Related papers: From open learners to open games

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

The main goal of this article is to convince you, the reader, that supervised learning in the Probably Approximately Correct (PAC) model is closely related to -- of all things -- bipartite matching! En-route from PAC learning to bipartite…

In a recent paper, Junge and Palazuelos presented two two-player games exhibiting interesting properties. In their first game, entangled players can perform notably better than classical players. The quantitative gap between the two cases…

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…

We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…

In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build…

A variety of practical problems can be modeled by the decision-making process in multi-player games where a group of self-interested players aim at optimizing their own local objectives, while the objectives depend on the actions taken by…

Open-ended algorithms aim to learn new, interesting behaviors forever. That requires a vast environment search space, but there are thus infinitely many possible tasks. Even after filtering for tasks the current agent can learn (i.e.,…

Evolutionary games are studied where the teaching activity of players can evolve in time. Initially all players following either the cooperative or defecting strategy are distributed on a square lattice. The rate of strategy adoption is…

We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games…

Humans rapidly learn abstract knowledge when encountering novel environments and flexibly deploy this knowledge to guide efficient and intelligent action. Can modern AI systems learn and plan in a similar way? We study this question using a…

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 propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are…

Recently, there has been growing interest in bicategorical models of programming languages, which are "proof-relevant" in the sense that they keep distinct account of execution traces leading to the same observable outcomes, while assigning…

The classical model of signaling games assumes that the receiver exactly know the type space (private information) of the sender and be able to discriminate each type of the sender distinctly. However, the justification of this assumption…

In mechanism design, for a given type space, there may be incentive compatible outcome functions which are not affine maximizers. Using tools from linear algebra and tropical geometry, we prove that for two-player games on a discrete type…

Every simple game is a monotone Boolean function. For the other direction we just have to exclude the two constant functions. The enumeration of monotone Boolean functions with distinguishable variables is also known as the Dedekind's…