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Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which…
This paper introduces a model based upon games on an evolving network, and develops three clustering algorithms according to it. In the clustering algorithms, data points for clustering are regarded as players who can make decisions in…
The act of bluffing confounds game designers to this day. The very nature of bluffing is even open for debate, adding further complication to the process of creating intelligent virtual players that can bluff, and hence play, realistically.…
Simulation-based planning with rollouts is a widely-deployed technique for decision making in stochastic environments. The primary instrument of simulation-based planning is a sampling model, which is repeatedly called to generate…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
We study the emergence of altruistic behaviour in collective games. In particular, we take into account Toral's version of collective Parrondo's paradoxical games, in which the redistribution of capital between agents, who can play…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
We show that the resolution of social dilemmas on random graphs and scale-free networks is facilitated by imitating not the strategy of better performing players but rather their emotions. We assume sympathy and envy as the two emotions…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
We give a general method for constructing a deterministic strategy of Reality from a randomized strategy in game-theoretic probability. The construction can be seen as derandomization in game-theoretic probability.
Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a $k$-king if it…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
Ultimate Tic-Tac-Toe is a variant of the popular Tic-Tac-Toe game. Two players compete to win three aligned "fields," with each field constituting its own miniature tic-tac-toe game. Each move determines which field the next player must…
Game dynamics theory, as a field of science, the consistency of theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is…
We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we…
In this paper we review some of the main results obtained in the field of truels. A "truel" is a generalization of a duel involving three players. Depending on the rules used for chosing the players, we may distinguish between the random,…