Do supermajority rules really deter extremism? the role of electoral competition

This study investigates how supermajority rules in a legislature affect electoral competition. We construct an extensive-form game wherein parties choose policy platforms in an election. Post election, the policy is determined based on a legislative voting rule. At symmetric equilibrium, supermajority rules induce divergence of policy platforms if and only if the parties are sufficiently attached to their preferred platform. Thus, supermajority rules may not always lead to moderate policies once electoral competition is considered.

Reactive Strategies: An Inch of Memory, a Mile of Equilibria

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash Equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

Auctioning risk: the all-pay auction under mean-variance preferences

We analyse the all-pay auction with incomplete information and variance-averse bidders. We characterise the unique symmetric equilibrium for general distributions of valuations and any number of bidders. Variance aversion is a sufficient assumption to predict that high-valuation bidders increase their bids relative to the risk-neutral case while low types decrease their bid. Considering an asymmetric two-player environment with uniformly distributed valuations, we show that a variance-averse player always bids higher than her risk-neutral opponent with the same valuation. Utilising our analytically derived bidding functions we discuss all-pay auctions with variance-averse bidders from an auction designer’s perspective. We briefly consider possible extensions of our model, including noisy signals, type-dependent attitudes towards risk, and variance-seeking preferences.

Simultaneous Search for Differentiated Products: The Impact of Search Costs and Firm Prominence

We extend the literature on simultaneous search by allowing for differentiated products and search cost heterogeneity. We show conditions under which a symmetric price equilibrium exists. We provide a necessary and sufficient condition under which an increase in search costs may result in a lower, equal or higher equilibrium price. We extend this analysis to the case with more than two firms. The effects of prominence on equilibrium prices are also studied. The prominent firm charges a higher price than the non-prominent firm and both their prices are below the symmetric equilibrium price. Consequently, market prominence increases the consumers’ surplus.

First‐price auctions with budget constraints

Consider a first‐price sealed‐bid auction with interdependent valuations and private budget constraints. Focusing on the two‐bidder case, we identify new sufficient conditions for the existence of a symmetric equilibrium in pure strategies. In equilibrium, agents may adopt discontinuous bidding strategies that result in a stratification of competition along the budget dimension. Private budgets can simultaneously lead to more aggressive bidding (a high‐budget agent leverages his wealth to outbid rivals) and more subdued bidding (competition becomes less intense among bidders at distinct budget levels). The presence of budget constraints may lead to multiple symmetric equilibria in the first‐price auction.

Soft Floors in Auctions

Several of the auction-driven exchanges that facilitate programmatic buying of internet display advertising have recently introduced “soft floors” in addition to standard reserve prices (called “hard floors” in the industry). A soft floor is a bid level below which a winning bidder pays his own bid instead of paying the second-highest bid as in a second-price auction most ad exchanges use by default. This paper characterizes soft floors’ revenue-generating potential as a function of the distribution of bidder independent private values. When bidders are symmetric (identically distributed), soft floors have no effect on revenue, because a symmetric equilibrium always exists in strictly monotonic bidding strategies, and standard revenue-equivalence arguments thus apply. The industry often motivates soft floors as tools for extracting additional expected revenue from an occasional high bidder, for example a bidder retargeting the consumer making the impression. Such asymmetries in the distribution of bidder preferences do not automatically make soft floors profitable. This paper presents two examples of tractable modeling assumptions about such occasional high bidders, with one example implying low soft floors always hurt revenues because of strategic bid-shading by the regular bidders, and the other example implying high soft floors can increase revenues by making the regular bidders bid more aggressively. This paper was accepted by Juanjuan Zhang, marketing.

Strategic Remanufacturing under Competition

We investigate firms’ remanufacturing strategies for the case of a duopoly. On the one hand, remanufactured products cannibalize sales of new products of the same firm thereby hurting its profits. On the other hand, they can be part of a profitable marketing strategy that targets different customer preferences by providing a larger number of alternatives to customers. This paper studies the tradeoff between these effects and how it is influenced by competition. We develop a model where demand functions for new and remanufactured products of each firm are derived from utility maximization by a representative consumer. This allows us to capture preference and substitution effects between all offered products in the market. We discuss how equilibrium strategies are affected by factors such as competition, substitutability, production cost as well as remanufacturing cost. For example, when competitive intensity between new and new products, and remanufactured and remanufactured products, is (high), both (neither) firms offer remanufactured products in a symmetric equilibrium. If substitution between new and remanufactured products of the same firm is low, but the remanufactured product has a lower margin than the new product, firms can be worse off from remanufacturing.

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsas et al., Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helically symmetric one. As special cases, the derivation of the corresponding equilibrium equations for incompressible plasmas is discussed and the helically symmetric equilibrium equations for the Hall MHD system are obtained upon neglecting electron inertia. An example of an incompressible double-Beltrami equilibrium is presented in connection with a magnetic configuration having non-planar helical magnetic axis.