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A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players,…
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…
We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…
We prove that for any 3-player game $\mathcal G$, whose query distribution has the same support as the GHZ game (i.e., all $x,y,z\in \{0,1\}$ satisfying $x+y+z=0\pmod{2}$), the value of the $n$-fold parallel repetition of $\mathcal G$…
The so called \emph{quantum game theory} has recently been proclaimed as one of the new branches in the development of both quantum information theory and game theory. However, the notion of a quantum game itself has never been strictly…
In this thesis, we answer several questions about the behaviour of prover-verifier interactions under parallel repetition when quantum information is allowed, and the verifier acts independently in them. We first consider the case in which…
Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We…
Proof-Number Search is a best-first search algorithm with many successful applications, especially in game solving. As large-scale computing clusters become increasingly accessible, parallelization is a natural way to accelerate…
We investigate a phenomenon of "one-to-two-player lifting" in infinite-duration two-player games on graphs with zero-sum objectives. More specifically, let $C$ be a class of strategies. It turns out that in many cases, to show that all…
We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…
We present a scheme for playing quantum repeated 2x2 games based on the Marinatto and Weber's approach to quantum games. As a potential application, we study twice repeated Prisoner's Dilemma game. We show that results not available in…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
In this work we study rank-one quantum games. In particular, we focus on the study of the computability of the entangled value $\omega^*$. We show that the value $\omega^*$ can be efficiently approximated up to a multiplicative factor of 4.…
Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives.…
We study algorithms for solving parity, mean-payoff and energy games. We propose a systematic framework, which we call Fast value iteration, for describing, comparing, and proving correctness of such algorithms. The approach is based on…
We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…