Some Anomalies of Farsighted Strategic Behavior

Quality of equilibria in resource allocation games

“…Our definition is sufficient for each of the results we have come across. Even though it might seem that this property is only a small restriction, it can have a big impact on the costs of decentralization, as implied by a comparison of results of Paes Leme et al [77] and Bilò et al [19]. Note that each generic sequential game has a unique subgame perfect equilibrium.…”

“…The authors proved bounds on the sequential price of anarchy for four classes of games, improving the quality of equilibria compared to a simultaneous setting, thereby revealing 'The curse of simultaneity'. Less than a year later, Bilò et al [19] "put the expected performances of subgame perfect equilibria back in their right perspective", by showing that multiple of the claims by [77] were in fact too optimistic and only hold for generic games. On the other hand, their results indicate the counterintuitive nature of sequential equilibria, which makes them very interesting from a theoretical perspective.…”

“…This is visualized in Figure 2.5. Bilò et al [19] use this technique to obtain an almost trivial upper bound of n for non-generic resource sharing games, where the guarantee M i of any player i, does not require any information on the action space of predecessors or successors of player i. The authors also obtain a tight upper bound of 3 for non-generic cut and consensus games, using guarantees that do depend on the action space of predecessors.…”

“…Another generalization of this technique is used by Bilò et al [19] for unrelated machine scheduling, where the cost of a player i can increase by actions of successors. However, the authors use backward induction to find an upper bound on this increase, yielding an upper bound of 2 n .…”

“…Therefore, opposed to some models for infinitely repeated games [44], players can't use threats that harm themselves. Lower bounds on the sequential price of anarchy that crucially include ties are 3 − for non-generic consensus and cut games [19], 2…”