arXiv subjects

Joe Bolt

Publications and source records attributed to Joe Bolt.

4 recordsLinked to original sources

arXiv2019

Bayesian open games

This paper generalises the treatment of compositional game theory as introduced by Ghani et al. in 2018, where games are modelled as morphisms of a symmetric monoidal category. From an economic modelling perspective, the notion of a game in the work by Ghani et al. is not expressive enough for many applications. This includes stochastic environments, stochastic choices by players, as well as incomplete information regarding the game being played. The current paper addresses these three issues all at once.

cs.GT↗

arXiv2018

Sequential games and nondeterministic selection functions

This paper analyses Escard\'o and Oliva's generalisation of selection functions over a strong monad from a game-theoretic perspective. We focus on the case of the nondeterminism (finite nonempty powerset) monad $\mathcal{P}$. We use these nondeterministic selection functions of type $\mathcal{J}^{\mathcal{P}}_R X = (X \rightarrow R) \rightarrow \mathcal{P} (X)$ to study sequential games, extending previous work linking (deterministic) selection functions to game theory. Similar to deterministic selection functions, which compute a subgame perfect Nash equilibrium play of a game, we characterise those non-deterministic selection functions which have a clear game-theoretic interpretation. We show, surprisingly, no non-deterministic selection function exists which computes the set of all subgame perfect Nash equilibrium plays. Instead we show that there are selection functions corresponding to sequential versions of the iterated removal of strictly dominated strategies.

cs.GT↗

arXiv2018

The algebra of predicting agents

The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a partially defined duality. There exist open games with the same types as unit maps, given by agents with the strategic goal of predicting a future value. Such agents appear in earlier work on selection functions. We explore the algebraic properties of these agents via the symmetric monoidal bicategory whose 2-cells are morphisms between open games, and show how the resulting structure approximates a compact closed category with a family of lax commutative bialgebras.

cs.GT↗

arXiv2017

Interacting Conceptual Spaces I : Grammatical Composition of Concepts

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.

cs.LO↗