Related papers: Game arguments in computability theory and algorit…
Given the scale of consequences attributable to cyber attacks, the field of cybersecurity has long outgrown ad-hoc decision-making. A popular choice to provide disciplined decision-making in cybersecurity is Game Theory, which seeks to…
We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are…
We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and…
Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits…
Negotiations, a model of concurrency with multi party negotiation as primitive, have been recently introduced in arXiv:1307.2145, arXiv:1403.4958. We initiate the study of games for this model. We study coalition problems: can a given…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom,…
Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
We present a game-theoretic perspective on the problems of quantum state estimation and quantum cloning. This enables us to show why the focus on universal machines and the different measures of success, as employed in previous works, are…
This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash…
We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Games Conjecture. The variant, which we call Count Unique Games,…
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…
Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
Game-theoretic approaches are envisioned to bring human-like reasoning skills and decision-making processes for autonomous vehicles (AVs). However, challenges including game complexity and incomplete information still remain to be addressed…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…