Competitive Equilibrium and Trading Networks: A Network Flow Approach

Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks, and is equivalent (after a restriction to equilibrium trades) to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient outcome as a generalized submodular flow problem on a suitable network. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability

Essays in Optimization Methods for Resource Allocation

This dissertation proposes and investigates the use of mathematical programming techniques to solve resource allocation problems that are typically handled using other techniques. This approach both simplifies proofs of earlier results as well as extends them. The first setting addresses a network of agents, initially endowed with resources, exchanging goods and services via bilateral contracts. Under full substitutability of preferences, it is known via fixed point arguments that a competitive equilibrium exists in trading networks. I formulate the problem of finding an efficient set of trades as a generalized submodular flow problem in a suitable network. Existence of a competitive equilibrium follows directly from the optimality conditions of the flow problem. This formulation enables me to perform comparative statics with respect to the number of buyers, sellers, and trades. For instance, I establish that if a new buyer is added to the economy, at equilibrium the prices of all existing trades increase. In addition, a polynomial time algorithm for finding competitive equilibria in trading networks is given. The second setting relates to dynamic resource allocation with the presence of uncertainty for future rewards. Prophet inequalities involve a set of results relating the reward attained in an on-line selection setting to the reward generated by a prophet possessing perfect information. I develop new, approximately efficient rules leveraging the reduced-form representation of on-line selection problems. I apply the method in an on-line mechanism design problem with verification and the on-line fractional knapsack selection problem

Competitive Equilibrium and Trading Networks: A Network Flow Approach

Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks, and is equivalent (after a restriction to equilibrium trades) to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient outcome as a generalized submodular flow problem on a suitable network. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability

Sponsored Search Auctions with Externalities

77 σ.Σε αυτήν την διπλωματική εργασία εξετάζουμε μια κλάση δημοπρασιών, τις δημοπρασίες σε μηχανές αναζήτησης, γνωστές και ως δημοπρασίες λέξεων- κλειδί. Είναι ένας νέος τύπος ηλεκτρονικής διαφήμισης, όπου οι διαφημιστές ανταγωνίζονται για μια θέση δίπλα στα αποτελέσματα αναζήτησης. Οι κολοσσοί του διαδικτύου, Google, Yahoo!, Microsoft, πουλάνε χώρο για διαφήμιση με αυτόν τον τρόπο, δημοπρατώντας θέσεις στις μηχανές αναζήτησης. Τα κέρδη από αυτές τις δημοπρασίες καταλαμβάνουν μεγάλο ποσοστό των συνολικών κερδών τους. Παρουσιάζω το βασικό μοντέλο για αυτές τις δημοπρασίες και τους κύριους σχεδιαστικούς στόχους. Συγκεκριμένοι κανόνες διανομής των θέσεων και πληρωμών παραθέτονται και εξετάζονται ώς προς την ευστάθεια τους, την αποδοτικότητα τους και τα κέρδη. Νέα πειραματική ανάλυση δείχνει ότι το βασικό μοντέλο είναι πολύ απλουστευμένο, μην μπορώντας να αποτυπώσει εξωγενείς επιδράσεις μεταξύ των διαφημιστών. Παρουσιάζω νέα μοντέλα που μπορούν να εκφράσουν τέτοιες επιδράσεις, επεκτείνοντας το βασικό μοντέλο και αναλύοντας την ευστάθεια και αποδοτικότητα μηχανισμών.In this thesis, I consider a special class of auctions, Sponsored Search Auctions, also known as keyword auctions. It is a new form of online advertising, where advertisers compete for a place next to the web search results. Internet giants Google, Yahoo!, Microsoft sell online advertising by this form, who auction positions for sponsored search links. Search revenues accounts for a large percentage of their massive revenues. I introduce the basic setting in sponsored search auctions and the main design goals. Certain types of allocation and payments are presented, judging their stability, allocation efficiency and resulting revenue. Having new experimental analysis, it is proven that the basic setting is inadequate and externalities between advertisers exist. I present new settings to express such externalities, by expanding the basic setting, and analyze them in terms of stability and allocation efficiency.Μάρκος-Σπυρίδων Π. Επιτρόπο