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Applications of combinatorial auctions (CA) as market mechanisms are prevalent in practice, yet their Bayesian Nash equilibria (BNE) remain poorly understood. Analytical solutions are known only for a few cases where the problem can be…
This work investigates a problem of simultaneous global cost minimization and Nash equilibrium seeking, which commonly exists in $N$-cluster non-cooperative games. Specifically, the agents in the same cluster collaborate to minimize a…
We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other…
This article presents a detailed technical framework for modeling with Bertrand-Nash equilibrium prices under Mixed Logit demand. Two coercive fixed-point equations provide more stable computational methods than those obtained from the…
In this paper, we present a new model and two mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments, and is applicable to a wide…
The study of equilibrium concepts in congestion games and two-sided markets with ties has been a primary topic in game theory, economics, and computer science. Ackermann, Goldberg, Mirrokni, R\"oglin, V\"ocking (2008) gave a common…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We study stochastic Nash equilibrium problems with expected valued cost functions whose pseudogradient satisfies restricted monotonicity properties which hold only with respect to the solution. We propose a forward-backward algorithm and…
Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
Reinforcement learning has been shown to be an effective strategy for automatically training policies for challenging control problems. Focusing on non-cooperative multi-agent systems, we propose a novel reinforcement learning framework for…
Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple…
Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of prior-free auction and focus on…
This paper uses Nash equilibrium reversion as an optimal tool for clearing dynamic prices and wages. Various exogenous competitive rigidities determine the balanced growth path of the efficiency wage and the outcome of repeated…
In a multi-unit market, a seller brings multiple units of a good and tries to sell them to a set of buyers that have monetary endowments. While a Walrasian equilibrium does not always exist in this model, natural relaxations of the concept…
Integrated hydrogen-enriched compressed natural gas (HCNG) and active distribution network (ADN) is providing efficient and sustainable flexibility for consuming renewable energies. Yet, cross-sector privacy and uncertain high-renewable…
The all-pay auction, a classic competitive model, is widely applied in scenarios such as political elections, sports competitions, and research and development, where all participants pay their bids regardless of winning or losing. However,…
Additively separable hedonic games (ASHGs) are a prominent model of coalition formation where agents' preferences are derived from their individual valuations of peers. While social welfare maximization in ASHGs has traditionally focused…
In the first-order query model for zero-sum $K\times K$ matrix games, players observe the expected pay-offs for all their possible actions under the randomized action played by their opponent. This classical model has received renewed…
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…