Related papers: Game-theoretic Investigation of Intensional Equali…
The main objective of this work is to study mathematical properties of computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as `sequences or rewrites', computational paths are taken to be terms of the identity type of…
This paper introduces Alympics (Olympics for Agents), a systematic simulation framework utilizing Large Language Model (LLM) agents for game theory research. Alympics creates a versatile platform for studying complex game theory problems,…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
Are Large Language Models (LLMs) a new form of strategic intelligence, able to reason about goals in competitive settings? We present compelling supporting evidence. The Iterated Prisoner's Dilemma (IPD) has long served as a model for…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
LLMs are increasingly used in applications where they interact with humans and other agents. We propose to use behavioural game theory to study LLM's cooperation and coordination behaviour. We let different LLMs play finitely repeated…
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
We present an index theory of equilibria for extensive form games. This requires developing an index theory for games where the strategy sets of players are general polytopes and their payoff functions are multiaffine in the product of…
Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging,…
This paper addresses the longstanding problem of determining the structure of the $\leq_{\mathrm{LT}}$-order in the Effective Topos, known to effectively embed the Turing degrees. In a surprising discovery, we show that the…
We consider quantitative extensions of the alternating-time temporal logics ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in which the value of a counter can be compared to constants using equality, inequality…
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq…
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the…
We introduce a modification of standard Martin-Lof type theory in which we eliminate definitional equality and replace all computation rules by propositional equalities. We show that type checking for such a system can be done in quadratic…
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically, we give a game semantics for a higher-order programming…
We develop a symmetric monoidal closed category of games, incorporating sums and products, to model quantum computation at higher types. This model is expressive, capable of representing all unitary operators at base types. It is compatible…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the…
In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. Firstly,…