Algebraic Theory of Multi-Product Decisions, An

The typical firm produces for sale a plural number of distinct product lines. This paper characterizes the composition of a firm?s optimal production vector as a function of cost and revenue function attributes. The approach taken applies mathematical group theory and revealed preference arguments to exploit controlled asymmetries in the production environment. Assuming some symmetry on the cost function, our central result shows that all optimal production vectors must satisfy a dominance relation on permutations of the firm?s revenue function. When the revenue function is linear in outputs, then the set of admissible output vectors has linear bounds up to transformations. If these transformations are also linear, then convex analysis can be applied to characterize the set of admissible solutions. When the group of symmetries decomposes into a direct product group with index K in N, then the characterization problem separates into K problems of smaller dimension. The central result may be strengthened ; when the cost function is assumed to be quasiconvex.

Discovering How Agents Learn Using Few Data

Decentralized learning algorithms are an essential tool for designing multi-agent systems, as they enable agents to autonomously learn from their experience and past interactions. In this work, we propose a theoretical and algorithmic framework for real-time identification of the learning dynamics that govern agent behavior using a short burst of a single system trajectory. Our method identifies agent dynamics through polynomial regression, where we compensate for limited data by incorporating side-information constraints that capture fundamental assumptions or expectations about agent behavior. These constraints are enforced computationally using sum-of-squares optimization, leading to a hierarchy of increasingly better approximations of the true agent dynamics. Extensive experiments demonstrated that our approach, using only 5 samples from a short run of a single trajectory, accurately recovers the true dynamics across various benchmarks, including equilibrium selection and prediction of chaotic systems up to 10 Lyapunov times. These findings suggest that our approach has significant potential to support effective policy and decision-making in strategic multi-agent systems

A new prospect of additivity in bankruptcy problems

This paper explores additivity-like properties ful led by bankruptcy rules. Our main result is that the unique rule satisfying an adittivity-like property is the Minimal Overlap proposed by O'Neill. We also propose some conections relative to additivity properties in close frameworks as bargaining rules.This work is partially supported by the Institut Valencià d´Investigacions Econòmiques and the Spanish Ministerio de Educación y Ciencia under projects SEJ2007-62656 (Alcalde) and SEJ2007-64649 (Marco-Gil and Silva). Marco-Gil also acknowledges support by the Fundación Séneca of the Agencia de Ciencia y Tecnología of the Murcian Region, under project 05838/PHCS/07 (Programa de Generación Cientìfico de Excelencia)

Externalities, Potential, Value and Consistency

We provide new characterization results for the value of games in partition function form. In particular, we use the potential of a game to define the value. We also provide a characterization of the class of values which satisfies one form of reduced game consistency

Bayes Correlated Equilibrium and the Comparison of Information Structures

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures — which we call individual sufficiency — under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell’s for the single player case

Thin Games with Symmetry and Concurrent Hyland-Ong Games

We build a cartesian closed category, called Cho, based on event structures. It allows an interpretation of higher-order stateful concurrent programs that is refined and precise: on the one hand it is conservative with respect to standard Hyland-Ong games when interpreting purely functional programs as innocent strategies, while on the other hand it is much more expressive. The interpretation of programs constructs compositionally a representation of their execution that exhibits causal dependencies and remembers the points of non-deterministic branching.The construction is in two stages. First, we build a compact closed category Tcg. It is a variant of Rideau and Winskel's category CG, with the difference that games and strategies in Tcg are equipped with symmetry to express that certain events are essentially the same. This is analogous to the underlying category of AJM games enriching simple games with an equivalence relations on plays. Building on this category, we construct the cartesian closed category Cho as having as objects the standard arenas of Hyland-Ong games, with strategies, represented by certain events structures, playing on games with symmetry obtained as expanded forms of these arenas.To illustrate and give an operational light on these constructions, we interpret (a close variant of) Idealized Parallel Algol in Cho