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We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…
Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…
A human-centered robot needs to reason about the cognitive limitation and potential irrationality of its human partner to achieve seamless interactions. This paper proposes an anytime game-theoretic planner that integrates iterative…
Noncooperative games with uncertain payoffs have been classically studied under the expected-utility theory framework, which relies on the strong assumption that agents behave rationally. However, simple experiments on human decision makers…
Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
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…
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…
This paper discusses a special type of multi-user communication scenario, in which users' utilities are linearly impacted by their competitors' actions. First, we explicitly characterize the Nash equilibrium and Pareto boundary of the…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
Blockchain-based smart contracts offer a new take on credible commitment, where players can commit to actions in reaction to actions of others. Such reaction-function games extend on strategic games with players choosing reaction functions…
The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
We propose a multi-agent based computational framework for modeling decision-making and strategic interaction at micro level for smart vehicles in a smart world. The concepts of Markov game and best response dynamics are heavily leveraged.…
We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum…
While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…
We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic…