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We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the…
We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of strategies using arbitrarily…
We consider approximating the minmax value of a multi-player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of epsilon log n digits (for any constant epsilon>0 is…
Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have…
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…
Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum…
We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random…
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…
Fictitious Play (FP) is a simple and natural dynamic for repeated play in zero-sum games. Proposed by Brown in 1949, FP was shown to converge to a Nash Equilibrium by Robinson in 1951, albeit at a slow rate that may depend on the dimension…
We show equivalences between several high-dimensional problems in extremal combinatorics and parallel repetition of multiplayer (multiprover) games over large answer alphabets. This extends the forbidden-subgraph technique, previously…
We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
We study Stackelberg equilibria in finitely repeated games, where the leader commits to a strategy that picks actions in each round and can be adaptive to the history of play (i.e. they commit to an algorithm). In particular, we study…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of $m$ priceable edges in a graph. The other edges have a fixed cost. Based on the leader's decision one or more…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between $\Pi^1_2$ principles over $\omega$-models of…
In Zeng et al. [Fluct. Noise Lett. 7 (2007) L439--L447] the analysis of the lowest unique positive integer game is simplified by some reasonable assumptions that make the problem tractable for arbitrary numbers of players. However, here we…
In this paper, we generalize to three players the well-known CHSH quantum game. To do so, we consider all possible 3 variables Boolean functions and search among them which ones correspond to a game scenario with a quantum advantage (for a…