Related papers: Computing the Strategy to Commit to in Polymatrix …

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…

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…

This paper studies multi-user communication systems with two groups of users: leaders which possess system information, and followers which have no system information using the formulation of Stackelberg games. In such games, the leaders…

The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…

This paper is an exposition of algorithms for finding one or all equilibria of a bimatrix game (a two-player game in strategic form) in the style of a chapter in a graduate textbook. Using labeled "best-response polytopes", we present the…

Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…

One of the most appealing aspects of the (coarse) correlated equilibrium concept is that natural dynamics quickly arrive at approximations of such equilibria, even in games with many players. In addition, there exist polynomial-time…

In 1996, Mallozzi and Morgan [33] proposed a new model for Stackelberg games which we refer here to as the Bayesian approach. The leader has only partial information about how followers select their reaction among possibly multiple optimal…

The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…

Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity…

To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…

Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

An important challenge in non-cooperative game theory is coordinating on a single (approximate) equilibrium from many possibilities - a challenge that becomes even more complex when players hold private information. Recommender mechanisms…

Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…

Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm…