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We consider priority-based school choice problems with farsighted students. We show that a singleton set consisting of the matching obtained from the Top Trading Cycles (TTC) mechanism is a farsighted stable set. However, the matching obtained from the Deferred Acceptance (DA) mechanism may not belong to any farsighted stable set. Hence, the TTC mechanism provides an assignment that is not only Pareto efficient but also farsightedly stable. Moreover, looking forward three steps ahead is already sufficient for stabilizing the matching obtained from the TTC.

We consider priority-based matching problems with limited farsightedness. We show that, once agents are sufficiently farsighted, the matching obtained from the Top Trading Cycles (TTC) algorithm becomes stable: a singleton set consisting of the TTC matching is a horizon-k vNM stable set if the degree of farsightedness is greater than three times the number of agents in the largest cycle of the TTC. On the contrary, the matching obtained from the Deferred Acceptance (DA) algorithm may not belong to any horizon-k vNM stable set for k large enough.

Alzheimer's disease has a long asymptomatic phase that offers a substantial time window for intervention. Using this window of opportunity will require early diagnostic and prognostic biomarkers to detect Alzheimer's disease pathology at predementia stages, thus allowing identification of patients who will most probably progress to dementia of the Alzheimer's type and benefit from specific disease-modifying therapies. Consequently, we searched for CSF proteins associated with disease progression along with the clinical disease staging. We measured the levels of 184 proteins in CSF samples from 556 subjective cognitive decline and mild cognitive impairment patients from three independent memory clinic longitudinal studies (Spanish ACE, n = 410; German DCN, n = 93; German Mannheim, n = 53). We evaluated the association between protein levels and clinical stage, and the effect of protein levels on the progression from mild cognitive impairment to dementia of the Alzheimer's type. Mild cognitive impairment subjects with increased CSF level of matrix metalloproteinase 10 (MMP-10) showed a higher probability of progressing to dementia of the Alzheimer's type and a faster cognitive decline. CSF MMP-10 increased the prediction accuracy of CSF amyloid-beta 42 (A beta(42)), phospho-tau 181 (P-tau(181)) and total tau (T-tau) for conversion to dementia of the Alzheimer's type. Including MMP-10 to the [A/T/(N)] scheme improved considerably the prognostic value in mild cognitive impairment patients with abnormal A beta(42), but normal P-tau(181) and T-tau, and in mild cognitive impairment patients with abnormal A beta(42), P-tau(181) and T-tau. MMP-10 was correlated with age in subjects with normal A beta(42), P-tau(181) and T-tau levels. Our findings support the use of CSF MMP-10 as a prognostic marker for dementia of the Alzheimer's type and its inclusion in the [A/T/(N)] scheme to incorporate pathologic aspects beyond amyloid and tau. CSF level of MMP-10 may reflect ageing and

We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to answer this question. We find that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsighted set whenever the degree of farsightedness of the criminals is larger than or equal to (n 1). Moreover, the complete network is the unique horizon-(n 1) farsighted set. Hence, the predictions obtained in case of completely farsighted criminals still hold when criminals are much less farsighted.

We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (no external deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (external stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (minimality) there is no proper subset satisfying no external deviation and external stability. Contrary to the notion of myopic-farsighted stable set [Herings, Mauleon and Vannetelbosch (J. Econ. Theory, 2020), Luo, Mauleon and Vannetelbosch (Econ. Theory, 2021)], we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.

We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to answer this question. We Önd that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsighted set whenever the degree of farsightedness of the criminals is larger than or equal to (n 1). Moreover, the complete network is the unique horizon-(n 1) farsighted set. Hence, the predictions obtained in case of completely farsighted criminals still hold when criminals are much less farsighted.

We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to study the R&D networks that will emerge in the long run when firms are neither myopic nor fully farsighted but have some limited degree of farsightedness. We find that a singleton set consisting of a pairwise stable network is a horizon-K farsighted set for any degree of farsightedness K ≥ 2. That is, each R&D network consisting of two components of nearly equal size satisfies both horizon-K deterrence of external deviations and horizon-K external stability for K ≥ 2. On the contrary, each R&D network consisting of two components with the largest one comprising three-quarters of firms, predicted when all firms are fully farsighted, violates horizon-K deterrence of external deviations. Thus, when firms are homogeneous in their degree of farsightedness, pairwise stable R&D networks consisting of two components of nearly equal size are robust to limited farsightedness.

We propose a framework of network formation where players can form two types of links: public links observed by everyone and shadow links generally not observed by others. We introduce a novel solution concept called rationalizable conjectural pairwise stability, which generalizes Jackson and Wolinsky (1996)'s pairwise stability notion to accommodate shadow links. We first show that a network is stable if there exist beliefs such that each player conjectures to be in a network that is stable under correct beliefs, and in which she does not want to alter her links unilaterally. We then derive a mechanism to construct a stable network that is not stable under correct beliefs. Third, we establish that the set of stable networks is shrinking in the players' observation radius. Finally, we illustrate our framework in the context of two specific models and show that players may over(under)estimate others' connections and hence under(over)connect.

We propose the notion of minimal instability to determine the networks that are more likely to emerge in the long run when agents are farsighted. A network is minimally farsighted unstable if there is no other network which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare networks by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating networks. We next compare networks in terms of their absorbtiveness by comparing both their sets of farsighted defeating networks (i.e. in terms of their stability) and their sets of farsighted defeated networks (i.e. in terms of their reachability). A network is maximally farsighted absorbing if there is no other network which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable networks and maximally farsighted absorbing networks, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.

This thesis studies effort choice and dynamics in games on a fixed social network with strategic complementarities. The three chapters of the thesis discuss different aspects of the social influence present in networks and affecting effort choices of the players. Chapter 1 presents a model of social learning where randomly partitioned groups play minimum effort game each period. The effort choice is based on expectations about the minimum effort which, in turn, is formed based on own experience and communication among social contacts. The results from extensive simulation analysis show that increasing the social influence through communication of beliefs in the social network significantly increases the long-run effort choices in the population. Chapters 2 and 3 study network games with social conflict, spillovers, and personal norms. Chapter 2 discusses the dynamics of efforts with players adapting their personal norms and provides the conditions for reaching consensus in a multi-layer network. Chapter 3 introduces unions in the network game with spillovers and conformity. Players in the unions choose efforts by maximizing their joint utility. A union-intercentrality is defined as a measure of player’s influence on the aggregate effort in the network with unions. Additionally, it is shown that, under certain conditions, joining a union increases the effort of the player herself, as well as, the aggregate effort in the network., (ECGE - Sciences économiques et de gestion) -- UCL, 2021

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

We consider marriage problems where myopic and farsighted players interact. To study such problems, we use the pairwise myopic-farsighted stable set. Blocking occurs by coalitions of size one or two. We require that all blocking players should strictly improve. We pay particular attention to the question whether core elements survive in this environment. This is the case when all players are myopic as well as when all players are farsighted. It also holds for matching problems satisfying the top-coalition property. For general matching problems where all women are farsighted, there is only one core element that can belong to the pairwise myopic-farsighted stable set, the woman-optimal stable matching, so all other stable outcomes are excluded for sure. If the woman-optimal stable matching is dominated from the woman point of view by an individually rational matching, then the pairwise myopic farsighted stable set cannot contain a core element. We show that blocking by coalitions of arbitrary size leads to identical results.