Séminaires 2017-2018

• Mardi 10 octobre 2017: Matt Leduc, "Networked Markets and Relational Contracts"

Empirical studies of commercial relationships between firms reveal that (i) suppliers encounter situations in which they can gain in the short run by acting opportunistically---for example, delivering a lower quality than promised after being paid; and (ii) good conduct is sustained not exclusively by formal contracts but through informal relationships and the expectation of future business. In such relationships, the need to offer each supplier a large enough share of future business to deter cheating limits the number of supply relationships each buyer can sustain. The market thus becomes networked, with trade restricted to durable relationships. We propose and analyze a simple dynamic model to examine the structure of such overlapping relational contracts in equilibrium. Due to exogenous stochastic shocks, suppliers are not always able to make good on their promises even if they wish to, and so links are constantly dissolving and new ones are forming to take their place. This induces a Markov process on networks. We study how the stationary distribution over networks depends on the parameters---most importantly, the value of trade and the probability of shocks. When shocks hit a networked market, making it impossible for some suppliers to meet their commitments, a destruction of social capital occurs, and restoring it takes time due to search frictions. This creates a novel way for shocks to be persistent. It also suggests new connections between the theory of relational contracting, on the one hand, and the macroeconomic analysis of recessions, on the other.

• Mardi 24 octobre 2017: Ibrahima Diarrassouba, "Conception de réseau fiable avec contrainte de longueur des chemins"

Dans un réseau, on considère un ensemble de paires origine-destination (s,t), appelées "demandes". Le problème de "conception de réseau fiable avec contrainte de longueur des chemins" consiste à construire un réseau tel que pour chaque demande (s,t), il existe k>=2 chemins disjoints entre s et t. De plus, ces chemins doivent être de longueur inférieure ou égale à un entier L >= 2. Dans cet exposé, nous présentons une étude polyédrale du problème lorsque k=2 ainsi qu'un algorithme de Branch-and-Cut pour sa résolution. Nous présentons différentes contraintes valides pour le polyêdre du problème ainsi que des conditions pour qu'elles définissent des facettes. Nous discutons aussi du problème de séparation associé à ces contraintes, et présentons l'agorithme de Branch-and-Cut utilisé pour résoudre le problème. Nous finissons l'exposé par une discussion sur les principales difficultés et enjeux liés à la résolution du problème.

• Mardi 14 novembre 2017: Nicolas Trotignon, "Graphs classes defined by excluding Truemper Configurations"

Tremper configurations are simple structures : prisms, thetas, pyramids and wheel. A prism is a graph made of two disjoint triangle that are matched by three disjoint paths. A theta is a graph made of two disjoint vertices that are linked by three disjoint paths. A pyramid is a graph made of a vertex and triangle that are linked by three disjoint paths. A wheel is a chordless cycle together with a vertex disjoint from it, and with at least three neighbors in it. In this abstract we omitted technical requirements on the lengths of the paths and cycles. Truemper configuration play an important in role in several theorems. For instance, they appear in an old characterisation of graph with no cycle through three prescribed vertices (due to Watkins and Mesner). They appear in a theorem of Truemper about signing edges of a graph in such way that several constraints on the parity of cycles are satisfied. And they play an important role in many recent decomposition theorems in structural graph theory (perfect graphs, even-hole-free graphs, claw-free graphs, bull-free graphs, and some others). The talk will focus on this last aspect. I will explain why Truemper Configuration are important in decomposition theorems. Then I will present a project about systematically studying the classes of graph where Truemper configuration are excluded. (Joint work with Marko Radovanovic and Kristina Vuskovic.)

• Mardi 5 décembre 2017: Vincent Merlin, "Evaluating the likelihood of the referendum paradox for mixed voting systems"

