Related papers: Analytical solution of $k$th price auction

This paper is merged with arXiv:2107.08965v2. We refer the reader to the full and updated version. We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an…

We study the price competition in a duopoly with an arbitrary number of buyers. Each seller can offer multiple units of a commodity depending on the availability of the commodity which is random and may be different for different sellers.…

We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and…

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear…

We consider a market in which both suppliers and consumers compete for a product via scalar-parameterized supply offers and demand bids. Scalar-parameterized offers/bids are appealing due to their modeling simplicity and desirable…

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 the distributed Nash equilibrium seeking for aggregative games has been studied over strongly connected and weight-balanced static networks and every time strongly connected and weight-balanced switching networks. In this…

Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…

This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting) with greedy or optimal allocation combined with generalized second-price (GSP) or Vickrey-Clarke-Groves (VCG) pricing. We make three…

We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…

In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player's payoff is the number of customers assigned to it.…

The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular,…

We generalize the classic problem of fairly allocating indivisible goods to the problem of \emph{fair public decision making}, in which a decision must be made on several social issues simultaneously, and, unlike the classic setting, a…

We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the…

This paper provides a comprehensive convergence analysis of the PoA of both pure and mixed Nash equilibria in atomic congestion games with unsplittable demands.

We study the efficiency of the proportional allocation mechanism, that is widely used to allocate divisible resources. Each agent submits a bid for each divisible resource and receives a fraction proportional to her bids. We quantify the…

The recent online platforms propose multiple items for bidding. The state of the art, however, is limited to the analysis of one item auction without resubmission. In this paper we study multi-item lowest unique bid auctions (LUBA) with…

We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…

In quasi-proportional auctions, each bidder receives a fraction of the allocation equal to the weight of their bid divided by the sum of weights of all bids, where each bid's weight is determined by a weight function. We study the…

We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out…