The value of information in zero-sum games

Discussion Paper
Olivier Gossner, Jean-François Mertens
Publication year: 2020

We study the description and value of information in zero-sum games. We define a series of informational relations between information schemes, and show that informational equivalence classes are captured by canonical information structures. Moreover, two information schemes induce the same value in every game if and only if they are informationally equivalent. We prove the existence of a revealing game in which unique optimal strategies are homeomorphic to canonical types.

The robustness of incomplete penal codes in repeated interactions

Discussion Paper
Olivier Gossner
Publication year: 2020

We study the robustness of equilibria with regards to small payoff perturbations of the dynamic game. We find that complete penal codes, that specify players’ strategies after every history, have only limited robustness. For some generic games, no complete codes exist that are robust to even arbitrarily small perturbations. We define incomplete penal codes as partial descriptions of equilibrium strategies and introduce a notion of robustness for incomplete penal codes. We prove a Folk Theorem in robust incomplete codes that generates a Folk Theorem in a class of stochastic games.

Group Testing against COVID-19

Discussion Paper
Olivier Gossner
Publication year: 2020

We show how group testing can be used in three applications to multiply the efficiency of tests: estimation of virus prevalence, releasing group to the work force, and testing for individual infectious status. For an infection level around 2%, group testing could potentially allow to save 94% of tests in the first application, 95% in the second, and 85% in the third one.

Group testing against Covid-19

Discussion Paper
Christian Gollier, Olivier Gossner
Publication year: 2020

We show how group testing can be used in three applications to multiply the efficiency of tests against COVID-19: estimating virus prevalence, releasing group to the work force, and testing for individual infectious status. For an infection level around 2%, group testing could potentially allow to save 94% of tests in the first application, 95% in the second, and 85% in the third one.

Attention, please!

Discussion Paper
Olivier Gossner, Jakub Steiner, Colin Stewart
Publication year: 2018

We study the impact of manipulating the attention of a decision-maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision-maker’s strategy, forcing attention toward one item increases the likelihood of its being chosen.

An instrumental approach to the value of information

Discussion Paper
Michel de Lara, Olivier Gossner
Publication year: 2017

We consider an agent who acquires information on a state of nature from an information structure before facing a decision problem. How much information is worth depends jointly on the decision problem and on the information structure. We represent the decision problem by the set of possible payoffs indexed by states of nature. We establish and exploit the duality between this set on one hand and the value of information function, which maps beliefs to expected payoffs under optimal actions at these beliefs, on the other. We then derive global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only.