Related papers: Gambits: Theory and Evidence
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…
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…
Understanding the evolution of human social systems requires flexible formalisms for the emergence of institutions. Although game theory is normally used to model interactions individually, larger spaces of games can be helpful for modeling…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution is varied, a game can undergo a phase transition, in which…
Game theory is a powerful analytical tool for modeling decision makers strategies, behaviors and interactions. Act and decisions of a decision maker can benefit or negatively impact other decision makers interests. Game theory has been…
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…
The main objective of this paper is to outline a theoretical framework to characterise humans' decision-making strategies under uncertainty, in particular active learning in a black-box optimization task and trading-off between information…
This paper explores the use of Generative Pre-trained Transformers (GPT) in strategic game experiments, specifically the ultimatum game and the prisoner's dilemma. I designed prompts and architectures to enable GPT to understand the game…
We carry out a game-theoretic analysis of the recursive game "Guts," a variant of poker featuring repeated play with possibly growing stakes. An interesting aspect of such games is the need to account for funds lost to all players if…
This paper investigates the dynamics of gambling and how they can affect risk-taking behavior in regions not explored by Kahneman and Tversky's Prospect Theory. Specifically, it questions why extreme outcomes do not fit the theory and…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…
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…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead…
Evolutionary game theory assumes that players replicate a highly scored player's strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone's strategy just by observing the…
Fighting Fantasy is a popular recreational fantasy gaming system worldwide. Combat in this system progresses through a stochastic game involving a series of rounds, each of which may be won or lost. Each round, a limited resource (`luck')…