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Risk measures and shortest paths in network games

9 febbraio 2016 ore 12:00 - 13:00

Sede di Viale Romania, 32

Speaker: Roberto Cominetti, Universidad de Chile

Abstract: We consider network congestion games with risk-averse players. We review some recent proposals for computing risk-sensitive optimal paths, starting from the simplest Markowitz approach based on mean-stdev optimization. This approach presents some significant drawbacks in terms of its computational complexity, lack of monotonicity, as well as a dynamic inconsistency phenomenon which arises when one re-evaluates an optimal path along the way. This inconsistency also affects other popular measures of risk such as VaR, CVaR, and semi-deviations. As a matter of fact, under minimal conditions, we show that the only risk measures that are dynamically consistent are the so-called "entropic risk measures". With these measures, and assuming that link travel times are independent, a risk-sensitive optimal path reduces to a standard shortest path problem which can be solved efficiently. This extends directly to equilibrium situations where the network is used concurrently by many players. However, link travel time correlations are to be expected in game situations,which gives rise to a number of issues and questions that will be pointed out during the talk.

This talk is based on joint work with Alfredo Torrico.