Murat R. Sertel

Advances in economic design

A: Social Choice and Electoral Systems.- Selecting a Social Choice Rule - An Exploratory Panel Study.- Weighted Scoring Rules That Maximize Condorcet Efficiency.- Incentive Contracts and Elections for Politicians and the Down-Up Problem.- B : Buyers and Sellers.- On Determination of Optimal Reserve Price in Auctions with Common Knowledge about Ranking of Valuations.- On Auctions with Interest Linkages among Bidders.- Substitutes, Complements, and Equilibrium in Two-Sided Market Models.- Core Convergence in Two-Sided Matching Markets.- C: Bargaining.- Can and Should the Nash Program Be Looked at as a Part of Mechanism Theory?.- Impossibility of a Walrasian Bargaining Solution.- Characterization of Competitive Allocations and the Nash Bargaining Problem.- Kalai-Smorodinsky and Maschler-Perles Solutions under Pre-donation.- D: Coalitional Stability and Efficiency.- Stable Cartel Structures in a Dismantling Game.- A Sequential Approach to the Characteristic Function and the Core in Games with Externalities.- Coalition Structural Games and the Voluntary Provision of Public Goods.- E: Regulating and Organizing Markets.- Regulation and Markets for Catastrophe Insurance.- Incentive Compatible Regulation of Quality Provision by Natural Monopolies - The Role of Technical Progress.- On the Importance of Sequencing of Markets in Monetary Economies.- F: Designing Rights.- The Stability and Efficiency of Economic and Social Networks.- Designing Severance Payments and Decision Rights for Efficient Plant Closure under Profit-Sharing.- Moral Hazard and Linear Contracts: Economies with Idiosyncratic Risks.- Equal Awards vs. Equal Losses: Duality in Bankruptcy.- G: Information.- Mechanism Design without Games.- Hierarchy Size and Environmental Uncertainty.

Manipulating Lindahl equilibrium via endowments

Abstract Simple examples of two- and three-person economies with a single private and a single public good are presented to show that the Lindahl equilibrium is individually manipulable, by donation , by destruction and by hiding of ones endowment, as well as coalitionally manipulable by intra-coalitional reallocation of endowments.

Strong equilibrium outcomes of voting games are the generalized Condorcet winners

Abstract.We consider voting games induced by anonymous and top-unanimous social choice functions. The class of such social choice functions is quite broad, including every “t-refinement” of the Plurality Rule, Plurality with a Runoff, the Majoritarian Compromise and the Single Transferable Vote, i.e., any selection from either of these social choice rules which is obtained via tie-breaking among candidates according to any total order t on the set of alternatives. As announced in our title, the strong equilibrium outcomes of the voting games determined by such social choice functions turn out to be nothing but generalized Condorcet winners, namely the “(n,q)-Condorcet winners”. In the case of social choice functions (such as those just listed) which are furthermore “top-majoritarian”, they coincide with the classical Condorcet winners.

Designing Mechanisms, in Particular for Electoral Systems: The Majoritarian Compromise

The Majoritarian Compromise proposal, aside from its substantive merits, provides an opportunity to illustrate various aspects of mechanism and institution design, and, in particular, to clarify the concepts used in the analysis of design. Many of these concepts also underlie models used in economic analysis. What follows is an outline of some of the issues.

Manipulability of the Men-(Women) Optimal Matching Rule via Endowments

Abstract We consider matching problems with endowments and analyze the manipulability of the men-optimal and the women-optimal matching rule via hiding, perfect hiding, destruction, and predonation of endowments. We show that the men- (resp., women-) optimal matching rule is manipulable by women (resp., men) via both types of hiding, as well as by destruction and by predonation of their endowments. In contrast, so long as the hidden part of one’s endowment cannot be consumed alone, a man (resp., woman) can manipulate the men- (resp., women-) optimal matching rule only by predonating a portion of his (resp., her) initial endowment (to men or women). We consider the manipulability of matching rules under monotonic consumption rules. We show that the men-optimal matching rule is non-manipulable via hiding by a man under any monotonic consumption rule. We also characterize the maximal subclass of monotonic consumption rules under which a woman can manipulate the men-optimal matching rule via destruction (or via hiding). We offer a similar analysis for the manipulability of the men-optimal matching rule via perfect hiding.

Comparison and choice

This paper develops the idea of a choice as a mapping of subsets of a set X into their respective subsets and the idea of the comparison, as a relation between elements of X, that is determined or ‘revealed’ by a choice. It then studies how certain properties of a choice imply or are implied by certain properties, such as acyclicity, quasi-transitivity, pseudo-transitivity and transitivity, of the comparison revealed, finally giving a complete logical diagram of all the implications between these latter properties of the comparison.

(Topological) Semivector Spaces: Convexity and Fixed Point Theory

Without speaking too roughly, (topological) semivector spaces are to (topological) semigroups as (topological) vector spaces are to (topological) groups. In Section 1 we introduce the notion of a (topological) semivector space. In Section 2 we study convexity in semivector spaces, in particular “Pointwise convexity,” i.e., convexity of singletons. The main results of the section are astructuretheorem (2.7), acancellationtheorem (2.11), and anembeddingtheorem (2.14). In Section 3 we identify and briefly study a hierarchy of local convexity properties in topological semivector spaces. Lastly, in Section 4 we presentfixedpointtheorems for compact convex subsets enjoying one or another local convexity property in a pointwise convex topological semivector space, indicating associatedminmaxtheorems.

Regulating a duopoly by a Pretend-but-Perform Mechanism

Abstract In a linear duopoly, participants are required to declare their costs under a Pretend—but—Perform Mechanism (PPM) which enforces accordance of performance with pretended (declared) cost. Specifically, under the PPM, each firms output in reaction to rival output is to maximize profit according to declared cost. Compared with the Cournot solution before PPM Regulation, Nash implementation of the PPM induces a Cournot solution, among the make—believe firms, giving greater industry output and efficiency along with increased consumer surplus even after compensating the duopolists for decreased profits, except in a trivial case which — educatively — thruthful declarations are confined.

Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.

A non-dictatorial compromise

Abstract aggregations are defined and pertinent conditions of decisiveness, anonymity, unanimity, independence of irrelevant alternatives (stronger than the Arrowian) and non-dictatoriality (logically independent of the Arrowian) are developed for aggregations of choices. The mode is identified as a compromise aggregating variable societies of choices into a social choice, and it is shown (Theorem 4.1) to satisfy these conditions. This non-dictatorial compromise is then characterized (Theorem 5.1) in terms of three axioms paralleling those characterizing the approval voting of Sertel [7].