Related papers: Mathematical Go: Revisited
In this paper we present a new theoretical model to find out an optimal weight associated with a soccer player under the presence of a stochastic goal dynamics by using Feynman path integral method, where the action of a player is on…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
As the earliest and one of the most fundamental learning dynamics for computing NE, fictitious play (FP) has being receiving incessant research attention and finding games where FP would converge (games with FPP) is one central question in…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
We extend the Fundamental Theorem of Epistemic Game Theory to games with Baire class one payoffs and locally compact Polish strategy spaces, and under Projective Determinacy, to games with analytically measurable payoffs and arbitrary…
We present new game semantics of Martin-L\"of type theory (MLTT) equipped with One-, Zero-, N-, Pi-, Sigma- and Id-types. Our game semantics interprets MLTT more accurately than existing ones. Another advantage of our game semantics over…
Multiagent decision-making in partially observable environments is usually modelled as either an extensive-form game (EFG) in game theory or a partially observable stochastic game (POSG) in multiagent reinforcement learning (MARL). One…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
Scoring rules serve to quantify predictive performance. A scoring rule is proper if truth telling is an optimal strategy in expectation. Subject to customary regularity conditions, every scoring rule can be made proper, by applying a…
This article is a prologue to the article "Why Markets are Inefficient: A Gambling 'Theory' of Financial Markets for Practitioners and Theorists." It presents important background for that article --- why gambling is important, even…
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…
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital processes corresponding to available betting strategies.…
Esports, despite its expanding interest, lacks fundamental sports analytics resources such as accessible data or proven and reproducible analytical frameworks. Even Counter-Strike: Global Offensive (CSGO), the second most popular esport,…
We prove that to find optimal positional strategies for stochastic mean payoff games when the value of every state of the game is known, in general, is as hard as solving such games tout court. This answers a question posed by Daniel…
We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…
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…
Game Theory (GT) has been used with significant success to formulate, and either design or optimize, the operation of many representative communications and networking scenarios. The games in these scenarios involve, as usual, diverse…
Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a…
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe…