Related papers: Binary Choice Games and Arithmetical Comprehension
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…
Among the strategic choices made by today's economic actors are choices about algorithms and computational resources. Different access to computational resources may result in a kind of economic asymmetry analogous to information asymmetry.…
There is a common belief that humans and many animals follow transitive inference (choosing A over C on the basis of knowing that A is better than B and B is better than C). Transitivity seems to be the essence of rational choice. We…
We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…
We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is $\mathrm{NP}$-complete to decide whether the classical value of a non-local game is 1 or $1- \epsilon$.…
The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation…
We consider infinite-state turn-based stochastic games of two players, Box and Diamond, who aim at maximizing and minimizing the expected total reward accumulated along a run, respectively. Since the total accumulated reward is unbounded,…
We show that every two-player stochastic game with finite state and action sets and bounded, Borel-measurable, and shift-invariant payoffs, admits an $\ep$-equilibrium for all $\varepsilon>0$.
Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…
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…
We present a formalization of Borel determinacy in the Lean 4 theorem prover. The formalization includes a definition of Gale-Stewart games and a proof of Martin's theorem stating that Borel games are determined. The proof closely follows…
Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…
We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
This article presents a unified probabilistic framework that allows both rational and irrational decision making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of…
We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily…
We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…