Abstract
We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium (NE) and a subgame perfect equilibrium (SPE). But sometimes several equilibria may coexist such that in one equilibrium no player reaches his target set whereas in another one several players reach it. It is thus very natural to identify “relevant” equilibria. In this paper, we consider different notions of relevant equilibria including Pareto optimal equilibria and equilibria with high social welfare. We provide complexity results for various related decision problems.
Research partially supported by the PDR project “Subgame perfection in graph games” (F.R.S.-FNRS) and by COST Action 16228 “GAMENET” (European Cooperation in Science and Technology).
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- 1.
We can easily adapt this definition to histories.
- 2.
For convenience, we prefer to say that p is Pareto optimal in \(\mathrm{Plays}(v_0)\) rather than in P.
- 3.
In the qualitative setting, each player obtains a gain that he wants to maximize: either 1 (if he visits his target set) or 0 (otherwise), all definitions are adapted accordingly.
- 4.
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Brihaye, T., Bruyère, V., Goeminne, A., Thomasset, N. (2019). On Relevant Equilibria in Reachability Games. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_5
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