A referendum paradox (Nurmi, 1999) occurs, in a two party competition, each time a party gets a majority of the seats in the parliament while it did not obtain a majority of votes nationwide. The election of George W. Bush in 2000 (with 271 electoral vote against 267, but less votes than Albert Gore) can be viewed as an occurrence of the paradox. In fact, any two tiers voting systems can be plagued by this flaw. This paradox can be also viewed as an instance of the Borda paradox, as the voting rules fails to select the Condorcet winner. Feix, Lepelley, Merlin and Rouet (2004), Wilson MC, G Pritchard (2007) and Lepelley, Merlin and Rouet (2011) computed the probability of the referendum paradox under the IC and IAC assumptions when two parties compete in A equal sized districts. A priori models for voting are extensively described in Gerhlein (2006). The same paradox may occur for mixed electoral systems. On the top of electing A representatives in districts, the voters also elect D members of the parliament at large. Hence, the parliament is of size A+D. Blais and Massicote (2009) propose an extensive survey of all the mixed electoral systems that are used worldwide. In this paper, assuming that A representative are elected in equal size jurisdictions, we estimate the probability of the referendum paradox for different mixed systems : 1) when the D at large seats are apportioned according to the proportional rule, 2) when the all the D at large seats are attributed to the party which obtained a majority of votes nationwide, and 3) when the D seats are apportioned on the basis of the wasted votes, that is, the sums of the votes of the party candidates that were not elected in districts. We perform our estimations both under the IC and IAC hypothesis. As a corollary, we estimate the probability of the referendum paradox as a function of the ratio D/A under the three scenarios. In an electoral design perspective, we are then able to suggest which values for D/A are sufficiently large for the referendum paradox to become negligible. (Joint work with D Lepelley and M. Le Breton.)

• Mardi 5 décembre 2017: Tomáš Kroupa, "Exact coalitional games and their facets"

An exact game is a coalitional game if, for every coalition, there exists a core element that allocates precisely the value of the coalition to its members. The convex cone of exact games was partially characterised in the paper "Minimal exact balancedness" by Lohmann, Borm and Herings (MSS, 2012). I will present the results of a joint work with M. Studený whose aim is to give a minimal (facet-defining) description of the exact cone. Our approach is based on minimal balanced collections of Shapley used in the description of games with nonempty cores.

• Mardi 9 janvier 2018: Bernard Cornet, "Hedging price as a Choquet integral"

The hedging price of a market with frictions, i.e., with bid and ask prices, that is, the price to buy financial assets may be different from the price to sell, what typically occurs in currency markets, (and its associated super-hedging price), allow to characterize such markets and are of fundamental use in finance to price by arbitrage a new financial asset to be introduced in the market. Both hedging and super-hedging prices are known to be sublinear as being defined by a convex and homogeneous programming problem. The paper studies the submodular properties of the hedging and super-hedging prices of such markets and give sufficient conditions for which they are additionally a Choquet integral. In this case, the associated capacity (non-additive probability) is defined by an explicit formula that provides better computational ways than solving the original mathematical programming problem. The study relies on a general characterization theorem that goes beyond the case of financial markets.

• Mardi 23 janvier 2018: Mustapha Ridaoui, "An alternative view of importance indices for multichoice games"

We consider MultiCriteria Decision Analysis (MCDA) models where the underlying attributes are discrete. Without any additional feature, such general models are equivalent to multichoice games in cooperative game theory. Our aim is to define an importance index for attributes. In specific models based on capacities, fuzzy measures, the Shapley value is often taken as an importance index. We show that in our general framework, taking the Shapley value extended to multichoice games is not meaningful, due to the efficiency axiom which has no natural interpretation in MCDA. We propose instead an importance index based on variational calculus and give an axiomatization of it.

• Mardi 6 février 2018: Georges Zaccour, "Sustainability of cooperation in dynamic games played over event trees"

In this tutorial, we recall the main ingredients of the theory of dynamic games played over event trees and show step-by-step how to build a sustainable cooperative solution.

• Mardi 13 février 2018: Stéphane Zuber, "Population-Adjusted Egalitarianism and resource management"

Egalitarianism focuses on the wellbeing of the worst-off person. It has attracted a lot of attention in economic theory, for instance when dealing with the sustainable intertemporal allocation of resources. Economic theory has formalized egalitarianism through the Maximin and Leximin criteria, but it is not clear how they should be applied when population size may vary. In this paper, I present possible justifications of egalitarianism when considering populations with variable sizes. I then propose new versions of egalitarianism that encompass many views on how to trade-off population size and wellbeing. I discuss some implications of egalitarianism for optimal population size in a model with a renewable resource. I first show how population ethical views affects population growth. I then show that utilitarianism always recommend a larger population than egalitarianism in two polar yet prominent population ethics views: the average and the total views.