Distributed learning is the iterative process of decision-making in the presence of other decision-makers. In recent years, researchers across fields as disparate as engineering, biology, and economics have identified mathematically congruous problem formulations at the intersection of their disciplines. In particular, stochastic processes, game theory, and control theory have been brought to bare on certain very basic and universal questions. What sort of environments are conducive to distributed learning? Are there any generic algorithms offering non-trivial performance guarantees for a large class of models? The first half of this thesis makes contributions to two particular problems in distributed learning, self-assembly and language. Self-assembly refers to the emergence of high-level structures via the aggregate behavior of simpler building blocks. A number of algorithms have been suggested that are capable of generic self-assembly of graphs. That is, given a description of the objective they produce a policy with a corresponding performance guarantee. These guarantees have been in the form of deterministic convergence results. We introduce the notion of stochastic stability to the self-assembly problem. The stochastically stable states are the configurations the system spends almost all of its time in as a noise parameter is taken to zero. We show that in this framework simple procedures exist that are capable of self-assembly of any tree under stringent locality constraints. Our procedure gives an asymptotically maximum yield of target assemblies while obeying communication and reversibility constraints. We also present a slightly more sophisticated algorithm that guarantees maximum yields for any problem size. The latter algorithm utilizes a somewhat more presumptive notion of agents' internal states. While it is unknown whether an algorithm providing maximum yields subject to our constraints can depend only on the more parsimonious form of internal state, we are able to show that such an algorithm would not be able to possess a unique completing rule--- a useful feature for analysis. We then turn our attention to the problem of distributed learning of communication protocols, or, language. Recent results for signaling game models establish the non-negligible possibility of convergence, under distributed learning, to states of unbounded efficiency loss. We provide a tight lower bound on efficiency and discuss its implications. Moreover, motivated by the empirical phenomenon of linguistic drift, we study the signaling game under stochastic evolutionary dynamics. We again make use of stochastic stability analysis and show that the long-run distribution of states has support limited to the efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a fact that is intuitively captured by the game's potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we expect monomorphic language states to eventually predominate. Homophily has been identified as a feature that potentially stabilizes diverse linguistic communities. We find that incorporating homophily in our stochastic model gives mixed results. While the monomorphic prediction holds in the small noise limit, diversity can persist at higher noise levels or as a metastable phenomenon. The contributions of the second half of this thesis relate to more basic issues in distributed learning. In particular, we provide new results on the problem of distributed convergence to Nash equilibrium in finite games. A recently proposed class of games known as stable games have the attractive property of admitting global convergence to equilibria under many learning dynamics. We show that stable games can be formulated as passive input-output systems. This observation enables us to identify passivity of a learning dynamic as a sufficient condition for global convergence in stable games. Notably, dynamics satisfying our condition need not exhibit positive correlation between the payoffs and their directions of motion. We show that our condition is satisfied by the dynamics known to exhibit global convergence in stable games. We give a decision-theoretic interpretation for passive learning dynamics that mirrors the interpretation of stable games as strategic environments exhibiting self-defeating externalities. Moreover, we exploit the flexibility of the passivity condition to study the impact of applying various forecasting heuristics to the payoffs used in the learning process. Finally, we show how passivity can be used to identify strategic tendencies of the players that allow for convergence in the presence of information lags of arbitrary duration in some games.

Η παρούσα διπλωματική εργασία πραγματεύεται την θεωρία παιγνίων και το πώς αυτή εφαρμόζεται στην οικονομική επιστήμη. Συγκεκριμένα, στόχος μας είναι να απαντήσουμε στο ερώτημα: «Πως αποφασίζονται οι τελικές στρατηγικές που θα επικρατήσουν σε ένα παίγνιο με την πάροδο του χρόνου;». Η εργασία είναι χωρισμένη σε δύο μέρη. Αρχικά αναφερόμαστε στην κλασσική θεωρία παιγνίων και αναλύουμε τα βασικά της στοιχεία και στη συνέχεια περνάμε στην ανάλυση της εξελικτικής θεωρίας παιγνίων. Στο 1ο μέρος της παρούσας εργασίας, λοιπόν, αναφέρουμε τα όσα είναι σχετικά με την κλασσικά θεωρία παιγνίων. Συγκεκριμένα, στο πρώτο κεφάλαιο γίνεται μία σύντομη ιστορική αναδρομή της θεωρίας αυτής και στο δεύτερο κεφάλαιο την ορίζουμε ως την επίσημη μελέτη που εξετάζει την ορθολογικότητα σε ένα επιχειρηματικό περιβάλλον και παρουσιάζουμε τα βασικά στοιχεία ενός παιγνίου. Αναφέρουμε τα δύο επίπεδα περιγραφής των παιγνίων, δηλαδή τα παίγνια συνεργασίας και μη-συνεργασίας, καθώς και τους δύο τρόπους αναπαράστασής τους που είναι η στρατηγική ή αλλιώς κανονική μορφή (μήτρες) και η εκτεταμένη ή αλλιώς αναλυτική μορφή (δέντρα παιγνίων). Στο τρίτο κεφάλαιο ορίζονται οι κυρίαρχες στρατηγικές και η αντίστοιχη ισορροπία κυρίαρχης στρατηγικής και στο τέταρτο κεφάλαιο ορίζεται η Ισορροπία Nash, η οποία αποτελεί τη στάνταρ έννοια της ισορροπίας στα οικονομικά. Στα δύο αυτά κεφάλαια (3 και 4) υπάρχουν παραδείγματα εφαρμογής που στοχεύουν στην καλύτερη κατανόηση, και αναλύεται και το Δίλημμα του Φυλακισμένου που αποτελεί το πιο κλασσικό παράδειγμα στη θεωρία παιγνίων. Στην περίπτωση, τώρα, όπου δεν υπάρχει Ισορροπία Nash (κάτι το οποίο συμβαίνει σε παίγνια στρατηγικής μορφής) το παίγνιο λύνεται με τη βοήθεια των μικτών στρατηγικών οι οποίες αναλύονται στο πέμπτο κεφάλαιο. Συνεχίζουμε με το έκτο κεφάλαιο, όπου παρουσιάζονται τα εκτεταμένα παίγνια πλήρους πληροφόρησης και αναλύεται η μέθοδος της προς τα πίσω επαγωγής (αναδίπλωση). Στο έβδομο κεφάλαιο παρουσιάζονται τα παίγνια ελλιπούς πληροφόρησης και στο όγδοο κεφάλαιο αναφέρονται τα παίγνια μηδενικού αθροίσματος (π.χ. σκάκι) και το πώς μπορούν να χρησιμοποιηθούν μαζί με τους τυχαιοποιημένους αλγόριθμους για την ανάλυση προβλημάτων στον απευθείας σύνδεσης υπολογισμό. Το 1ο μέρος κλείνει με ένα παράδειγμα εφαρμογής της θεωρίας παιγνίων, τις δημοπρασίες. Τι γίνεται όμως όταν ένα παίγνιο επαναλαμβάνεται και παίζεται περισσότερες από μία φορές; Το ερώτημα αυτό έρχεται να μας το απαντήσει η εξελικτική θεωρία παιγνίων στο 2ο μέρος της παρούσας διπλωματικής εργασίας. Στα δύο πρώτα κεφάλαια, του μέρους αυτού, ορίζονται τα εξελικτικά παίγνια, γίνεται αναφορά για το που μπορούν να βρουν εφαρμογή καθώς και στους λόγους που δεν είναι ακόμη γνωστές οι οικονομικές εφαρμογές τους. Το τρίτο και το πέμπτο κεφάλαιο αποτελούν τα πιο σημαντικά κεφάλαιο του 2ου μέρους. Στο τρίτο κεφάλαιο παρουσιάζεται αναλυτικά το μοντέλο των εξελικτικών παιγνίων και τα στοιχεία που το αποτελούν (αναμενόμενες ανταμοιβές, πληθυσμός, καταστάσεις). Περιγράφεται το στάδιο παιγνίου το οποίο ορίζεται από μία συνάρτηση καταλληλότητας και δίνεται έμφαση στις δύο γραμμικές προδιαγραφές που έχουν οι συναρτήσεις αυτές. Στη συνέχεια, αναλύεται πλήρως το πιο αντιπροσωπευτικό παράδειγμα της εξελικτικής θεωρίας παιγνίων, το παίγνιο Hawk-Dove, που αποτελεί ένα γενικό μοντέλο καταστάσεων με επιθετικές και αμυντικές αγορές. Το παίγνιο αυτό έχει δύο ειδών παίκτες, αυτοί που επιλέγουν να είναι επιθετικοί (Hawk) και αυτοί που επιλέγουν να είναι αμυντικοί (Dove), και ερευνάται το ποιο είδος παικτών θα επικρατήσει τελικά. Μέσα από την διαφορική εξίσωση που αναλύεται στο πέμπτο κεφάλαιο, στις δυναμικές, φαίνεται πως το αποτέλεσμα εξαρτάται από τρεις παραμέτρους: από τον αρχικό πληθυσμό, από την πιθανότητα να παιχτεί η καθεμία στρατηγική και από τον πίνακα με τις ανταμοιβές των παικτών. Έτσι απαντάται το αρχικό μας ερώτημα και προκύπτει η στρατηγική που τελικά θα επικρατήσει, που ονομάζεται εξελικτική στρατηγική (evolutionary stable strategy-ESS). Στο τέταρτο κεφάλαιο ορίζεται η Ισορροπία Nash (I.N.), η Εξελικτική Σταθερή Στρατηγική (ESS) και η Εξελικτική Ισορροπία (E.E.) και στο έκτο κεφάλαιο αναφέρουμε την τοπική κατάταξη συστημάτων με χαμηλές διαστάσεις και συγκεκριμένα τα γραμμικά παίγνια μίας-διάστασης, τα συστήματα δύο μεταβλητών και άλλα συστήματα δύο-διαστάσεων και μη-γραμμικά. Κλείνοντας το 2ο μέρος και γενικά την παρούσα εργασία, παρουσιάζουμε τρία παραδείγματα στα οποία φαίνεται η εφαρμοσιμότητα των όσων αναφέραμε. Συγκεκριμένα αναλύονται τρία γνωστά παίγνια τα οποία χρησιμοποιήθηκαν από την πολιτική και παραλληλίστηκαν με καταστάσεις που είχαν να αντιμετωπίσουν εκείνη τη στιγμή. / This thesis deals with the evolutionary game theory and how it applies to economics. First of all, it is necessary to refer the original game theory and to analyze the key elements and then move to the analysis of evolutionary game theory. In the first part of this study, therefore, we indicate what is on game theory. Specifically, in the first chapter is a brief history of game theory and the second chapter defined game theory as a formal study examining the rationality in a business environment and presents the basics elements of a game. Also, at this chapter i reffer to the description of games, namely, games of cooperation and non-cooperation, and the two ways of representing their strategy, the normal form (matrix) and the extensive form (game tree). The third chapter sets out the dominant strategy and the corresponding dominant strategy equilibrium and in the fourth chapter we define the Nash Equilimbrium, which is the standard notion of equilibrium in economics. In these two chapters (third and fourth) there are examples of the application for better understanding, and we analyze the prisoner's dilemma, which is the most classic example of game theory. If there is no Nash Equilimbrium (this could happen at narmal strategy games) the game is solved by mixed strategies, which are analyzed in the fifth chapter. Continuing, at the sixth chapter we can see the extensive games with perfect information and we analyze the method of backward induction. In the seventh chapter, we can see the extensive games with imperfect information and the eighth chapter refers to the zero-sum games and how they can be used together with randomized algorithms for the analysis of problems on-line calculation. Finally, the first part closes with an example application of game theory, the auctions. The question is “What happens when a game is played more than once?” The answer comes from the second part of this thesis in which we analyse the evolutionary game theory. In the first two chapters of this part we define evolutionary games, we refere where evolutionary games might be applicable and why economic application aren’t common already. The third and fourth chapter are the most important chapters of the second part. At the third chapter we present the model of the evolutionary game and its elements (expected payoffs, population, states). We describe the stage game which is defined by a fitness function and we emphasize at its two linear specifications. Then we make a full analysis one of the most representative example of evolutionary game theory, the Hawk-Dove game. This game has two types of players, aggressive (Hawk) and defensive (Dove), which reflects the situation where there is a competitive and an uncompetitive business, and the point is to find which of the two types will eventually prevail. Based on a differential equation, we conclude that the result depends on three parameters: the initial population, the probability with which each strategy is played and the payoff matrix. All this leads in a strategy which is known as evolutionary stable (ESS). In chapter five, we define the Nash Equilibrium, the Evolutionary Stable Strategy (ESS) and Evolutionary Equilibrium (EE) and in chapter six we analyze the local classification of low dimensions systems. To make clear the applicability of all those we mention at this thesis, we are closing with three examples. More specific we analyze three well-known games which were used by the political and paralleled with situations they had to face with.

This thesis contains four essays that analyze the behaviors that evolve when populations of boundedly rational individuals interact strategically for a long period of time. Individuals are boundedly rational in the sense that their strategy choices are determined by simple rules of adaptation -- learning rules. Convergence results for general finite games are first obtained in a homogenous setting, where all populations consist either of stochastic imitators, who almost always imitate the most successful strategy in a sample from their own population's past strategy choices, or stochastic better repliers, who almost always play a strategy that gives at least as high expected payoff as a sample distribution of all populations' past play. Similar results are then obtained in a heterogeneous setting, where both of these learning rules are represented in each population. It is found that only strategies in certain sets are played in the limit, as time goes to infinity and the mutation rate tends to zero. Sufficient conditions for the selection of a Pareto efficient such set are also provided. Finally, the analysis is extended to natural selection among learning rules. The question is whether there exists a learning rule that is evolutionarily stable, in the sense that a population employing this learning rule cannot be invaded by individuals using a different rule. Monte Carlo simulations for a large class of learning rules and four different games indicate that only a learning rule that takes full account of hypothetical payoffs to strategies that are not played is evolutionarily stable in almost all cases. / Diss. Stockholm : Handelshögsk., 2001

No description available.

Em uma perspectiva evolutiva, a emergência e a manutenção de comportamentos altruísticos e de cooperação não é de fácil entendimento. O impulso por ajudar um indivíduo desconhecido não pode significar um prejuízo na capacidade reprodutiva, o que muitas vezes parece ser o mais óbvio. Muito se tem feito no sentido de compreender os ganhos indiretos da cooperação, ou o que se espera em retorno por este comportamento. A espera por reciprocidade é um dos modos de se tornar a cooperação atraente. Os seres humanos possuem uma capacidade singular de expandir a reciprocidade para interações organizadas em que não necessariamente se recebe a retribuição de um favor, mas sim o favor de um terceiro indivíduo. Para estes sistemas, de reciprocidade indireta, são necessários elaborados processos cognitivos que sustentam uma capacidade para linguagem, julgamentos morais e organização social. Entende-se que esta forma de cooperação é um fator essencial para a evolução do intelecto e da estrutura social atuais dos seres humanos. A teoria dos jogos evolucionária é uma ferramenta matemática muito utilizada na sistematização analítica dos problemas envolvendo cooperação e processos evolutivos no geral. A capacidade reprodutiva é traduzida em termos de funções matemáticas, sendo possível realizar dinâmicas populacionais que modelam a pressão seletiva. Neste trabalho, utilizamos métodos de teoria dos jogos evolucionária para explorar modelos de reciprocidade indireta, expandindo o tratamento de um modelo para interações opcionais envolvendo estratégias de cooperadores condicionais. Mostramos que a presença de cooperadores incondicionais ameaça a estabilidade da cooperação e que erros de execução podem ser uma solução. / At an evolutionary perspective, the emergence and maintenance of altruistic and cooperative behaviours is of no easy understanding. The impulse of helping an unrelated individual cannot mean a loss of reproductive fitness, as many times may seem the obvious. Much has been done in the way of knowing the indirect benefits of cooperation, or what to expect in retribution for this behaviour. To expect reciprocity is one way of looking at cooperation as more attractive. Human beings have a singular capacity of expanding reciprocity to organized interactions where retribution of a favour is not necessary, but one can expect the favour of a third-party. For these systems, of indirect reciprocity, elaborate cognitive processes are necessary, ones that maintain the capacity for language, moral judgements and social organization. One can understand this form of cooperation as an essential factor for the evolution of humans nowadays´ intellect and social structure. Evolutionary game theory is a mathematical tool that is largely used in the analytical systematization of problems involving cooperation and evolutionary processes in general. Reproductive fitness is understood in terms of mathematical functions, making possible the work on population dynamics that model selective pressure. In this work, we use methods in evolutionary game theory to explore models of indirect reciprocity, expanding the treatment of a model for optional interactions involving conditional cooperators strategies. We show that the presence of unconditional cooperators threatens the stability of cooperation and that execution errors might be a solution.

Mutualismos são interações em que os parceiros se exploram reciprocamente com benefícios líquidos para ambos os indivíduos que interagem. Sistemas mutualistas multiespecíficos podem ser descritos como redes de interação, tais como aquelas formadas por sistemas de polinização, dispersão de sementes, estações de limpeza em ambientes recifais, formigas defensoras de plantas, mimetismo mülleriano e bactérias fixadoras de nitrogênio em raízes de plantas. As interações mutualísticas estão sujeitas à trapaça por indivíduos que, por meio de algum comportamento, alcançam o benefício oferecido pelo parceiro sem oferecer nada ou oferecer muito pouco em troca. No entanto, interações mutualísticas persistem apesar da existência de trapaceiros. Neste trabalho, mostro que os parasitas de interações mutualísticas, os trapaceiros, aumentam a resiliência das redes mutualísticas às perturbações mais rapidamente em redes aninhadas, redes tipicamente encontradas em mutualismos ricos em espécies. Portanto os efeitos combinados de trapaceiros, estrutura e dinâmica das redes mutualísticas podem ter implicações para a forma como a biodiversidade é mantida. Em seguida, estudo as condições em que flores tubulares, que sofrem maiores danos ao interagirem com ladrões de néctar, conseguem coexistir com flores planares, polinizadores e pilhadores por meio de efeitos indiretos da trapaça em seu sucesso reprodutivo. O roubo do néctar pode aumentar o sucesso de uma planta se as interações com pilhadores gerarem maior quantidade de polinização cruzada, aumentando assim o sucesso reprodutivo das plantas que interagem com ambos os visitantes florais. Tal resultado sugere uma nova fonte de manutenção da cooperação e da diversidade de estratégias por meio de efeitos não lineares das interações entre diferentes estratégias. Finalmente, estudo como as interações locais promovem a prevalência de mímicos (trapaceiros) em uma certa população na ausência de seus modelos. Mostro que presas que interagem localmente podem favorecer a predominância de mímicos e predadores que os evitam após algumas gerações e que uma distribuição não aleatória de indivíduos no espaço pode reforçar ainda mais este efeito inesperado de alopatria de modelo e mímico / Mutualisms are interactions in which organisms of different species exploit each other with net benefits for both interacting individuals. Multispecific mutualistic system can be depicted as interaction networks, such as those formed by plant-pollinator interactions, dispersal systems, species interacting in cleaning stations in reef environments, protective ants in plants, müllerian mimicry, and nitrogen fixing bacteria on the roots of plants. Mutualistic interaction is subject to cheating by individuals who, by means of a diversity of behavioral strategies, achieve the benefit provided by the partner offering nothing or few in return. However, the mutualistic interactions persist despite the existence of cheaters. In this work I show that the parasites of mutualistic interactions increase the resilience of mutualistic networks to disturbances in nested networks, typically found in species-rich mutualisms. Therefore the joint effect of cheating, structure and dynamics of mutualistic networks have implications for how biodiversity is maintained. I subsequently study the conditions under which tubular flowers, which suffer stronger damages when interacting with nectar robbers, can coexist with planar flowers, pollinators, and robbers through indirect effects of cheating on their reproductive success. The theft of nectar may increase the success of a plant if its interactions with robbers generate higher degrees of cross-pollination, thus increasing the reproductive success of plants that interact with both floral visitors. This study suggests a new source of continued cooperation and diversity strategies through non-linear effects of the interactions between different strategies. Finally, I study how local interactions can promote the prevalence of mimic (the cheaters) in a given population in the absence of their models. I found that prey interacting locally may favor the predominance of mimic preys and avoid predators that, after a few generations and under a non-random distribution of individuals in space, can further strengthen this unexpected effect allopatry of the mimic and its model

This research involves the design, development, and theoretical demonstration of models resulting in integrated misbehavior resolution protocols for ad hoc networked devices. Game theory was used to analyze strategic interaction among independent devices with conflicting interests. Packet forwarding at the routing layer of autonomous ad hoc networks was investigated. Unlike existing reputation based or payment schemes, this model is based on repeated interactions. To enforce cooperation, a community enforcement mechanism was used, whereby selfish nodes that drop packets were punished not only by the victim, but also by all nodes in the network. Then, a stochastic packet forwarding game strategy was introduced. Our solution relaxed the uniform traffic demand that was pervasive in other works. To address the concerns of imperfect private monitoring in resource aware ad hoc networks, a belief-free equilibrium scheme was developed that reduces the impact of noise in cooperation. This scheme also eliminated the need to infer the private history of other nodes. Moreover, it simplified the computation of an optimal strategy. The belief-free approach reduced the node overhead and was easily tractable. Hence it made the system operation feasible. Motivated by the versatile nature of evolutionary game theory, the assumption of a rational node is relaxed, leading to the development of a framework for mitigating routing selfishness and misbehavior in Multi hop networks. This is accomplished by setting nodes to play a fixed strategy rather than independently choosing a rational strategy. A range of simulations was carried out that showed improved cooperation between selfish nodes when compared to older results. Cooperation among ad hoc nodes can also protect a network from malicious attacks. In the absence of a central trusted entity, many security mechanisms and privacy protections require cooperation among ad hoc nodes to protect a network from malicious attacks. Therefore, using game theory and evolutionary game theory, a mathematical framework has been developed that explores trust mechanisms to achieve security in the network. This framework is one of the first steps towards the synthesis of an integrated solution that demonstrates that security solely depends on the initial trust level that nodes have for each other.

[pt] Utilizando o instrumental da teoria dos jogos evolucionários, a proposta desta dissertação é analisar as interações entre emissores de dívida e agências de avaliação de risco de crédito em um ambiente com assimetria de informação. Enquanto os primeiros precisam das notas emitidas pelas agências para acessar fontes de financiamentos no mercado, as agências são remuneradas pela prestação desse serviço. Os resultados mostram que, de forma geral, quando o número de emissores grau de investimento é pequeno, incentiva-se a adoção de uma estratégia pouco transparente de divulgação de informação por parte do emissor, aumentando a assimetria de informação. A melhor resposta das agências é utilizar uma análise básica do perfil de crédito de seus clientes. O aumento do número de emissores grau de investimento na economia incentiva o aperfeiçoamento das políticas corporativas de transparência, enquanto as agências sofisticam sua análise com o objetivo de evitar os custos de reputação associados a erros de avaliação. Empiricamente, os resultados são condizentes com a evolução da economia colombiana nas últimas décadas. A melhoria do ambiente macroeconômico desse país atraiu emissores grau de investimento incentivando a atuação de agências que utilizam metodologia de análise sofisticada e emissores que adotam uma estratégia transparente de divulgação de suas informações. / [en] Using evolutionary game theory, this work aims to analyse the interactions between debt issuers and credit rating agencies in an asymmetric information environment. While the ratings grades are required by issuers to access funding sources for their investment projects, the agency s revenue is provided by this service. The results show that when the number of investment grade issuers is small, non-transparency strategy and basic methodology of analysis dominate, worsening the information asymmetry problem. The increase in the number of investment grade issuers encourages transparency policies while the agencies adopt a sophisticated analysis, avoiding the reputation costs associated with errors. Empirically, the results are consistent with the evolution of the Colombian economy in recent decades. The country s improvement in the macroeconomic environment attracted investment grade issuers encouraging the proliferation of sophisticated rating agencies and transparent issuers.

This dissertation is an attempt at establishing a bridge between biology and physics leading naturally from the field of phase transitions in physics to the cooperative nature of living systems. We show that this aim can be realized by supplementing the current field of evolutionary game theory with a new form of self-organized temporal criticality. In the case of ordinary criticality, the units of a system choosing either cooperation or defection under the influence of the choices done by their nearest neighbors, undergo a significant change of behavior when the intensity of social influence has a critical value. At criticality, the behavior of the individual units is correlated with that of all other units, in addition to the behavior of the nearest neighbors. The spontaneous transition to criticality of this work is realized as follows: the units change their behavior (defection or cooperation) under the social influence of their nearest neighbors and update the intensity of their social influence spontaneously by the feedback they get from the payoffs of the game (environment). If units, which are selfish, get higher benefit with respect to their previous play, they increase their interest to interact with other units and vice versa. Doing this, the behavior of single units and the whole system spontaneously evolve towards criticality, thereby realizing a global behavior favoring cooperation. In the case when the interacting units are oscillators with their own periodicity, homeodynamics concerns, the individual payoff is the synchronization with the nearest neighbors (i.e., lowering the energy of the system), the spontaneous transition to criticality generates fluctuations characterized by the joint action of periodicity and crucial events of the same kind as those revealed by the current analysis of the dynamics of the brain. This result is expected to explain the efficiency of enzyme catalyzers, on the basis of a new non-equilibrium statistical physics. We argue that the results obtained apply to sociological and psychological systems as well as to elementary biological systems.

Ces travaux de recherche abordent un problème de défense anti-aérien, usuellement appelé problème d'allocation d'armes à des cibles dans la littérature. L'allocation d'armes à des cibles est un problème bien connu de la recherche opérationnelle militaire qui a rencontré un franc succès parmi la communauté des chercheurs, et qui aujourd'hui encore suscite un large engouement puisque sa propriété démontrée NP-difficile en fait un problème qui reste irrésolu. Que ce soit par des méthodes analytiques ou meta-heuristiques, le problème d'allocation d'armes à des cibles a fait l'objet de nombreuses propositions de résolution. Cependant, il est assez surprenant de voir que la modélisation proposée pour ce problème n'a guère évolué depuis qu'il est apparu pour la première fois dans la littérature en 1950. Cette modélisation peut être considérée comme obsolète aujourd'hui et ne répond plus aux exigences qui accompagnent les technologies modernes. En effet, en 60 ans le champ de bataille a complètement changé, et dans la littérature seulement un nombre limité d'études proposent de prendre en compte ces évolutions. L'étude menée dans cette thèse propose de s'intéresser aux systèmes de Commandes et Contrôles (C2) pour des applications anti-aériennes. Habituellement un système C2 est composé de senseurs, d'un centre d'opérations tactiques et d'un ou plusieurs lanceurs. Les senseurs alimentent le centre d'opérations tactiques à partir des informations qu'ils recueillent, puis, une fois ces informations reçues, le centre d'opérations tactiques va interpréter ces données afin de calculer l'atteignabilité des menaces. Enfin, un plan d'engagement qui comprend l'allocation des munitions disponibles aux cibles et une date de tir sont proposés à un opérateur humain qui aura pour mission de valider cette proposition en totalité ou partiellement, puis va procéder à l'engagement des menaces. Pour remplir cet objectif, une approche innovante et faisant l'objet d'un dépôt de brevet a été développée afin de répondre aux difficultés relatives aux problèmes d'optimisation multi-objectifs. Ensuite, un algorithme d'optimisation continue basé sur la combinaison de l'optimisation par essaim particulaires avec la théorie des jeux évolutionnaires est proposé pour optimiser les dates de tirs. L'allocation optimale, elle, est obtenue en adaptant cette méthode continue au cas discret. La preuve que l'algorithme développé est localement convergent est donnée dans cette thèse. D'autre part, l'aspect temps-réel a également fait l'objet d'une recherche attentive et l'algorithme précédemment cité a été hybridé avec les réseaux de neurones afin d'accélérer le temps de calcul des composants identifiés comme "lourds" en termes de charge de calcul. Enfin, cette étude ne se limite pas à une application de recherche opérationnelle militaire, mais inclut quelques concepts élémentaires de guidage et de navigation pour le calcul d'atteignabilité des menaces. Finalement, cette thèse permet d'identifier que les points suivants doivent faire l'objet d'une attention très particulière afin de développer un outil d'aide à la décision efficace. D'abord, la métrique d'évaluation d'un bon plan d'engagement doit être clairement analysée. Ensuite, le plan d'engagement proposé doit être stable et ne pas proposer de changements soudains qui pourraient perturber l'opérateur. Le troisième point concerne la robustesse de la solution proposée et sa capacité à faire face aux situations les plus compliquées. Quatrièmement, le temps et la charge de calcul sont des contraintes techniques qui ne peuvent pas être outrepassées. Finalement, les exigences posées lors de la préparation de mission et qui dépendent du contexte doivent faire l'objet d'une attention particulière. C'est pourquoi, l'outil d'aide à la décision proposé doit permettre un allègement significatif de la charge de travail de l'opérateur ainsi que la réduction considérable du stress lié à ce contexte / This research investigates a practical air defence problem, usually named Weapon Target Assignment (WTA) in the literature. The WTA problem is a well-known problem of military operation research that encountered a wide success in the research community, but still nowadays since it remains an unsolved problem because of its NP-hardness property. From analytical to heuristic methods, the WTA was deeply investigated and many attempts to solve this problem have been proposed. However, the proposed modelling of this problem is consistent with the 1950's technologies. Thus, the proposed modelling found in the literature can be considered as obsolete and cannot fit the requirement of the current technology advances. Indeed, the battle field dramatically changes over 60 years, and the recent literature proposes only few studies taking into account these amendments. The herein study proposes to investigate a Command & Control system (C2) in air defence applications. Usually a C2 system includes sensors, a Tactical Operation Centre (TOC) and one or more launchers. The sensors provide information about aerial tactical situation to the TOC. This TOC is in charge of evaluating the received information in order to compute the attainability of the targets, then an engagement plan that includes the assignment of the available weapons to the incoming targets and a date to fire for each assignment. This engagement plan is then proposed to one human operator in charge of accepting whole or part of this engagement plan and engage the targets following the received instructions. To achieve this goal, an innovative and patented approach to mitigate the issues related to multi-objective optimisation is proposed. Then, a continuous optimisation algorithm based on the combination of the Particle Swarm Optimisation and the Evolutionary Game Theory was proposed to determine the best dates to fire. The optimal assignment was obtained by adapting the aforementioned algorithm to the discrete case. This thesis also gives the proof that the designed algorithms are locally convergent and intensive benchmarking confirms the developed theory. In order to respect the real-time requirement, it was also devised to use the Neural Networks to lighten the identified burdensome parts of the algorithm and decrease computational time. Not limited to the military operation research field, the herein study reuse some basic concepts of missile guidance and navigation to compute the attainability of the targets. From this thesis, it can be identified that following aspects need to be carefully considered to provide an efficient decision making support to a human operator: First, clearly define what a good engagement plan is. Second, the engagement plan must be steady to avoid high rate changing in the assignments that could significantly disturb the operator. Third, the proposed engagement also must be reliable and robust to face any possible situations. Fourth, the computation time and computation load are technical constraints that cannot be overstepped. Finally, the operational constraints related to the mission context defined during a pre-mission stage must also be taken into account. Therefore, the proposed decision making support must help and significantly reduce the operator's work load in this situation of high stress and sensitive context