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Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$…
Wordle is a single-player word-based game where the objective is to guess the 5-letter word in a maximum of 6 tries. The game was released to the public in October 2021 and has since gained popularity with people competing against each…
The multilayer garbage disposal game is an evolution of the garbage disposal game. Each layer represents a social relationship within a system of finitely many individuals and finitely many layers. An agent can redistribute their garbage…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
Character diversity in competitive games, while enriching gameplay, often introduces balance challenges that can negatively impact player experience and strategic depth. Traditional balance assessments rely on aggregate metrics like win…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
A Subtraction-Division game is a two player combinatorial game with three parameters: a set S, a set D, and a number n. The game starts at n, and is a race to say the number 1. Each player, on their turn, can either move the total to n-s…
Multiple Artificial Intelligence (AI) methods have been proposed over recent years to create controllers to play multiple video games of different nature and complexity without revealing the specific mechanics of each of these games to the…
The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often…
Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(log(N)) complexity. We…
In real-world social systems, individual interactions are frequently shaped by reputation, which not only influences partner selection but also affects the nature and benefits of the interactions themselves. We propose a heterogeneous game…
Creating and evaluating games manually is an arduous and laborious task. Procedural content generation can aid by creating game artifacts, but usually not an entire game. Evolutionary game design, which combines evolutionary algorithms with…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…
We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions,…