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We propose a new dynamics for equilibrium selection of finite player discrete strategy games. The dynamics is motivated by optimal transportation, and models individual players' myopicity, greedy and uncertainty when making decisions. 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…
The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing…
We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…
How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing.…
For effective matching of resources (e.g., taxis, food, bikes, shopping items) to customer demand, aggregation systems have been extremely successful. In aggregation systems, a central entity (e.g., Uber, Food Panda, Ofo) aggregates supply…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
In this paper we consider a stochastic game for modelling the interactions between smugglers and a patroller along a border. The problem we examine involves a group of cooperating smugglers making regular attempts to bring small amounts of…
Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing…
Lane changes are complex safety and throughput critical driver actions. Most lane changing models deal with lane-changing maneuvers solely from the merging driver's standpoint and thus ignore driver interaction. To overcome this…
The Team-maxmin equilibrium prescribes the optimal strategies for a team of rational players sharing the same goal and without the capability of correlating their strategies in strategic games against an adversary. This solution concept can…
Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given…
First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…
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…
This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
We consider a class of adversarial classification problems in the form of zero-sum games between a classifier and an adversary. The latter is able to corrupt data, at the expense of some optimal transport cost. We show that quite general…
In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who…
In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…
We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…