Efficiency of Correlation in a Bottleneck Game

20 Pages Posted: 25 Jul 2018

See all articles by Thomas J Rivera

Thomas J Rivera

HEC Paris - Economics & Decision Sciences, Students

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza

Tristan Tomala

HEC Paris - Economics & Decision Sciences

Date Written: July 25, 2018

Abstract

We consider a model of bottleneck congestion in discrete time with a penalty cost for being late. This model can be applied to several situations where agents need to use a capacitated facility in order to complete a task before a hard deadline. A possible example is a situation where commuters use a train service to go from home to office in the early morning. Trains run at regular intervals, take always the same time to cover their itinerary, and have a fixed capacity. Commuters must reach their office in time. This is a hard constraint whose violation involves a heavy penalty. Conditionally on meeting the deadline, commuters want to take the train as late as possible. With the intent of considering strategic choices of departure, we model this situation as a game and we show that it does not have pure Nash equilibria. Then we characterize the best and worst mixed Nash equilibria, and show that they are both inefficient with respect to the social optimum. We then show that there exists a correlated equilibrium that approximates the social optimum when the penalty for missing the deadline is sufficiently large.

Keywords: Nash equilibrium, correlated equilibrium, efficiency of equilibria, price of anarchy, price of stability, price of correlated stability.

Suggested Citation

Rivera, Thomas and Scarsini, Marco and Tomala, Tristan, Efficiency of Correlation in a Bottleneck Game (July 25, 2018). HEC Paris Research Paper No. ECO/SCD-2018-1289. Available at SSRN: https://ssrn.com/abstract=3219767 or http://dx.doi.org/10.2139/ssrn.3219767

Thomas Rivera (Contact Author)

HEC Paris - Economics & Decision Sciences, Students ( email )

1 rue de la Liberation
Jouy-en-Josas Cedex
France

Marco Scarsini

LUISS, Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Tristan Tomala

HEC Paris - Economics & Decision Sciences ( email )

1 rue de la Liberation
Paris, 78351
France

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