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Building upon the results in [Hinterm\"uller et al., SIAM J. Optim, '15], generalized Nash equilibrium problems are considered, in which the feasible set of each player is influenced by the decisions of their competitors. This is realized…
In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer, or a group of producers, can attain depends on the amount of common-pool…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
The paper deals with a class of parametrized equilibrium problems, where the objectives of the players do possess nonsmooth terms. The respective Nash equilibria can be characterized via a parameter-dependent variational inequality of the…
This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…
We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a…
We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…
This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility…
We discuss and solve a model for a game with many players, where a subset of truely deciding players is embedded into a hierarchy of dependent agents. These interdependencies modify the game matrix and the Nash equilibria for the deciding…
We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance…
We define and study a lending game to model the interbank money market, in which lending banks strategically allocate their cash to borrowing banks. The interest rate offered by each borrowing bank is within the interest rate corridor set…
In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within…
This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best…
We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the…
We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
Convertible instruments are contracts, used in venture financing, which give investors the right to receive shares in the venture in certain circumstances. In liquidity events, investors may have the option to either receive back their…