Time in discrete agent-based models of socio-economic systems

We formulate the problem of computing time in discrete dynamical agent-based models in the context of socio-economic modeling. For such formulation, we outline a simple solution. This requires minimal extensions of the original untimed model. The proposed solution relies on the notion of agent-specific schedules of action and on two modeling assumptions. These are fulfilled by most models of pratical interest. For models for which stronger assumptions can be made, we discuss alternative formulations.Agent-based models, time.

A note on the stochastic stability of equilibrium in some exchange economies

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2009.htmDocuments de travail du Centre d'Economie de la Sorbonne 2009.84 - ISSN : 1955-611XBuilding upon recent work of Gintis, we study evolutionary dynamics in an economy with Leontieff preferences and corner endowments for which the equilibrium is completely indeterminate. We exhibit a class of dynamics which selects, via stochastic stability, the equilibrium minimizing the quantities traded.Prolongeant des travaux récents de Gintis, nous analysons des dynamiques évolutionnaires dans des économies d'échange où l'équilibre est complètement indéterminé. Nous caractérisons une classe de dynamiques qui sélectionne par stabilité stochastique l'équilibre qui minimise les quantités échangées

Semantic verification of dynamic programming

We prove that the generic framework for specifying and solving finite-horizon, monadic sequential decision problems proposed in (Botta et al.,2017) is semantically correct. By semantically correct we mean that, for a problem specification $P$ and for any initial state $x$ compatible with $P$, the verified optimal policies obtained with the framework maximize the $P$-measure of the $P$-sums of the $P$-rewards along all the possible trajectories rooted in $x$. In short, we prove that, given $P$, the verified computations encoded in the framework are the correct computations to do. The main theorem is formulated as an equivalence between two value functions: the first lies at the core of dynamic programming as originally formulated in (Bellman,1957) and formalized by Botta et al. in Idris (Brady,2017), and the second is a specification. The equivalence requires the two value functions to be extensionally equal. Further, we identify and discuss three requirements that measures of uncertainty have to fulfill for the main theorem to hold. These turn out to be rather natural conditions that the expected-value measure of stochastic uncertainty fulfills. The formal proof of the main theorem crucially relies on a principle of preservation of extensional equality for functors. We formulate and prove the semantic correctness of dynamic programming as an extension of the Botta et al. Idris framework. However, the theory can easily be implemented in Coq or Agda.Comment: Manuscript ID: JFP-2020-003

On the correctness of monadic backward induction

In control theory, to solve a finite-horizon sequential decision problem (SDP) commonly means to find a list of decision rules that result in an optimal expected total reward (or cost) when taking a given number of decision steps. SDPs are routinely solved using Bellman\u27s backward induction. Textbook authors (e.g. Bertsekas or Puterman) typically give more or less formal proofs to show that the backward induction algorithm is correct as solution method for deterministic and stochastic SDPs. Botta, Jansson and Ionescu propose a generic framework for finite horizon, monadic SDPs together with a monadic version of backward induction for solving such SDPs. In monadic SDPs, the monad captures a generic notion of uncertainty, while a generic measure function aggregates rewards. In the present paper, we define a notion of correctness for monadic SDPs and identify three conditions that allow us to prove a correctness result for monadic backward induction that is comparable to textbook correctness proofs for ordinary backward induction. The conditions that we impose are fairly general and can be cast in category-theoretical terms using the notion of Eilenberg-Moore algebra. They hold in familiar settings like those of deterministic or stochastic SDPs, but we also give examples in which they fail. Our results show that backward induction can safely be employed for a broader class of SDPs than usually treated in textbooks. However, they also rule out certain instances that were considered admissible in the context of Botta et al. \u27s generic framework. Our development is formalised in Idris as an extension of the Botta et al. framework and the sources are available as supplementary material

A note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"

In two recent contributions, Herbert Gintis introduces agent-based imitation models built upon evolutionary bargaining games where agents use private prices as strategies. He reports surprising convergence results for simulations performed in exchange economies where goods are strict complement. We investigate analyt- ically these results using the notion of stochastic stability.Exchange economies ; Bargaining Games ; Equilibrium Selection ; Stochastic Stability.

