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Games in Intrinsic Form with Witsenhausen Model

Abstract : In a strategic context, information (who knows what and before whom) plays a crucial role. In this thesis, we consider game theory models with information, and we present a new model which does not rely on trees. Indeed, on the one hand, working without a tree proves interesting in the context of modelling information and, on the other hand, there are examples of games that can be played but cannot be written on a tree. The manuscript is in two parts.In the first part, we focus on three models where the concept of information is present: Kuhn extensive tree model (K-model), Al ́os-Ferrer and Ritzberger infinite tree model (AFR-model) and Witsenhausen model (W-model). Whereas a tree is given in both K- and AFR-models among the primitives, in the W-model it is rather an object that can possibly be induced by a proper information structure. We prove that, on the one hand, causal and finite W-models can be embedded into AFR-models and, on the other hand, that a restricted class of finite AFR-models can be embedded into W-models. Moreover, we translate definitions of perfect recall and memory of past information into the language of W-model, and we formulate conjectures relating them to the corresponding information structures in the AFR-model.In the second part, we discuss W-games. When supplied with players and preferences, any of the three above models becomes a game. We introduce W-games, that is, W-models with a partition of the set of agents into sets of players’ representative agents, supplying each player with a preference relation (for instance, a payoff function and a belief). We give a definition of the Nash equilibrium for W-games. Then, for a subclass of Principal-Agent games that we call Enough Informed Agent W-games, we provide conditions under which a Nash equilibrium can be obtained by backward induction.In conclusion, we discuss several open leads, such as extension to infinite sets or players and the study of subgame perfect equilibrium in W-games.
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Danil Kadnikov. Games in Intrinsic Form with Witsenhausen Model. Probability [math.PR]. Université Paris-Est, 2020. English. ⟨NNT : 2020PESC1045⟩. ⟨tel-03528607⟩

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