Related papers: Analytical solution of $k$th price auction
The fair division of resources is an important age-old problem that has led to a rich body of literature. At the center of this literature lies the question of whether there exist fair mechanisms despite strategic behavior of the agents. A…
The Nash Equilibrium is a much discussed, deceptively complex, method for the analysis of non-cooperative games. If one reads many of the commonly available definitions the description of the Nash Equilibrium is deceptively simple in…
We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled…
This paper establishes the Price of Stability (PoS) for First Price Auctions, for all equilibrium concepts that have been studied in the literature: Bayes Nash Equilibrium $\subsetneq$ Bayes Correlated Equilibrium $\subsetneq$ Bayes Coarse…
We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our…
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
The rise of automated bidding strategies in online advertising presents new challenges in designing and analyzing efficient auction mechanisms. In this paper, we focus on proportional mechanisms within the context of auto-bidding and study…
Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction,…
This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…
We study interactions with uncertainty about demand sensitivity. In our solution concept (1) firms choose seemingly-optimal strategies given the level of sophistication of their data analytics, and (2) the levels of sophistication form best…
In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal…
We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
We derive the rate of convergence to Nash equilibria for the payoff-based algorithm proposed in \cite{tat_kam_TAC}. These rates are achieved under the standard assumption of convexity of the game, strong monotonicity and differentiability…
In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed…
The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and…
In lowest unique bid auctions, $N$ players bid for an item. The winner is whoever places the \emph{lowest} bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium…
We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state…
Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…
We study a toy two-player game for periodic double auction markets to generate liquidity. The game has imperfect information, which allows us to link market spreads with signal strength. We characterize Nash equilibria in cases with or…