Time in discrete agent-based models of socio-economic systems

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2010.76 - ISSN : 1955-611XWe formulate the problem of computing time in discrete dynamical agent-based models in the context of socio-economic modeling. For such formulation, we outline a simple solution. This requires minimal extensions of the original untimed model. The proposed solution relies on the notion of agent-specific schedules of action and on two modeling assumptions. These are fulfilled by most models of pratical interest. For models for which stronger assumptions can be made, we discuss alternative formulations.On formule le problème du décompte du temps dans des modèles multi-agents à dynamique discrète dans le contexte de la modélisation socio-économique et on en donne une solution simple qui requiert une extension minimale du modèle initial

The impact of uncertainty on optimal emission policies

We apply a computational framework for specifying and solving sequential decision problems to study the impact of three kinds of uncertainties on optimal emission policies in a stylized sequential emission problem.We find that uncertainties about the implementability of decisions on emission reductions (or increases) have a greater impact on optimal policies than uncertainties about the availability of effective emission reduction technologies and uncertainties about the implications of trespassing critical cumulated emission thresholds. The results show that uncertainties about the implementability of decisions on emission reductions (or increases) call for more precautionary policies. In other words, delaying emission reductions to the point in time when effective technologies will become available is suboptimal when these uncertainties are accounted for rigorously. By contrast, uncertainties about the implications of exceeding critical cumulated emission thresholds tend to make early emission reductions less rewarding

Extensional equality preservation and verified generic programming

In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $f, g : A \rightarrow B$ are extensionally equal, that is, $\forall x \in A, \ f \ x = g \ x$, then $map \ f : List \ A \rightarrow List \ B$ and $map \ g$ are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-L\"of's intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution towards pragmatic, verified generic programming.Comment: Manuscript ID: JFP-2020-003

High Density Lipoproteins Inhibit Oxidative Stress-Induced Prostate Cancer Cell Proliferation

Recent evidence suggests that oxidative stress can play a role in the pathogenesis and the progression of prostate cancer (PCa). Reactive oxygen species (ROS) generation is higher in PCa cells compared to normal prostate epithelial cells and this increase is proportional to the aggressiveness of the phenotype. Since high density lipoproteins (HDL) are known to exert antioxidant activities, their ability to reduce ROS levels and the consequent impact on cell proliferation was tested in normal and PCa cell lines. HDL significantly reduced basal and H2O2-induced oxidative stress in normal, androgen receptor (AR)-positive and AR-null PCa cell lines. AR, scavenger receptor BI and ATP binding cassette G1 transporter were not involved. In addition, HDL completely blunted H2O2-induced increase of cell proliferation, through their capacity to prevent the H2O2-induced shift of cell cycle distribution from G0/G1 towards G2/M phase. Synthetic HDL, made of the two main components of plasma-derived HDL (apoA-I and phosphatidylcholine) and which are under clinical development as anti-atherosclerotic agents, retained the ability of HDL to inhibit ROS production in PCa cells. Collectively, HDL antioxidant activity limits cell proliferation induced by ROS in AR-positive and AR-null PCa cell lines, thus supporting a possible role of HDL against PCa progression

Types, equations, dimensions and the Pi theorem

The languages of mathematical physics and modelling are endowed with a rich "grammar of dimensions" that common abstractions of programming languages fail to represent. We propose a dependently typed domain-specific language (embedded in Idris) that captures this grammar. We apply it to explain basic notions of dimensional analysis and Buckingham's Pi theorem. We hope that the language makes mathematical physics more accessible to computer scientists and functional programming more palatable to modelers and physicists.Comment: Submitted for publication in the "Journal of Functional Programming" in August 202