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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…
Equilibrium finding in two-player zero-sum games with perfect recall is a well-studied topic that has led to many breakthroughs in computational game theory. This paper aims to generalize such techniques to (timeable) two-player zero-sum…
We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial…
In interactive multi-agent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained…
Multi-turn LLM evaluation is typically reported as a single win-rate scalar, conflating distinct capabilities. We introduce AIDG (Adversarial Information Deduction Game), formalizing multi-turn adversarial dialogue as a two-player partially…
Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable…
We address in this paper Reinforcement Learning (RL) among agents that are grouped into teams such that there is cooperation within each team but general-sum (non-zero sum) competition across different teams. To develop an RL method that…
This paper aims to solve the optimal strategy against a well-known adaptive algorithm, the Hedge algorithm, in a finitely repeated $2\times 2$ zero-sum game. In the literature, related theoretical results are very rare. To this end, we make…
Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…
The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…
Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…
Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…
We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume…
Many real-world applications involve some agents that fall into two teams, with payoffs that are equal within the same team but of opposite sign across the opponent team. The so-called two-team zero-sum Markov games (2t0sMGs) can be…
Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the…
Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of…
We introduce a simple extensive-form algorithm for finding equilibria of two-player, zero-sum games. The algorithm is realization equivalent to a generalized form of Fictitious Play. We compare its performance to that of a similar…
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…
Synthesizing near-optimal mixed strategies for zero-sum differential games (ZSDGs) has been a longstanding challenge. Existing research mainly focuses on characterizing the theoretical value function, while the practical design of…
The multi-cluster games are addressed in this paper, where all players team up with the players in the cluster that they belong to, and compete against the players in other clusters to minimize the cost function of their own cluster. The…