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COCA is a project selected for the ANR Jeunes chercheuses - jeunes chercheurs 2009 call to projects*Project number:* JC09_461625*Decision number:* ANR-09-JCJC-0066-01*Partners:* LAMSADE (UMR 7243), LIP6 (UMR 7606)

The COCA project aims at introducing and to studying some ways to put reasonable constraints in the way a game works in order to make the global system more efficient. Let us introduce a seminal example due to Pigou in order to illustrate this idea. Consider a population of agents that want to go from one point to one another, with a choice between two routes (home to office). The first route takes one hour, whatever the number of people using it. On the second route, the time equals the proportion of individuals using it. For instance, if 50 percent of the population use this route, the time is half an hour. To minimize the average travel time in the population, half of the people should use the first route (one hour), and the other half the second route (half an hour). It yields an average time of 45 minutes. However, if the agents are selfish, no one will use the first route, and therefore the travel time will be one hour for everybody (Wardrop equilibrium). Clearly, the global efficiency of the traffic can here be improved by encouraging some people to use the first route (by establishing alternating traffic on the other route for instance). One of the first scopes of this project is to propose formal concepts capturing this kind of concern, and to apply them to discrete combinatorial problems.