相关论文: Simple Recursive Games

Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…

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…

The dynamics in games involving multiple players, who adaptively learn from their past experience, is not yet well understood. We analyzed a class of stochastic games with Markov strategies in which players choose their actions…

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r! n) where n is the number of positions of the simple stochastic game and r is the number of its coin toss positions. Chatterjee et al. pointed out…

Infinitely repeated games support equilibrium concepts beyond those present in one-shot games (e.g., cooperation in the prisoner's dilemma). Nonetheless, repeated games fail to capture our real-world intuition for settings with many…

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…

The main objective of this work is to describe games which fall under title of Potential and simplify the conditions for class of aggregative games. Games classified as aggregative are ones in which, in addition to the player's own action,…

Number games play a central role in alternating normal play combinatorial game theory due to their real-number-like properties (Conway 1976). Here we undertake a critical re-examination: we begin with integer and dyadic games and identify…

People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

We propose a new deterministic symmetric recursive algorithm for solving mean-payoff games.

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…

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and…

We consider discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we come up with a pair of…

Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in…

It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with…

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…