In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of distributional preferences of the contest designer. In contests with complete information, the representation significantly simplifies the characterization of the equilibria.
The ethic of proportional redistribution is a compromise between the extremely compensatory ethic of full redistribution and the needs-blind ethic of laissez-faire. In a basic model of redistribution problems with needs, we characterize proportional redistribution with a combination of axioms that formalize minimal requirements of accountability, functionality, and impartiality. Consequently, we provide a new ethical rationalization for the ancient Aristotelian maxim of proportionality.
We introduce a new microeconomics foundation of a specific type of competitive market equilibrium that can be used to study several markets with information asymmetry such as commodity market, credit market, and insurance market.
In this paper, we analyze how global optima of an agent's preferences can be reconstructed from the solutions found for local problems. A sheaf-theoretic analysis provides an abstract characterization of the global solution, and polynomial approximations are obtained when only a few local instances are available.
Adding a capacity constraint to a hidden-action principal-agent problem results in the same set of Pareto optimal contracts as the unconstrained problem where output is scaled down by a constant factor. This scaling factor is increasing in the agent's capacity to exert effort.
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential experiment to dominate another in the sense that the dominant experiment is preferred to the other for any decision problem in the specified class. We use these results to study the timing of information arrival in additively separable problems.
This paper introduces an explicit algorithm for computing perfect public equilibrium (PPE) payoffs in repeated games with imperfect public monitoring, public randomization, and discounting. The method adapts the established framework by Abreu, Pearce, and Stacchetti (1990) into a practical tool that balances theoretical accuracy with computational efficiency. The algorithm simplifies the complex task of identifying PPE payoff sets for any given discount factor δ. A stand-alone implementation of the algorithm can be accessed at: https://github.com/jasmina-karabegovic/IRGames.git.
I propose a new approach to solving standard screening problems when the monotonicity constraint binds. A simple geometric argument shows that when virtual values are quasi-concave, the optimal allocation can be found by appropriately truncating the solution to the relaxed problem. I provide an algorithm for finding this optimal truncation when virtual values are concave.
In this paper, we consider an environment in which the utilitarian theorem for the NM utility function derived by Harsanyi and the utilitarian theorem for Alt's utility function derived by Harvey hold simultaneously, and prove that the NM utility function coincides with Alt's utility function under this setup. This result is so paradoxical that we must presume that at least one of the utilitarian theorems contains a strong assumption. We examine the assumptions one by one and conclude that one of Harsanyi's axioms is strong.
The idea of this paper comes from the famous remark of Piketty and Zuckman: "It is natural to imagine that $σ$ was much less than one in the eighteenth and nineteenth centuries and became larger than one in the twentieth and twenty-first centuries. One expects a higher elasticity of substitution in high-tech economies where there are lots of alternative uses and forms for capital." The main aim of this paper is to prove the existence of a production function of variable elasticity of substitution with values greater than one.
In this discussion draft, we explore heterogeneous oligopoly games of increasing players with quadratic costs, where the market is supposed to have the isoelastic demand. For each of the models considered in this draft, we analytically investigate the necessary and sufficient condition of the local stability of its positive equilibrium. Furthermore, we rigorously prove that the stability regions are enlarged as the number of involved firms is increasing.
Choice functions over a set $X$ that satisfy the Outcast, a.k.a. Aizerman, property are exactly those that attach to any set its maximal subset relative to some total order of ${2}^{X}$.
We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.
Always, if the number of states is equal to two; or if the number of receiver actions is equal to two and i. The number of states is three or fewer, or ii. The game is cheap talk, or ii. There are just two available messages for the sender. A counterexample is provided for each failure of these conditions.
We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -- in terms of number of assignments -- in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium.
We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we investigate some existing models and propose a new one as special cases of the general $n$-dimensional Lotka-Volterra system of eco-dynamics.