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Recently Cole and Gkatzelis gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash Social Welfare. We give constant factor…
We study the problem of maximizing Nash social welfare, which is the geometric mean of agents' utilities, in two well-known models. The first model involves one-sided preferences, where a set of indivisible items is allocated among a group…
Prices of tradables can only be expressed relative to each other at any instant of time. This fundamental fact should therefore also hold for contigent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables.…
We study the relationship between two central concepts in the allocation of divisible goods: competitive equilibrium (CE) and allocations that maximize Nash welfare, i.e., allocations where the weighted geometric mean of the utilities is…
We solve the two-player bargaining problem employing Weber's law in psychophysics, which is applied to the perception of utility changes. Using this law, the players define the jointly acceptable range of utilities on the Pareto line, which…
We consider the problem of allocating a set of divisible goods to $N$ agents in an online manner, aiming to maximize the Nash social welfare, a widely studied objective which provides a balance between fairness and efficiency. The goods…
This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
Nash equilibrium is a common solution concept that captures strategic interaction in electricity market analysis. However, it requires a fundamental but impractical assumption that all market participants are fully rational, implying…
In cooperative games with transferable utilities, the Shapley value is an extreme case of marginalism while the Equal Division rule is an extreme case of egalitarianism. The Shapley value does not assign anything to the non-productive…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
We investigate a portfolio selection problem involving multi competitive agents, each exhibiting mean-variance preferences. Unlike classical models, each agent's utility is determined by their relative wealth compared to the average wealth…
We study the problem of efficiently and fairly allocating a set of indivisible goods among agents with identical and additive valuations for the goods. The objective is to maximize the Nash social welfare, which is the geometric mean of the…
In bandwidth allocation, competing agents wish to transmit data along paths of links in a network, and each agent's utility is equal to the minimum bandwidth she receives among all links in her desired path. Recent market mechanisms for…
This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact…
We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and…
In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio-economic models is usually thought to…