vignette|Le dilemme du prisonnier : chacun des deux joueurs dispose de deux stratégies : D pour dénoncer, C pour ne pas dénoncer. La matrice présente le gain des joueurs. Si les deux joueurs choisissent D (se dénoncent), aucun ne regrette son choix, car s'il avait choisi C, alors que l'autre a opté pour D, sa « tristesse » aurait augmenté. C'est un équilibre de Nash — il y a « non-regret » de son choix par chacun, au vu du choix de l'autre. En théorie des jeux, un équilibre de Nash est une situation où :

Chaque joueur prévoit correctement le choix des autres ;

Chaque joueur maximise son gain, compte tenu de cette prévision.

Autrement dit, un profil de stratégie s^=((s^i){i\in[![1,n]!]}) est un équilibre de Nash si chaque joueur i joue une stratégie optimale s^_i (qui maximise son gain \pi) compte tenu des stratégies des autres joueurs s^_j, où j\in[![1,n]!] : \forall (i,j)\in[![1,n]!]^

Informational frictions in financial markets

Erik Hapnes

This thesis consists of three chapters on informational frictions in financial markets. The chapters analyze problems related to markets' ability to guide real investment, and what drives liquidity. Both problems are important to ensure efficient resource allocation in the economy. The first chapter studies the interaction between financial markets and real investments. I develop a model that simultaneously study the equilibrium in financial markets, the choice of investors to produce information, and real decisions by the firm. The chapter provides a new method to overcome non-linearities in the security price, and the equilibrium is surprisingly simple. The results provide insights into when real investments have a substantial impact on market efficiency and when we can analyze equilibrium market efficiency separately. Equilibrium behavior may hide some inefficiencies from standard empirical tests. Some changes in financial markets may increase or have little effect on market efficiency, but reduce real efficiency by increasing the cost of information production. The second chapter analyzes time-variation in liquidity. I develop a tractable model where conditions among traders vary over time. The resulting equilibrium offers several new predictions on what drives liquidity variation. For example, there may be significant reductions in liquidity from even tiny changes among the traders' conditions. Strategic behavior drives the results, and the model explains how liquidity may suddenly evaporate without a clear cause. Empirical results are in line with the predictions of the model. Surprisingly, everyone may benefit from sometimes restricting some traders from the market. Doing so can reallocate liquidity to periods with more significant liquidity needs. The third chapter studies the choice of anonymity among traders. All traders end up revealing their identity unless doing so is costly, or the order flow is noisy. The intuition is that there is always at least one trader who prefers to reveal his or her identity. If the order flow is noisy, then there is a threshold type, and more patient traders stay anonymous. The results suggest that a fully anonymous market is most efficient, but the gains from anonymity are distributed unevenly. This result explains why different markets vary significantly in choices related to anonymity.

EPFL2021

Singularly perturbed piecewise deterministic games

Alain Haurie

In this paper we consider a class of hybrid stochastic games with the piecewise open-loop information structure. These games are indexed over a parameter

\varepsilon

which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic games when the time scale ratio tends to 0. We also establish that an approximate equilibrium can be obtained for the hybrid stochastic games using a Nash equilibrium solution of a reduced order sequential discrete state stochastic game and a family of local deterministic infinite horizon open-loop differential games defined in the stretched out time scale. A numerical illustration of this approximation scheme is also developed.

Society for Industrial and Applied Mathematics2008

Singularly perturbed piecewise deterministic games

Alain Haurie

In this paper we consider a class of hybrid stochastic games with the piecewise open-loop information structure. These games are indexed over a parameter

\varepsilon

Society for Industrial and Applied Mathematics2008

Informational frictions in financial markets

Erik Hapnes

EPFL2021

Équilibre de Nash

Chaque joueur prévoit correctement le choix des autres ;

Chaque joueur maximise son gain, compte tenu de cette prévision.

Informational frictions in financial markets

Singularly perturbed piecewise deterministic games

Singularly perturbed piecewise deterministic games

Informational frictions in financial markets