a pair of an education level and a wage level, and a wage schedule specifies a contract for each education level. The incumbent set is finite, and is fixed throughout the analysis (so free entry/exit is excluded). The paper studies endogenous determination of the wage schedules offered by the incumbents. The applicants behave noncooperatively. Two equilibrium concepts are proposed: a noncooperative equilibrium, a version of the Nash equilibrium which postulates noncooperative and passive behavior of the incumbents, and a cooperative equilibrium, a version of the strong equilibrium which postulates cooperative and passive behavior of the incumbents. It is shown that a cooperative equilibrium does not exist. By studying noncooperative equilibria, which do exist in many cases, it is concluded that it is not the informational advantage (defined as the abundance of measurable sets), but rather possession of the right information (in the sense that it best serves the needs of applicants) that enables an incumbent to win.

Bayesian Regulatory Mechanisms: Corruption and Learning

Regulation can be described as central interference with industrial activities, aiming to achieve social efficiency when it cannot be reached through the market by itself. This area of economics basically deals with the design of artificial rules under which outcomes which otherwise can only be attained through cooperation can be reached through the non-cooperative and decentralized behaviour of agents. Although the theory of regulation can be traced back to Hotelling (1938) and Dupuit (1952), it is only in the past two decades that it gained a crucial impetus through its formulation within the game-theoretic framework of mechanism design. It is even more recently that the principal—agent setting has been employed in this area to treat the asymmetry of information between the regulating and the regulated agents.

Implementation via rights structures

Abstract Implementation of socially desirable alternatives can be thought of as a way to design power distribution in a society such that the equilibrium outcomes coincide with the alternatives chosen at each preference profile. In this paper, we introduce a new institutional framework for implementation, which takes power distribution in a society as its point of departure. We use the notion of a rights structure, introduced by Sertel (2001) , to formalize the power distribution in a society. We formulate and characterize implementability via rights structures under different specifications, which require having well-defined convergence dynamics and being consistent with farsighted behavior. We identify how implementation via rights structures is related to implementation via mechanisms. In the presence of at least three agents, we find the class of rights structures, implementability via which is equivalent to Nash and strong Nash implementability. We also introduce a strategic counterpart of implementation via rights structures in terms of deviation-constrained mechanisms.

Maskin-monotonic scoring rules

We characterize which scoring rules are Maskin-monotonic for each social choice problem as a function of the number of agents and the number of alternatives. We show that a scoring rule is Maskin-monotonic if and only if it satisfies a certain unanimity condition. Since scoring rules are neutral, Maskin-monotonicity turns out to be equivalent to Nash-implementability within the class of scoring rules. We propose a class of mechanisms such that each Nash-implementable scoring rule can be implemented via a mechanism in that class. Moreover, we investigate the class of generalized scoring rules and show that with a restriction on score vectors, our results for the standard case are still valid.